M+ sc--- X

VOLUME AND SURFACE AREA OF SOLIDS

1) If the volume of a right circular cone of height 9cm is 48π cm³,  then diameter of its base is

a) 6cm b) 7cm c) 8 cm d) 10 cm

2) A hemispherical bowl has a radius of 3.5cm.  The volume of water it would contain would be :

a) 86.5cm² b) 89.8cm³ c) 92.5cm⅔ d) 93.5cm³

3) The height of a right circular cone is 12cm. If its volume be 100π cm³, then its slant height is:

a) 12cm b) 13cm c) 15cm d) 16cm

4) A conical flask of base radius r and height h is full of milk. The milk is now poured into a cylindrical flask of radius 2r. What is the height to which the milk will rise in the flask?

a) h/2 b) h/6 c) h/9 c) h/12

5) the radius of base and the height of a right circular cylinder are each increased by 20%. The volume of the cylinder will increase by 

a) 72.8% b) 80% c) 82% d) 92% 

6) A sphere of radius R has volume equal to that of a cone of radius R, the height of the cone is:

a) R b) 3R c) 3R d) 4R

7) A sphere and a cube have the same surface area. The ratio of their volume is:

a) √6: √π b) √3: √π  c) π: √2 d) √5:π

8) A medicine capsule is in the shape of a cylinder of diameter 0.5cm, with two hemispheres stuck to each of its ends. The length of entire capsule is 2cm. The capacity of the capsule is 

a) 0.21cm³ b)  0.42cm³ c) 1.33cm³ d) 0.33 cm³

9) If two solid hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is:

a) 4πr² b)  6πr² c) 3πr² d) 8πr²

10) A right circular cylinder of radius r cm and the height h cm (h > 2r) just encloses a spher of a diameter:

a) r cm b) 2r cm c) h cm d) 2h cm

11) During conversion of solid from one shape to another, the volume of the new shape will be

a)  increase  b) decrease c) remains unaltered  d) be doubled 

12) Volume up two Sphere are in the ratio 64 : 27. The ratio of their surface area is:

a)  3:4 b) 4:3 c) 9 : 16 d) 16:9 

13) A solid metallic sphere of diameter 21cm is melted and recast into a number of smaller cones, each of diameter 7cm and height 3cm. The number of cones so firmed is:

a) 121  b) 123 c) 125  d) 126 

14) A hemispherical bowl of internal diameter 30cm contains some liquid. This liquid is to be filled into cylindrical shaped bottles, each of diameter 5 cm and height 6cm. The number of bottles necessary to empty the bowl is:

a) 30  b) 40 c) 55 d) 60 

15) The base radius and height of a right circular solid cone are 2cm and 8cm respectively. It is melted and recast into sphere of diameter 2cm each. The number of spheres so formed is:

a) 6 b) 8 c) 10 d) 12

16) In a cylinder, if radius is halved and height is doubled, the volume will be 

a) same b) doubled c) halved d) four times 

17) The radius of a sphere is 3r, then its volume will be:

a) 4πr³/3 b) 36πr³ c) 8πr³/3 d) 32πr³/3

18) A cone is 8.4 cm high and the radius of its base is 2.1cm. it is melted and recast into a sphere. The radius of the sphere is:

a) 4.2 b) 2.1cm c) 2.4cm d) 1.6 cm

19) In a cylinder, radius is doubled and height is halved, curved surface area will be:

a) halved b) doubled c) same d) four times 

20) The total surface area of a cone whose radius is r/2 and slant height 2L is 

a) 2πr(L+ r) b) πr(L+ r/4)  c) πr(L+ r)  d) 2πrL

21) The radius of two cylinders are in the ratio of 2:3 and their heights are in the ratio 5:3. The ratio of their volumes is:

a) 10:17 b) 20:27 c) 17:27 d) 20:37

22) The circumference of the base of a cylindrical vessel is 132cm and its height is 50 cm. How many litres of water can it hold?

a) 34.39 litres b) 78.50 litres c) 69.30 litres d) 67.67 litres 

23) The diameter of a cone is 28cm and slant height is 10.5cm. Then, its lateral surface area is 

a) 480cm² b) 490cm² c) 462cm² d) 466cm²

24) The diameter of a cone is 10cm and vertical height is 12cm. Then, the area of curved surface area is:

a) 205.15 cm² b) 214.16 cm² c) 204.28 cm² d) 241.20 cm²

25) The lateral surface area of a cone is 60π cm². If the slant height of the cone be 8cm, then the diameter of its base is 

a) 25 cm b) 18cm c) 12cm d) 15 cm

1c 2b 3b 4d 5a 6d 7a 8d 9a 10b 11c 12d 13d 14d 15b 16c 17b 18b 19c 20b 21b 22c 23c 24c 25d

SHORT ANSWER TYPE QUESTIONS 

1) 2.2 dm³ of copper is to be drawn into a cylindrical wire of diameter 0.50cm. find the length of the wire.

2) A wall of diameter 1m is dug 7m deep. The earth taken out of it is completely used for making a conical body of scare-crow. The base diameter of the body is 2m. Find the height of scare crow.

3) The total surface area of a right circular cone of slant height 13cm is 90π cm². Calculate 

a) its radius in cm.

b) Its volume in cm³, in terms of π.

4) If the volume of two cylinders are in the ratio 128:75 then, find the ratio of their curved surface areas. It is given that the ratio of their heights is 2:3.     

5) How many metres of cloth 5m wide will be required to make a conical tent, the radius of whose base is 7m and whose heights is 24m ?

6) How long would it take to fill a conical vessel whose diameter of base is 20cm and depth is 21cm, if it is filling through a pipe of diameter 5mm, at the rate of 10 m/minutes.

7) An iron sphere of radius 5cm has been melted and recast into smaller sphere each of radius 2.5cm. How many smaller spheres are made.

8) A cone and a hemisphere have equal bases and equal volume. Find the ratio of their heights.

1) 112m 2) 5.25m 3) 5cm, 100π cm³ 4) 16:15 5) 110m 6) 11.20 min 7) 8 8) 2:1

LONG ANSWER TYPE QUESTIONS 

1) The given solid figure is a cylinder surmaunted by a cone. The diameter of the base of the cylinder is 6cm. The height of the cone is 4cm and the total height of the solid is 26cm. (π= 22/7). Find 

a) volume of the solid 

b) curved surface area of the solid 

Give your answers correct to the nearest whole number.

2) A solid metallic sphere of radius 6cm is melted and made into a solid cylinder of height 32cm. Find the 

a) radius of the cylinder.

b) curved surface area of the cylinder (π= 3.1).

3) The volume of a conical tent is 1232 m³ and the area of the base floor is 154 m². Find 

a) radius of the floor.

b) height of the tent 

c) length of the canvas required to cover this conical tent, if its width is 2m.

4) The given figure

represents a hemisphere surmounted by a conical block of wood. The diameter of their bases is 6cm each and the slant height of the cone is 5cm. Find 

a) the height of the cone 

b) the volume of the solid.

5) A plumber fits a pipe of internal radius 10cm from a tap to a cylindrical tank, which is 5m in radius and 2m deep. If the water flows through the pipe at the rate of 3 km/hr, in how much time will tank filled?

6) Two solid iron poles are lying one over other. The pole at the lower position has height 220 cm and base diameter 24cm, whereas the pole above it has height of 60cm, and base diameter 16cm. Calculate the weight of the pole, if 1 cm³ of iron weight 10g.

7) A small cone is cut off at the top of a cone by a plane parallel to the base. The volume of the small cone is 1/8 of the volume of the bigger cone. At what height above the base is the section made, it is given that height of the complete cone is 40 cm ?

8) From a solid cylinder whose height is 2.4 cm, and diameter 1.4cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm².

1) 632cm³, 443 cm² 2) 3cm, 595.2 cm² 3) 7m, 24 m, 275m 4) 4cm, 94.29 cm³ 5) 100 min 6) 1115.328 kg 7) 20cm 8) 18 cm²

MATRIX 

1) Which of the following is a row matrix ?

a) matrix P of order 2x2 

b) matrix Q of order 1x2 

c) Matrix R of order 2x1 

d) Matrix S of order 3x2

2) The order of matrix is 2x3. It has:

a) 5 element  b) 6 elements  c) 1 elements d) none 

3) If A= 4    -2 B= 3   5 & C= 1   3

              5     7     -4  -2         -2   4 , then the value of A+ B C is

a) 6 1 b) 6   0  c) 6   3   d) 6   6

    3  0     3   1      0    1       3   1

4) If A= 4   x & B= y   -3 C= 10   0 with the relation 3A+ 2B = C, then:

a) x=1, y=0 b) x=-1, y=0 c) x=2, y= -1 d) x=-2, y=1

5) Order of matrix A is 2x3 and the order of matrix B is 3x1. The order the matrix AB is:

a) 2x1  b) 1x 2  c) 3 x 1  d) 2x 3

6) Which of the following is a diagonal Matrix ?

a) 0     6    1 b) 2   0     0

     2    0     4     0  -1     0

     1    8     0     0   0    -2

c) 4   0    0  d) 1.   0    0

    0   -2   0       0    1    1

                         0    0    1

7) In a null matrix:

a) all the elements are 0 

b) every diagonal element is zero

c) every non-diagonal element is zero 

d) every element is one.

8) 1    8     9 is a:

a) row matrix  b) column matrix c) diagonal matrix  d) null matrix

9) The transpose of matrix 

2       -1       4

1        7       3

-4       1       5 is:

a) 2   1     4  b) 2    4     -1

    -1   1    5       1    3      7

     4   7    3      -4    5      1

c) -1    4    2    d) 2       1      -4

     7     3    1       -1       7       1

     1     5   -4        4       3       5

10) The order of matrix A is 2x 3 and that of B is 3x1.

a) AB is possible, but BA is not possible.

b) BA is possible but AB is not possible

c) AB as well as BA are not possible 

d) AB as well as BA are possible 

11) if A= 2    -4 & B= 1     -1

                0     1          0      5, then the value of B+ A is 

a) 3  -5 b) 6  2 c) 1  -2  d) -3  5

    0    6    -1  4    -4   1        0 -6

12) If A= 2   5 B= 1     -1

                1   3     -3      2 then AB is equal to 

a) -13   5 b) 8   -1 c) -13  8 d) -1   0

       1    8     5    2       -8   5      7   -2

13) If A= 3     -4 &B= -1   2

                5      6          5   7 then the order of 3A - 2B is

a) 2x1 b) 4x4 c) 1x1 d) 2x2

14) If A= 2    5 & B= 1    -3

               -3    7          2     5 then B - A is equal to 

a) 4  -1 b) -1  -8 c) -1   8  d) -2  4

    6  -2       5  -2       5   4     -1  -2

15) If M= 1   -2 & N= 2     1

                                   -1     2 then the order of MN is

a) 1x2 b) 2x1 c) 1x1 d) 2x2

16) If A= -2   3 B= 5    2

                 4   5      -7   3 then transpose of matrix (A+ B) is:

a) 3  5 b) 3  -3 c) 3   8 d) 3   5

   -3   8     5   8    -3   5     -8   3

17) If A= 2     1 & B= 5     -1

               -1     4          2     -1 then Aᵗ - Bᵗ is equal to:

a) 1  -1 b) 7  -1 c) -3. -1  d) -3  -3

    4    2     2   5      2    4        2   5

18) If A= 1   2 B= x.   0 

                3   3      0    y then the order of the matrix BA is

a) 1x2 b) 2x1 c) 2x3 d) 2x2

19) If A= 2   0 B= 0    1

               -3   1      -2   3 then the matrix BA is 

a) -3  1 b) -4   5 c) -3  2 d) 4   -1

   -13 3     -2    7      5  -7     2   19

20) If A= x   3 & A²= 3I, where I= 1    0

               y    3.                               0    1 the order of A² is 

a) 2x2 b) 2x3 c) 1x2 d) 3x2

Short Answer type Questions 

1) If A= 3    -1

              0     2 find matrix B such that A²- 2B = 3A + 5I, where I is 2x2 identity matrix.

2) Given matrix 

A= 4sin30°       cos0° & B= 4

        Cos0°     4sin30°         5 if AX = B

a) Write the order of matrix X.

b) Find the matrix X.

3) Find the value of x and y if

A= x   7      B= 6    -7 C= 10    7

     9  y-5          4     5       22   15 with the relation 2A+ B = C

4) Simplify:

A= sinA    -cosA & B= cosA     sinA

     CosA    sinA          -sinA      cosA with the relation A sinA+ B cosA

5) A= x   3

          y    3 if A²= 3I where I is the identity matrix of order 2, find x and y 

6) A= 1    4 & B= 3    2

          -2.  3.         0   -3 with the relation A+ 2M = 3B, find the matrix M

7) If A= p    0 B= 0  -q  C= 2   -2

              0    2      1    0       2    2 and BC = C², find the values of p and q 

8) If A= 2x   x B= 3 & C= 16

               y   3y     2            9 with the relation AB = C then find x and y 

9) If A= 3  -2 B= 6 C= -4  D= 2

             -1   4      1        5        2 find the value of AB+ 2C - 4D.

10) Evaluate: 

A= 4sin30     2cos60 B= 4    5

      Sin90      2 cos0        5     4 find the value of AB

LONG ANSWER TYPE QUESTIONS 

1) If A= 2   5 B= 4    -2

              1   3     -1     3 and I is the identity matrix of the same order and A' is the transpose of matrix A, find A'B + BI.

2) Let A= 2  1 B=4  1 & C=-3  2

                 0 -2.   -3  -2       -1   4 find A²+ AC - 5B

3) A= 2   0 I= 1   0

         -1   7     0   1 and A²= 9A + mI. Find m.

4) If A= 1   3 B= -2   1

              3   4      -3   2 and A²- 5B²= 5C, find matrix C, where C is a 2 by 2 matrix.

5) B= 1    1

          8    3 find the matrix X if X= B²- 4B. Hence solve for a and b given 

X= a & C= 5

     b          50 with X= C

6) If A= 2   3 B= 0   4 C= 1   0

              5  7      -1   7      -1   4, find AC + B²- 10C.

7) If A= 4    2

             -1    1 with relation AM=6I where M is a matrix and I is unit matrix of order 2x2.

a) State the order of oM

b) Find the matrix M.

8) A= 3   0 B= -4   2

          5   1        1   0 find A²- 2AB + B².

SIMILARITY (AS A SIZE TRANSFORMATION)

1) Figures which have exactly the same shape , but not necessary the same___, are said to be similar.

a) angle  b) side c) size  d) volume 

2) all regular polygons having the same number of ___are similar.

a) sides  b) medians c) diagonals d) altitudes

3) Two circles are always :

a) congruent b) similar c) enarged d) concentric 

4) in size transformation, the given figure is called an object and the resulting figure is called its:

a) pre- image b) image c) post image d) enlarge object 

5) let K be the scale factor of a given size transformation . Then K< 1 as the transformation is a:

a) enlargement b) identify transformation c) transformation d) preserved

6) Each side of the resulting figure= ____ times the corresponding side of the given figure.

a) k² b) k c) k³ d) 2k

7) The transformation is an____ if k= 1 where k is the scale factor of a given size transformation.

a) identify transformation b) reduction c) enlargement d) none

8) in case of solids, we have volume of the resulting figure = ____x (volume of the given figure), where k is the scale factor.

a) k b) k² c) k³ d) 3k

9) if scale factor, k= 1/p, then area of the model= ____ x (area of the actual figure).

a) k² b) k c) k² d) 1/p

10) Let the map of a plane figure be drawn to the scale 1: p. Then scale factor k= ____, length in the map= k x (actual length (.

a) p/1 b) 1/p c) 1/k d) k

1c 2a 3b 4b 5c 6b 7a 8c 9a 10b 

SHORT ANSWER TYPE OF QUESTIONS 

1) ∆ ABC with sides AB= 12cm, BC= 8cm and AC= 14cm is enlarged to ∆A'B'C' such that the smallest side of ∆ A'B'C'= 12cm. Find the scale factor and use it to find the length of the other sides of the image A'B'C'.     3/2, 18cm, 21cm

2) ∆ ABC is reduced by scale factor 0.72. if the area of ∆ ABC is 62.5cm²,  find the area of the image.      32.4 cm²

3) A rectangle hving an area of 60cm² is transferred under enlargement about a point in space. If the area of its image is 135cm², find the scale factor of the enlargement.    1.5

4) In the map of a rectangular plot of land the length= 2.5 cm and breadth=1.4cm. if the scale 1: 1000, then find the area of the plot in m².      35000 cm²

5) The surface area of a solid is 5m², while surface area of its model is 20 cm². Find 

a) the scale factor.    1/50

b) the volume of the solid if the volume of the model is 100cm³.     12.5 m³

6) Two bottles of sauce of circular cross-section are completely similar in every respect. One is 24cm high and the other is 32 cm high.

a) Calculate the external diameter of the smaller bottle, given that the corresponding diameter for the other bottle is 8cm.    6cm

b) The smaller bottle can hold it 270cm³ of sauce. How much souce can the bigger bottle hold?      640 cm³

7) The model of a building is constructed with scale factor 1:30.

a) If the height of the model is 80cm, find the actual height of the building in metre.    24

b) If the actual volume of the tank on the tap of the building is 27m³, find the volume of the tank on the top of the model .     1000 cm³

8) Two similar jugs have heights of 4cm and 6cm respectively. If the capacity of the smaller jug is 48 cm³, find the capacity of the larger jug.     162cm³

Two similar cylindrical tins have base radii of 6cm and 8cm respectively. Find the capacity of the smaller tin, if the capacity of the largest tin is 256 cm³.    108cm³

LONG ANSWER TYPE QUESTIONS 

1) The model of a ship is made to a scale 1:200.

a) The length of the model is 4m. Calculate the length of a ship.   800m

b) The area of the deck of the ship is 160000m². Find the area of the deck of the model.    4m²

c) The volume of the model is 200 litres . Calculate the volume of the ship in m².    1600000

2) On a map drawn to a scale of 1:250000 a triangular plot of land has the following measurements: AB= 3cm, BC = 4cm, angle ABC= 90°

Calculate:

a) the actual length of AB in km.       7.5 km

b) the area of the plot in km².      37.5 km²

3) On a map drawn to a scale of 1:25000, a rectangular plot of land ABCD has the following measurements .

a) The diagonal distance of the plot in km.    5km

b) The area of the plot in km².     12 km²

4) The scale of a model ship is 1:300.

a) if the length of the model is 250cm, find the actual length in m.    750m

b) if the desk area of the model is 1 m², find the deck area of the ship and the cost of painting it at Rs10 per m².     90000 m², Rs900000

c) If the volume of the ship is 108000000 m³, find the volume of the model.    4m²

5) The dimension of the model of the multistoreyed building are 1m x 60 cm x 1.25m. if the model is drawn to a scale 1:60, find the actual dimensions of the model in metres . Also find 

a) the floor area of a room of the building, whose area in the model 250 cm².    60m x 36m x75m , 90m²

b) the volume of the room in the model whose actual volume is 648 m³.   3600 cm³

SIMILARITY OF TRIANGLES 

1) If in two triangles ABC and PQR, AB/QR = BC/PR = CA/PQ, then 

a) ∆ PQR~ ∆ CAB b) ∆ PQR~∆ ABC c) ∆ CBA~ ∆ PQR d) ∆ BCA~ ∆ PQR 

2) If in a triangles DEF and PQR, angle D= angle Q, and angle R = angle E, then which of the following is not true ?

a) EF/PR= DE/QR b) DE/PQ= EF/RP  c) DE/QR = DF/PQ  d) EF/RP= DE/QR

3)  In the figure,

if ∆ ABC ~ ∆ ADE, then BC is equals to

a)  4.5 b) 3  c) 3.6 d) 2.4

4) If ∆ ABC~∆ EDF and ∆ ABC is not similar to ∆ DEF, then which of the following is not true?

a) BC xEF= AC x FD 

b) AB x EF = AC x DE

c) BC x DE = AB x EF

d) BC x DE = AB x FD

5) If ∆ ABC~ ∆ PQR, and angle P= 50° and angle B =60°, then angle R is 

a) 80° b) 70° c) 60° d) 50°

6) In ∆ LMN and ∆ PQR, if Angle L= 50°, angle M =70°, angle P= 60° and angle Q= 70°, then

a) ∆ LMN~ ∆ RQP b) ∆ LMN ~∆ PQR c) ∆ LMN ~ ∆ PRQ d) ∆ LMN ~ ∆ RQP

7) in the figure,

if AO/OC= BO/OD = 1/2 and AB= 5cm, then the value of DC is

a) 10cm b) 12cm c) 15 cm d) none 

8) The perimeter of two similar triangles are 30cm and 20cm. If one side of first triangle is 12cm, then the corresponding side of the second triangle is 

a) 10cm b) 8cm c) 7 cm d) 6cm

9) In ∆ ABC and ∆ DEF, angle B= angle E, angle F= angle C and AB= 3 DE, then the two triangles are

a) congruent but not similar 

b) similar but not congruent 

c) neither congruent not similar

d) congruent as well similar 

10) In the given figure,

if Angle BAC= angle ADB=90°, then the value of of x is 

a) 6 cm b)  7cm c)  4.8cm d) 5.2 cm

11) If ∆ ABC~ ∆ QRP, ar(∆ ABC)/ar(∆ PQR)= 9/4, AB = 18cm, BC= 15cm, then PR is equal to 

a) 10cm b) 12 cm c) 20/3 cm d) 8 cm

12) if it is given that ∆ ABC~∆ PQR with BC/QR= 1/4, then ar(∆ PQR)/ar(∆ ABC) is equals to 

a) 4 b) 16  c) 1/4 d) 1/16

13) ∆ ABC~∆ DEF such that AB= 9.1cm and DE=6.5 cm. if perimeter of ∆ DEF is 25cm, then the perimeter of ∆ ABC is 

a) 35cm b) 28 cm c) 42cm d) 40cm

14) ∆ AOQ~∆ BOP, AO=10cm, BO= 6cm and PB=9cm, then length of AQ is:

a) 10cm b) 11cm c) 12cm d) 15 cm

15) If P, Q, R are respectively the midpoints of the sides BC, CA and AB of ∆ ABC, then the ratio of the areas of ∆ PQR to ∆ ABC is 

a) 1:2 b) 2:1 c) 1:4  d) 4:1 

16) If in ∆ ABC and ∆ DEF AB/DE= BC/FD, they will be similar when

a) angle B= angle E 

b) angle A= angle D

c) angle B= angle D

d) angle F= angle F

17) In the figure,

∆ MNL is similar to

a) ∆ PQR b) ∆ RPQ c) ∆ QPR d) angle PRQ 

18) In the given figure,

DE || BC and all measurement are in cm. The value of x is 

a) 3cm b) 3.5 cm c) 4 cm d) 4.2cm

19) In the figure,

if D, E and F are made points of the sides BC, AC and AB respectively. then the two triangles ABC and DEF are :

a) similar b) congruent c) both a and b d) neither similar nor congruent 

20) In the given figure,

LM || NQ and LN || PQ. If MP= (1/3) MN, then the ratio of the areas of ∆ LMN and ∆ QNP is 

a) 9:4 b) 16 : 4 c) 25 :16 d) 64:9

21) M and N are respectively the points on the sides XY and XZ of a triangle XYZ such that XM= 3cm, MY = 5 cm, and YZ =12cm. If MN || YZ, then the length of MN is 

a) 6cm b) 5cm c) 4.5cm d) 4 cm

22) In the figure,

if ∆ ADE~∆ ABC,  then the length of BC is 

a) 3cm b) 3.2 cm c) 3.8cm d) 4.5 cm

23) In the figure,

DE || BC. The value of x is 

a) 10cm b) 8cm c) 7cm d) 6cm

24) The perimeters of two similar triangles are ABC and XYZ are 60 cm and 48cm respectively. If XY =8cm, then the length of AB is 

a) 12 cm b) 11cm c)  10 cm d) 9cm

25) in the given figure

DE|| BC and AD: BD= 5: 4. ar(∆ DEF): ar(∆ CFB) is 

a) 25:81 b) 16:9 c)  9: 16 d) 64: 25

1a 2b 3c 4c 5b 6a 7a 8b 9b 10c 11a 12b 13a 14d 15c 16c 17c 18a 19a 20d 21c 22d 23d 24c 25a 

Short Answer Type Questions 

1) In the given figure,

PQRS is a cyclic quadrilateral, PQ and SR produced meet at T.

a) Prove ∆ TPS ~ ∆ TRQ

b) Find SP if TP= 18cm, RQ = 4cm and TR= 6 cm.      12cm

2) In the adjoining figure,

ABC is a right angled triangle with angle BAC= 90°.

a) prove ∆ ADB ~∆CDA.

b) if BD = 18cm, CD= 8cm, find AD .      12cm

3) in the given figure 

∆ ABC and ∆ AMP are right angled at B and M respectively. Given AC= 10 cm, AP=15 cm and PM= 12cm

a)  Prove ∆ ABC~∆ AMP

b) find AB and BC .     6cm, 8cm

4) In ∆ ABC,

angle ABC= angle DAC, AB= 8cm, AC= 4cm and AD= 5cm.

a) Prove that ∆ ACD~∆ BCA

b) find BC and CD.    6.4cm, 2.5cm

c) find ar(∆ ACD: ar(∆ ABC ).     25:64

5) ABC is a right angled triangle with angle ABC=90°.

D is any point on AB and DE is perpendicular to AC, prove that :

a) ∆ ADE~∆ACB

b) If AC= 13cm, BC= 5cm and AE= 4cm, find DE and AD.      1.66cm, 4.33 cm

Long answer type questions 

1) In the figure,

ABCD is a trapezium in which AB|| DC and the diagonals AC and BD Intersect at O. Show that 

a) ∆ OCD~∆OAB, 

b) If OA= (2x +1) cm, OB= (5x -3)cm, OC= (6x -5) cm and OD=(3x -1) cm, find the value of the x.     4/3

2) in the figure

PQ || BC. prove that medium AD bisects PQ.

3) in the figure,

DE || BC and AD: DB= 4:3.

a) Show that  ∆ ADE~∆ABC

b) Find AD/AB and DE/BC .     4/7

c) prove that ar(∆ DEF): ar(∆DEC)= 4:11.      4/7

4) Through the midpoint M of the side CD of a parallelogram ABCD,

the line BM is drawn intersecting AC at L and AD produced at E. Show that EL= 2BL.

5) In a trapezium ABCD,

AB= (1/2) CD, EF drawn parallel to AB cuts AD at F and BC at E, such that BE/EC = 3/4. If diagonal BD Intersect EF at G, find EF/AB.     10/7

SHARES AND DIVIDEND 

1) The total amount of money needed to run the company is called:

a) shares  b) capital c) dividend d) principle

2) The whole capital to run a company is divided into small units, called:

a) Shares  b) Share holders  c) face value  d) dividend 

3) The annual profit distributed among share holders is called:

a) nominal value  b) market value c) dividend  d) face value 

4) The value of a share printed on the share certificate is called its :

a) nominal value b) market value c) discount  d) below par

5) The shares of different companies can the brought or sold in the market through stock exchange. The price at which the share is share or purchased is called its 

a) face value b) market value  c) par value d) Nominal value

6)  A share is said to be____,  if its market value is the same as its face value.

a) premium b) discount  c) par  c) nominal value 

7) A share is said to be at premium, if its market value is ____then its face value.

a) more  b) less  c) same  d) equal

8) A share is said to be____, if its market value is less than its face value.

a) At par b) above par c) below par d) premium 

9) The face value of a share 

a) change every year  b) changes from time to time  c) always remains the same d) none 

10) Dividend is always paid on the____ of a share.

a) market value b) face value  c) investment d) dividend 

11) The market value of a share.

a) never changes b) changes from time to time  c) changes every month  d) none

12) Number of share hold by a person=

a) total nominal value/face value of one share 

b) total market value/ face value of one share.

c) dividend/market value of one share.

d)  dividend/investment   x 100

13) dividend =

a) number of shares x nominal value 

b) number of shares x market value 

c) face value x number of shares x rate of dividend/100 

d) none

14) Rate of return on investment=

a) investment/dividend 

b) dividend/investment 

c) dividend/ investment   x 100

d) investment/dividend  x 100

15) investment/ sale proceeds =

a) number of shares x market value 

b) number of shares x nominal value 

c) face value x number of shares x  rate of dividend 

d) dividend/investment 

16) annual income of a share holder

a) number of shares x face value 

b) number of shares x rate of dividend x face value of 1 share 

c) number of shares x market value x face value 

d) market value x nominal value x 100

17) If a share of of Rs100 is selling at Rs125, then it is said to be selling at a ___ of Rs25.

a) discount  b) premium  c) at par d) below par

18) if a share of Rs125 is selling at Rs96, then it is said to be selling at Rs 29___.

a) below par b) at par c) above par d) premium

19) if Kabir invests Rs 10320 on Rs100 shares at a discount of Rs14, then the number of shares he buys is 

a) 110  b) 121  c) 150 d) 100

20)  Shahrukh has some shares of Rs50 of a company paying 15% dividend. If his annual income is Rs 3000, then the number of shares he processes is

a) 400 b) 600 c) 800  d) 200

21) If Kiran invests Rs19250 on Rs50 shares at a premium of 20%, then the number of shares she buys is 

a) 640 b) 160 c) 320 d) 240

22) Varun possesses 600 shares of Rs25 of a company. If the company announces a dividend of 8%, then his annual income is 

a) Rs600 b) Rs1200 c) Rs480 d) Rs120

23) A man invests Rs24000 on Rs60 shares at a discount of 20%. If the dividend declared by the company is 10%, then his annual income is

a) Rs2880  b) Rs1500 c) Rs3000 d) none

24) Rs25 shares of a company are selling at Rs20. If the company is playing a dividend of 12%, then the rate of return is 

a) 10%  b) 18%  c) 15%  d) 12%

25) Rs 40 shares of a company are selling at 25% premium. If Mr Washim wants to buy 280 shares of the company, then the investment required by him is

a) Rs14000 b) Rs16800 c) Rs8400 d) Rs10000 

SHORT ANSWERS:

1) Find the % return on investment in 

a) 6% Rs100 shares at Rs120 

b) 25/3% Rs100 share at Rs150

2) Find the price of 5% Rs100 shares when an investor gets a dividend of Rs65 by investing Rs1430.

3) At what price should a 25/4% Rs 100 shares be quoted when the money is worth 5% 

4) A person invested Rs1284 in 8/2% Rs100 shares . His dividend was Rs54. Calculate the M.V of the shares.

5) A company pays 7% dividend . For how much should a man buy a Rs100 shares for getting 8% on his investment.

6) Which share is more profitable: 4% Rs100 share at Rs80 or 9/2% Rs100 share at Rs88 ?

7) A part of Rs3020 is invested in 6% Rs100 shares at Rs97 and the rest in 12% Rs100 share at Rs108. If both bring the same dividend, find the sum invested in the share selling

a) at discount 

b) above par

c) the total dividend 

8) A person bought 360 ten rupee share paying 12% dividend at par and sold them at Rs21. The proceeds were invested in 5 rupees shares paying 9/2% at 3.5 per share. Find 

a) sale proceeds 

b) the number of 5 rupees shares bought 

c) the percentage in income 

9) A person invests Rs4368 in 100 rupees share at Rs91. Shares worth Rs24000 face value are sold at Rs95 and the rest at Rs85. Find 

a) the number of shares bought Rs91

b) the number of shares sold at Rs85

c) the loss or gain in the deal .

10) Rs8000 and Rs 10000 were invested in Rs100 shares giving dividends 12% and 8% respectively. The dividend are collected and all the shares are sold at a loss of 2% and 3% respectively on the investment. Find 

a) the dividend collected 

b) the total sell proceeds

c) gain percent on the whole transaction.

LONG ANSWER 

1) A man has a choice to invest in Rs 100 shares of two firms at Rs120 each or at Rs132 each. The first firm pays a dividend at 5% per annum and the second firms pays a dividend of 6% per annum. How much more will his annual return be if he invests Rs 26400 with the firm from which he gets a better return on his investment ?

2) A man bought one thousand shares each of face value Rs5 at Rs7 per share . At the end of the year, the company from which he bought the shares declared a dividend of 8%. Calculate 

a) the amount of money invested by the man

b) the percentage return on his outlay. (Correct to one decimal place).

3) Ajay owns 560 share of a company. The face value of each share is Rs25. The company declares a dividend of 9%. Calculate 

a) the dividend that Ajay will get.

b) the rate of interest on his is investment, if Ajay had to pay Rs30 for each share.

4) A company with 4000 shares of nominal value of Rs110 each declares an annual dividend of 15%. Calculate 

a) the total amount of dividend paid by the company.

b) the annual income of shah Rukh who holds 88 shares of the company.

c) If he received only 10% on his investment, find the price Shah Rukh paid for each share.

5) Amit Kumar invests Rs36000 in buying Rs100 shares at Rs20 premium. The dividend is 15 percent per annum. Find 

a) the number of shares he buys .

b) his yearly dividend

c) the percentage return on his investment 

6) Vivek invested Rs45000 in 8% Rs10 shares at Rs15 sells the shares when the price rise to Rs30 and invests the proceeds in 12% Rs100 shares at Rs125. Calculate 

a) the sale proceeds 

b) the number of Rs125 shares he buys 

c) the change in his annual income from dividend.

Biology 

1) The foetus draws its oxygen from the ____ (amniotic fluid, placenta, umbilical cord)            

2) The condition of a cell when it cannot accommodate any more water is ____(turgor pressure/ turgid/ flaccid).        

3) The blood vessel which carries oxygenated blood to the heart is ____ (aorta, pulmonary vein/ pulmonary artery).      

4) The respiratory centre is located in the ____ (cerebrum/hypothalamus/ medulla oblongota). 

5) Myopia can be corrected by ____(convex lens/ concave lens/ surgery).    

6) The duct which leads from the epididymis to the urethra is the ____.       

7) The swelling on a nerve in which the cell bodies of neurones are situated is termed ____.          

8) The embryo in the uterus is protected from machanical shocks or jerks by the ____.          

9) ATP stands for _____

10) Light enters the eye through the aperture called ____.      

11) The liquid portion of the blood is___.        

12) ____ is a pigment in mammalian body which is responsible for the transport of oxygen.       

13) Nucleated blood cells are called ___.        

14) A protein called an ____ destroys harmful injective micro-organisms.     

15) A protein called ___ is ingredient in the clotting reaction of the blood.   

16) Fill the blanks by given words:( osmosis, ciliary muscles, aorta, stapes, alveoli, WHO, malleus, diffusion, dorsal aorta, bronchioles, iris, red cross, cardiac cycle, ventilation, iron, iodine, liver, kidney) 

a) The blood vessel leaving the left ventricle of the mammalian heart is the ____.                      

b) The process by which molecules distribute themselves evenly within the space they occupy is termed __.            

c) The sequence of muscular movements performed by the heart is called ___.                         

d) Goitre results from the deficiency of ___ in our diet.       

e) Urea is produced in the ____.    

17) Each kidney is composed of ___.        

18) The process of removing the metabolic waste from the body is known as ____.                  

19) ____ is the structure, which carries urine from kidney to the urinary bladder.                        

20) Apart from urea ____ is also found in normal human urine.      

21) Automatic self regulation of salt and water within the body is known as ____.                    

22) The defect of hypermetropia is corrected by ____.      

23) In spinal cord ____ is inside.      

24) "Green house effect" is due to increase in amount of ___ in the atmosphere.                      

25) The _____ are the ones which are between the ends of sensory neuron.                             

26) The storage of sugar as glycogen in the liver is increased by the presence of ____.       

27) The valve present between the left atrium and the left ventricle is the ____.      

28) Food is translocated in plants through___.         

29) The average life of RBC is ____.        

30) Receptor cells in the eye concerned with colour vision.   

31) The part of the nervous system which prepares the body of an emergency.                       

32) The stage of mitosis during which chromatids and move apart.       

33) The process of getting rid of the waste products of metabolism is called___.      

34) One of the products formed by the___ of water is oxygen.    

35) The blood vessel which transport blood from the heart to an organ is called___.       

36) The cell in which oxyhemoglobin is formed is____.   

37) The level of health in India is low due to___ and____.          

38) In India life expectancy in____ is lower than in males because of causes associated with____.    

39) The yellow fluids which remain after blood has clotted is termed ____.      

40) ____ is the force developed during Osmosis (turgor pressure/diffusion pressure deficit/osmotic pressure).   

41) Flaccid and turgid ____(opposite/ same/ not related) to each other.     

42) ____ is an organ which serve as a blood reservoir during emergency (spleen /lumg/ heart).       

43) pH of blood is_____( 7.3 to 7.5/ 7 to 8/ 6.5 to 7).      

44) Potometer is an instrument for measuring the rate of___ ( transpiration/ photosynthesis/ flow of blood in an artery).       

45) WBC's count is higher in _____(adults/children/ middle aged persons).   

46) Largest region of the brain is____ ( Cerebellum/ cerebrum/ medulla).     

47) The basic unit of the human brain is the____.     

48) The end product of the fermentation is___.    

49) A non degradable pollutant is____.       

50) The period of the complete development of the foetus till birth is termed ____.                 

51) The foetus draws its oxygen from the___ (ammonia fluid/ placenta/umbilical cord).    

52) The condition of a cell when it cannot accommodate any more of water is___( turgor pressure/ turgid/ Flaccid).       

53) The respiratory Centre is located in the ____.(cerebrum/ hypothalamus/ medulla oblongota).     

54) The function of root is____(secretion/absorption/sinthesis).    

55) colour blindness is a____.    ( mistake/ genetic disorder/ infectious disease).                   

56) The modified Golgi complex in a sperm is ____.    (tail/end piece /acrosome ).                   

57) Largest pregnancy seen in a mammal is in the____.( Asiatic elephant/Asiatic lion/ tiger).     

58) Placenta has____( 50% maternal component/ 50% paternal component/ no maternal component).      

59) Cell division in plants take place by____.    (centrosome/ microtubules/ vesicles ).              

60) Diabetes mellitus is caused due to____ of insulin. ( hyposecration/hypersecretion/ normal separation).       

61) All animals would die on Earth if there was no____ (hemoglobin/ chlorophyll/ penicillin).        

62) ____:is a genetic disorder. (Thalassemia/typhoid/cholera).      

63) Deficiency of growth hormone causes____(gigantism /achromegaly/ dwarfism).             

64) Guttation occurs through____. (Hydathode / lenticel/cuticle).    

65) _____ is a cross between F₁ (individual and any of the two parents. (Test cross /back cross/ simple cross).    

66) ___genetic disorder(Cholera/ typhoid/colour blindness).   

67) Mendel's ____ is often known as purity of gamets .         

68) ___' is a 5-carbon compound formed in light reaction and enters into the dark reaction.  (PGA/ RUDP/NADPH₂).    

69) 'Fight' and 'Flight' harmone is_____.(adrenaline/insulin/glucagon).   

70) The energy-rich compound is_____( ADP/ATP/NADPH₂).     

EQUATION OF A STRAIGHT LINE 

1) The slope of a line whose angle of inclination is 30° is 

a) √3 b) 1/√3 c) -1/√3 d) -√3

2) The angle of inclination of a line having slope 1, is

a) 30° b) 45° c) 60° d) 90°

3)  The slope of the line passing through the points (0,-4) and (-6,2) is 

a) 0 b) 1 c) -1 d) 6

4) The slope of the line passing through the points (3,-2) and (-7,-2) is 

a) 0 b) 1 c) -1 d) not defined 

5) The slope of a line parallel to y-axis is 

a) 0 b) 1 c) -1 d) not defined 

6) The slope of a line parallel to x-axis is 

a) 0 b) 1 c) -1  d) not defined 

7) The slope of the line passing through the points (3,-2) and (3,-4) is 

a) -2 b) 0 c) 1  d) not defined 

8) The angle of inclination of the line y= x/√3 -5 is

a) 0° b) 30° c) 45° d) 60°

9) If the slope of the line passing through the points (5,2) and (3, k) is 2, then the value of k is 

a) -1 b) -2 c) -3  d) - 6

10) The slope of a line parallel to the line passing through the points (6,0) and (-3,7) is 

a) 7/9 b) -7/9  c) 9/7  d) - 9/7 

11) The slope of a line perpendicular to the line passing through the point (2,5) and (-3,6) is 

a) 5 b) - 5  c) 15 d) - 15

12) The slope of a line parallel to the line 3x + 2 y - 7 = 0 is 

a) -2/3 b) 2/3  c) -3/2  d) 3/2

13) The slope of the line x - 2y = 1 is 

a) 0 b) 1 c) 1/2  d) -1/2

14) The angle of inclination of the line √3 x - y - 1 = 0 is

a)n30° b) 45° c) 60° d) 90°

15) The equation of the line whose inclination is 45° and which interesects the y-axis at the point (0, - 4) is

a) x - y = 4  b) x + y = 4  c) y - x = 4 d) x - y = - 4 

16) if the point (a,2a) lies on the line y= 3x -6, then the value of a is 

a) 1 b) 3 c) 6  d) 7

SHORT ANSWER TYPE QUESTIONS 

1) Show that the points (1,-9), (7,6) and (3,-4) are collinear.

2) The equation of a line 2√3 x -2y +5 = 0. Find 

a) the slope 

b) the inclination

c) y- intercept of the line.

3) if the lines 2x+ 3y= 5 and Kx - 6y = 7 are parallel then find the value of k.

4) if the lines 3x- 4y +7= 0 and 2x+ ky= - 5 are perpendicular to each other, then find the value of k.

5) Find the equation of the line whose inclination is 30° and which intersects the y-axis at the point (0,-4).

6) P(3,4), Q(7,-2) and R(-2,-1) are the vertices of ∆ PQR. Write down the equation of the median of the triangle through R.

7) Write down the equation of the line whose slope is 3/2 and which passes through the point P, where P divides the line segment joining A(-2,6) and B (3,-4) in the ratio 2:3.

8) Find the equation of a line passing through the point (-2,3) and having the x-intercept of 4 units.

9) The line 4x- 3y= -12 meets the x-axis at A. Write down the coordinates of A .

10) Determine the equation of the line passing through A and perpendicular to 4x- 3y +12= 0.

11) ABCD is a rhombus. The coordinanates of A and C are (3,6) and (-1,2) respectively. Write down the equation of BD.

LONG ANSWER TYPE QUESTIONS 

1) Find the equation of the line perpendicular to the line joining the points A(1,2) and B (6,7) and passing through the point which divides the line segment AB in the ratio 3:2.

2) A straight line passes through P(2,1) and cuts the x and y-axis at the point A, B respectively. If BP: PA=  3:1, find 

a) the coordinates of A and B.

b) the equation of the line AB .

3) A straight line makes positive intercepts on the coordinanate axes whose sum is 7. If the line passes through the point (-3,8), find the equation.

4) if the coordinates of the vertex A of a square ABCD are (3,-2) and the equation of the diagonal BD is 3x - 7y+ 6= 0, find the equation of the diagonal AC. Also , find the coordinates of the centre of the square.

5) Find the equation of the perpendicular from the point (1,-2) on the line 4x- 3y= 5. Also, find the coordinanates of the foot of the perpendicular.

6) A line AB meets x-axis at A and y-axis at B. P(4,-1) divides AB in the ratio 1:2.

a) Find the coordinates of A and B.

b) Find the equation the line through P and perpendicular to AB.

7) Find the value of P if the lines, 5x- 3y+2= 0 andn6x - py +7= 0 are perpendicular to each other. Hence, find the equation the line passing through (-2,-1) and parallel to 6x- py+ 7= 0.

8) Points A and B have coordinanates (7,-3) and (1,9) respectively. Find

a) the slope of AB .

b) the equation of the perpendicular bisector of the line segment AB .

c) the value of P if (-2, p) lies on it.

9) A and B are two points on the x-axis and y-axis respectively. P(2,-3) is the mid point of AB . Find 

a) the co-ordinate of A and B.

b) slope of line AB.

c) equation of line AB.

SECTION AND MIDPOINT FORMULA 

1) The centroid of the triangle whose vertices are (3,7),(-8,6) and (5,10) is

a) (0,9) b) (0,3) c) (1,3) d) (3,3)

2) A line interestc the y-axis and x-axis at the points A and B respectively. If (2,-5) is the midpoint of AB, then the coordinates of A and B are, respectively :

a) (0,-5) and (2,0) b) (0,10) and (-4,0) c) (0,4) and (-10,0) d) (0,-10) and (4,0)

3) If O (a/3,4) is the midpoint of a line segment joining the point X(-6,5) and Y(-2,3), then the value of a is 

a) -4 b) -6  c) 12  d) -12

4) If the centroid of the Triangle formed by (7,x),( y,- 6) and (9,10) is (6,3), then the values of x and y respectively are:

a)( 5,3) b) ( 5,2) c) (-3,2) d) (6,5)

5) The ratio in which the point (3/4, 5/12) divides the line segment joining the point A(1/2, 3/2) and (2,-5) is

a) 1:2 b) 3 : 2  c) 1:5 d) 2 :3 

6) The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2,3), B(6,7) and C(8,3) is 

a) (0,1) b) (0,-1) c) (-1,0) d) (1,0)

7) The ratio in which the point P(4, m) divides the line segment joining the points A(2,3) and B(6,-3) is 

a) 1:2 b) 2:1 c) 1:3 d) 1:1

8) If A(m/2,5) is the midpoint of the line segment joining the points Q(-6,7) and R(-2,3), then the value of m is 

a) -8 b) -4 c) 12 d) 6

9) The midpoint of the line segment joining the points(-5,7) and (-1,3) is 

a) (-3,7) b) (- 3,5) c) (- 1,5) d) ( 5,-3)

10) In the figure,

AB is a diameter of the circle with centre O(4,5). If A is (1,1), then B=

a) (6,9) b) (7,9) c) (-7,9) d) (7,-9)

11) The ratio in which P(m,4) divides the line segment joining the points A(2,5) and B(6,-3) is 

a) 1:2  b) 2: 1 c) 1:3 d) 1 :7 

12) if the midpoint of the line segment joining the points P(6, b - 2) and Q(- 2,4) is (2,-3), then the value of b=

a) -5  b) -6  c) -7 d) - 8 

13) If the coordinates of one end of a diameter of a circle are (2,3) and the coordinates of its centre are (-2,5), then the co-ordinates of the other end of the diameters are:

a) (-6,7) b) (6,-7) c)  (6,7) d) (-6,-7)

14) The point which lies on the perpendicular bisector of the line segment joining the points A(-2,-5) and B(2,5) is 

a) (0,0) b) (0,2) c) (2,0) d) (-2,0)

15) The vertices of a parallelogram in order are A(1,2), B(4, y), C(x, 6), D(3,6). The value of x and y respectively are:

a) 6, 2 b) 3, 6  c) 5, 6 d) 1,4

16) If A(1,3), B(-1,2), C(2,5) and D(x, y) are the vertices of a parallelogram ABCD, then the value of x is 

a) 3 b) 4 c) 0 d) 3/2

SHORT ANSWER TYPE QUESTIONS 

1) Find the ratio in which the line segment joining (-2,5) and (-5,-6) divided by the line y= -3. Hence find the point of intersection .

2) P(1,-2) is a point on the line segment joining A(3,-6) and B(x, y) such that AP: PB is equal to 2:3. Find the coordinates of B.

3) In what ratio is the line segment joining P(5,3) and Q(-5,3) divided the y-axis ? Also find the coordinanates of the point of intersection.

4)  In what ratio does the point C(3/5,11/5) divide the line segment joining the points A(3,5) and B (-3,-2)?

5) Find the coordinanates of the point of trisection (i.e., points dividing into three equal parts) of the line segment joining the points A(2,-2) and B(-7,4).

6) Find the ratio in which the y-axis divides the line segment joining the points (5,-6) and (-1,-4). Also, find the point of intersection.

7) If the points A(6,1), B(8,2), C(9,4) and D(p,3) are the vertices of a parallelogram, taken in order, find the value of p.

8) In the figure, 

line APB meets the x-axis at A and y-axis at B. P is the point (-4,2) and AP: PB= 1:2. Write down coordinanates of A and B.

LONG ANSWER TYPE QUESTIONS 

1) Find the ratio in which the point (-3, p) divides the line segment joining the points (-5,-4) and (-2,3). Hence, find the value of p.

2) If the co-ordinate the midpoints of the sides of a triangle are (1,2),(0,1) and (2,-1), find the coordinates of its vertices.

3) The base BC of an equilateral triangle ABC lies on y-axis. The co-ordinates of point C are (0,-3). If the origin is the mid point of the base BC, find the coordinates of the points A and B.

4) P and Q are the points on the line segment joining the points A(3,-1) and B(-6,5) such that AP= PQ= QB. Find the co-ordinates of P and Q.

5) Find the length segment joining P(-4,5) and Q(3,2) intersects the y-axis at R. PM and QN are perpendicular from P and Q on x-axis. Find 

a) the ratio PR: RQ.

b) the co-ordinates of R.

c) the area of the quadrilateral PMNQ

6) The line segment joining the points (3,-4), and (1,2) is trisected at the points P and Q. If the coordinates of P and Q are (p, -2) and (5/3, q) respectively, find the value of p and q.

EXERCISE - 1

1) Find the probability of getting a head in a throw of a coin.       1/2

2) In a simultaneous throw of two dice, find the probability of getting a total of 7 ?      1/6

3) A coin is toss successively three times. Find the probability of getting exactly one head or two heads.       3/4

4) Three unbiased coins are tossed . What is the probability of getting 

a) all head.            1/8

b) Two heads.        3/8

c) one head.             3/8

d)  at least one head.    7/8

e) at least two heads.    1/2

5)  What is the probability that a number selected from the numbers 1, 2, 3,... 24, 25, is a prime number, when each of the given numbers is equally likely to be selected ?     9/25

6) Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the ticket has a number which is a multiple of 3 or 7 ?       2/5

7) One card is drawn from a back of 52 cards, each of the 52 cards being equally likely to be drawn . Find the probability that 

a) the card drawn is red.      1/2

b) the card drawn is a king.      1/13

c) the card drawn is red and a king.       1/26

d) the card drawn is either red or a king.       7/13

8) What is the probability that a leap year selected at random will contains 53 Sundays ?     2/7

9) A bag contains 9 black and 12 white balls. One ball is drawn at random. What is the probability that the ball drawn is black ?        3/7

10) The odds in favour of an event are 3:5. Find the probability of occurrence of this event.          3/8

14) Three dice are thrown together. Find the probability of getting a total of atleast 6.             103/108

RAW- 1

1) What is the probability of getting tails in a throw of a coin?      1/2

2) A die is thrown. Find the probability of 

a) getting 5.              1/6

b) getting 2 or 4.          1/3

c) getting an odd numbers.      1/2

d) getting a multiple of 3.      1/3

e) getting a prime number.      1/2

3) Two coins are tossed. Find the probability of 

a) getting 2 heads.       1/4

b) getting atleast one Heads.       3/4

c) getting no heads.      1/4

d) getting 1 head and 1 tails.        1/2

4) What is the probability that an ordinary year has 53 Sundays?     1/7

5) Tickets numbered from 1 to 12 mixed up together and then a ticket is drawn at random. Find the probability that the ticket has a number, which is multiple of 2 or 3.            2/3

6) A bag contains 4 white and 5 black balls. A ball is drawn at random from the bag. Find the probability that the ball is white.        4/9

7) In a single throw of two dice, find the probability of 

a) getting a total of 10.         1/12

b) getting a sum greater than 9.      1/6

c) getting a total of 9 or 11.       1/6

d) getting a doublet.      1/6

e) getting a doublet of even numbers.     1/12

8) Three coins are tossed. Find the probability of 

a) getting exactly 2 heads.      3/8

b) getting at least 2 heads.        1/2

c) getting at least one head and one tail.      3/4

9) In a lottery, there are 10 pricpzes and 25 blanks. Find the probability of getting a prize .       2/7

10) if there are two childrens in a family, find the probability that there is atleast one boy in the family.            3/4

11) Find the probability of getting a king or a queen, in a single draw, from a well shuffled pack of 52 cards.         2/13

12) An urn contains 9 red, 7 white and 4 black balls. A. Ball is drawn at random. Find the probability that the ball drawn is

a)  red.        9/20

b) white.     7/20 

c) red or White.      4/5

d) white or black.      11/20

e)  not red.        11/20

13) A card is drawn at random from a pack of 52 cards. Find the probability for drawing

a) a red card .          1/2

b) a black king.       1/26

c) a jack, a queen or a king.       3/13

d) either a red card or a king.        7/13

e) a card which is neither a heart nor a king.      9/13

14) In a single through of three dies, find the probability getting a total of 17 or 18.     1/54

15) Two dice are thrown. Find the probability that a multiple of 2 occurs on one die and a multiple of 3 occurs on the other.           11/36

16) A card is drawn at random from a well shuffled pack of 52 cards. Find the probability that it is neither an ace nor a king.       

29) In a single throw of two dice, find the probability of not getting the same number on both the dice .        5/6

31) Two dice are thrown together. What is the probability that the sum of the numbers on the two faces is divisible by 3 or 4 ?       5/9

32) Find the probably getting the sum as a prime number when two dice are thrown together.        5/12

GEOMETRIC PROGRESSION 

EXERCISE - 1

1) Find the ninth and the n-th term of the series 4, - 8,16, - 32,...     1024, (-2)ⁿ⁺¹

2) The 4-th and the 7-th term of a GP are -135 and 3645 respectively. Find the progression. What is the 6-th term of the GP?       -1215.

3) Which term of the GP √6, 2√3, 2√6, 4√3,....is 64√3?      12

4) if x, y, k be the p-th, q-th, and r-th terms respectively both of an AP and of a GP, then show that xʸ⁻ᵏ. yᵏ⁻ˣ. zˣ⁻ʸ=1.

5) Insert three geometric means between 2 and 162.      6,18,54 or -6,18,-54

6) Find the sum :

a) 1 - 1/2 + 1/2²+..... up to 20 terms.         (2/3)(1- 2⁻²⁰

b) 5+ 555 + 55555+....up to n terms.     (50/891) (10²ⁿ -1) - 5n/9.

7) Find the sum to n terms of the GP series: 1+ 1/2+ 1/2²+....     2 - 1/2ⁿ⁻¹ 

8) If the 6th and the 9th terms of a GP are 64 and 512, find the sum of first 9 terms of the GP.        1022

9) If the sum of first n terms of a GP is p and the sum of the first 2n terms is 3p, then show that the sum of first 3n terms is 7p.

10) If in a GP first term is a, n-th term is b, and product of first n term is P, then prove that P²= (ab)ⁿ.

12) Find three numbers in GP whose sum is 35 and product is 1000.    20,10,5

13 The sum of three numbers in AP is 15. If 1, 4 and 19 are added to them respectively, the results are in GP. Find the numbers.      26,5,16 or 2,5,8

21) In a GP, first term is 7, last time is 448 and sum of the terms is 889; find the common ratio and number of terms of the GP.      2, 7

EXERCISE - B

3) The second term of a GP is b and the common ratio is r. If the product of the first three terms of the GP is 64, find b.      4

4) The n-th term of a series is 4.3ⁿ⁻¹. show that the series is a GP.

5) If the (p + q)th term of a GP is m and (p - q )th terms is n, then find its p-th term.      ±√(mn)

7)  Find 10th term and n-th term of 16,8,4,2,.....       1/32, 2⁵⁻ⁿ

8) The 8th and 2p-th terms of 6, -12,24, -48,......(p is an integer).     -768, -3.2²ᵖ

9) The 10th and (2n +1)-th terms of the series 4, 2√2, 2, √2,....      √2/8, 2²⁻ⁿ

10) The fourth term of a GP is 32 and the common ratio is (-1/2), find the 10th term.      1/2

11) The first term of a GP is 64 and 4th term is 216; find the 7th term.     729

12) the second term of a GP is 9/16 and the fifth term is 1/6; find the 7th term.    2/27

13) The 9th term of a GP is 36 and 21-st term is 972; find the 5-th term.     12

15) Which term of the series 4, -8, 16,-32,.... 1024?      9

16) Can 640 be any term of the GP 5, -10, 20,....?       No

EXERCISE - 3

1) Insert two Geometric means between 5 and 135.       15,45

2) if 5, x, y, z , 405 are in GP, then find the value of x, y, z.      ±15,45,±135

3) Find the sum of the following series:

a) 1- 3+ 9 - 27+....to 9 terms.    4921

b) 0. 3+ 0.03+ 0.003 + .....to n terms.     (1/3)(1- 1/10ⁿ)

c) 1/8+ 1/4+ 1/2+.....+64.     127+7/8

d) 2+ √2+1+....to 12 terms.        (63/32)(2+ √2)

e) (a+b)/(a- b) + 1+ (a - b)/(a+ b)+.... n-th term.      (a+ b)²/2b(a- b)[1- {(a - b)/(a+ b)}ⁿ]

f) 1/2 - 1/3 + 1/4 - 1/9 + 1/8 - 1/27+....up to 2n terms.       1/2 - 1/2ⁿ + 1/(2.3ⁿ)

g) .9+ .99+ .999+......up to n terms.       n - (1/9)(1- 1/10ⁿ)

h) 11+ 103+ 1005+.... to n-th term.       (10/9)(10ⁿ -1)+ n²

i) 4 + 44 + 444+....up to n terms.        (40/81)(10ⁿ -1) - 4n/9

j) 0.6+ 0.66+ 0.666+.... upto n terms.        2n/3 - (2/27)(1- 10ⁿ)

k) (2+ 1/2)²+ (2²+ 1/2²)²+ (2³+ 1/2³)²+....to n-th term.    (4/3) 2²ⁿ - 1/(3.2²ⁿ)+ 2n -1

4) How many terms of the series. 3+ (-6)+ 12+ (-24)+ .... must be added from the first so that the sum maybe -1023 ?        10

5) if the 4th term of a GP is 24 and 7th term is 192, find the sum of its first 10 terms.     3069

6) in a GP, the sum of first and second terms is 16 and the sum of the fourth and 5th terms is 432. Find the sum of first 6 terms of the GP.      1456

7) The sum of the first three terms of a GP is 84 and the sum of the first 6 terms is 756. Find the sum of the first 8 terms of the GP.       3060

8) The ratio of the sum of first three terms and first 6 terms of a GP is 125 :152. Find the common ratio of the GP.       3/5

12) Find three numbers in GP whose sum is 21 and product is 64.     1,4,16 or 16,4,1

13) The sum of thhree consecutive numbers in GP is 21 and the sum of their square is 189. Find the numbers .      12,6,3 or 3,6,12

14) Divide 26 into 3 parts such that the parts form a GP and the sum of the products taking two parts at a time is 156.      2,6,18 or 18,6,2

15) Sum of the four numbers in GP is 180; sum of their two extreme members is 108; find the numbers .     12,24,48,96 or 96,48,24,12

16) The sum of three positive numbers of AP is 21. If 4, 5 and 8 are added respectively to the numbers , the results are in GP.  Find the numbers.      4,7,10 

17)  The first, 8th and 22-nd terms of an AP are 3 consecutive terms of a GP. Find the common ratio of the GP .           2

18) A number consists of 3 digits which are GP and the product of the digits is 216. If  495 be added to the number, the digits will be reversed. Find the original number.    469

19) The Arithmetic mean of two positive numbers is 15, and their Geometric mean is 9. Find the numbers.      3 and 27

EXERCISE - 4

1) If a,b,c are in GP, then show that 

a) a²+ b², ab+ bc, b²+ c² are in GP 

b) (a²+ ab+ b²)/(bc+ ca+ ab)= (a+ b)/(b+ c).

c) a²b²c²(1/a³ + 1/b³+ 1/c³)= a³+ b³+ c³.

d) 1/(a+ b) , 1/2b, 1/(b + c) are in AP 

8) If a,b,c,d are in GP then show that 

a) a²+ b², b²+ c², c²+ d² are in GP 

b) (a - b)², (b - c)², (c - d)² are in GP 

c) (b - c)²+ (c - a)²+ (d - b)²= (a - d)²

d) (a²+ ac + c²)(b²+ bd + d²)= (ab + bc + CD)².

e) a²+ b²+ c², ab + bc + cd, b²+ c²+ d² are in GP 

13) The first and last terms of a GP are respectively 36 and 972 and the sum of the terms is 1440. Find the common ratio and number of terms of the GP.     3,4

14) Three numbers are in GP whose product is 216. If 4 be added to the first term and 6 to the second term, then the resulting numbers and the third number are in AP. Obtain the numbers in GP.        2,6,18 or 18,6,2

15) The sum of three numbers in GP is 70. If the two extremes be multiplied each by 4 and the mean by 5, the product are in AP. Find the numbers.     10,20,40 or 40,20,10

16) The sum of three numbers in GP is 14. If the first two numbers are each increased by 1 and the third number decreased by 1, the resulting numbers are in AP. Find the numbers in GP.       2,4,8 or 8,4,2

17) Insert two numbers between 6 and 16 such that the first three numbers are in AP and the last three numbers are in GP.          9 and 12

18) Insert two numbers between 4 and 12 such that the first three numbers are in GP and the last three numbers are in AP.         6 and 9

19) The first terms of an AP and of a GP are each 4 and their third terms are same. If the second term of the AP exceeds that of the GP by 8, find AP and the GP.     4,20,36. 4,12,36

EXERCISE - 5

1) Solve for x:

a) 1+ a + a²+ a³+....aˣ = (1+ a)(1+ a²)(1+ a⁴)(1+ a⁸)(1+ a¹⁶).     31

b) 2+ 4+8+.....+ x= 1022.         512

8) The product of first three terms of a GP is 27/8; find the middle term.   3/2

9) The first term of a GP is 5 and 4-th term is 320; find the common ratio.     4

10) The second term of a GP is - 24 and 5th term is 81; find its first term.    16

11) The first two terms of a GP are 9 and 3. Which term of the series is 1/243 ?   8th 

13) 2x, 2x +1 and 2x +3 are in GP; find the common ratio.     2

14) If 3a +1, 6a - 4 and 3a - 2 are in GP. Find the value of a.    1

15) The third term of a GP is equal to the square of the first term and 4th term is 32, find the common ratio.      2

16) The sum of first two terms of a GP is 16 and sum of next two terms is 144. Find the common ratio of the series.     ±3

17) if the r-th term of the series is 4. 3ʳ⁻², show that the series is a GP 

18) the sum of first n terms of a series is 4(3ⁿ -1). Show that the series is a GP.

19) Find the geometric mean between 3/4 and 16/27.     ±2/3

EXERCISE - 6

1) If p,q,r are in GP, find the value of (q - p)/(q - r) + (q + p)/(q+ r).

2) Can any terms of a GP be 0 ?       No

3) Is there any two different real numbers such that AM and GM are equal ?    No

4) What type of series will be formed by the reciprocals of the term of a GP ?     GM 

5) Can three different quantities be in AP and GP at the same time ?     No

7) The sum of the first n terms of a GP is denoted by Sₙ. If S₂ₙ = 4Sₙ, then what is the value of S₃ₙ/Sₙ ?       13

ARITHMETIC PROGRESSION 

R. N- 1

1) Find the 35th and n-th term of the progression -2, 1, 4, 7,......         3n -5

2) In an AP the 11th term is 22 and 25th term is 65. Find the AP.      -7,-4,-1,2...,   80

3) Can (-447) be a term of the AP: 8, 5, 2....?   No

4) The pth term of an AP is 3p - 5. Find the common difference and the 15th term of the AP .      3, 40

5) If pth term of an AP is q and qth term is p, then find (p+ q)th term.     0

6) Insert 5 Arithmetic mean between (-5) and 7.         -3,-1,1,3,5

7) There are n arithmetic means between 5 and 35. If the ratio of second and the last mean is 1:4, find the value of n.     17

8) Find the middle term of the series: 5+ 8+ 11+...+ 89.     47

9) Find the sum:

a)  35 + 32+ 29+...+ (-25).            105

b)  1+ 4+ 6+ 9+ 11+ 14 .... up to 21 terms.         551

10) Find the sum of 4+7+10+13+....+100.           1716

11) The 3rd terms of an AP is 1/5 and 5th term is 1/3; show that the sum of the 15th of the series' is 8.

12) The  sum of the first n terms of an AP 3n²+ 5n; find the value of the 10th term of the series. Which term of the series is 152 ?        62, 25

13) The first term of an AP is 22 and the common difference is (-4). If the sum of n terms of this progression is 64, find the value of n.     4 or 8

16) The sum of 4 integers in AP is 24 and their product is 945. Find the integers.      3,5,7,9 or 9,7,5,3

23) The first term of an AP is 2, last term is 29 and the sum of the terms is 155. Find the number of terms of the series.     10

24) If the sum of the first n terms of an AP is n², find the common difference.    2

R. N- 2

1) Find the indicating terms of the following series:

a)  21st and n terms of 5, 8, 11,.....             65, (3n +2)

b) 25th and p-th terms of 16+ 11+ 6+......        -104, 21- 5p

c) (n + 1)th term of 1/n , (n+1)/n, (2n +1)/n, .....n+ 1/n

2) The 15-th term of an AP is 49 and common difference is 4; find the 25th term.   89

3) The first term of an AP is 10 and 16th term is 0; find the 31st term.     -10

4) The 12th term and the 21st term of an AP are respectively 82 and 145. Find the 32nd term.      222

5) The ratio of third and the 5th term of an AP is 2:3.  Find the ratio of 7th and 9th terms.      4:5

6) In the AP 7, 12, 17,.......which term is 162 ?     32th

7) Can 103 be any term of the AP 5, 9, 13,.....?      No

8) The n-th term of an AP is 4n -1. Find the common difference and 10th term of the AP.           4,39

9) The p-th term of an AP is q and q-th term is p; find the n-th and (p + q - n)-th terms.      p+ q - n, n

10) The m-th terms of an AP is 1/n and n-th term is 1/m, find its mn-th term.       1

11) If p times the p-th term of an AP be q times the q-th term, find (p+ q)-th term.    0

12) If 9th term of an AP is 0, show that the 29th term is double and the 19th term.

16) There are n arithmetic means between 4 and 40. If the ratio of first mean and last mean is 2:9, then find the value of n.         8

17) Find the middle terms of the following series:

a) 2 +4 +6 +......198.      100

b) 1+ 5 + 9+ ....+333.        165, 169

18) Find the sum of the following series:

a) 2 +5 +8+.... up to 25 terms.       950

b) 49 +44 +39+.... up 21 terms.       -21

c) 1/2+ 3/2+ 5/2+...... up to n terms.      n²/2

d) 1+ 4 + 7+......+ 37.             246

e) 9 + 7 + 5+.....+ (- 25).         -144

f) (a - b)²+ (a²+ b²)+ (a+ b)²+......(a²+ 20ab + b²).       12(a²+ 9ab + b²)

g)  3 + 4 + 8+ 9 +13 +14 +.....up to 20 terms.      520

h) 1 - 3 + 5 - 7+ 9 - 11+.....up to 101 terms.       101

19) Find the sum of each of the following series without using the summation formula of AP

a)  1 + 3 + 5+.....up to n terms.       n²

b) 5+ 8 + 11+..... up to 51 terms.      4080

20) The 5th and 11th terms of an AP are 41 and 20 respectively. What is its first term ? Find the sum of its first 11 terms.      55, 425/2

21) The 5th and 12th terms of an AP are 30 and 665 respectively. Find the sum of its first 20 terms.     1150

R. N- 3

1) The sum of first 9 terms of an AP is 171 and the sum of first 24 terms is 996. Find the sum of the first 16 term of the AP.       472

2) The 12th term of an AP 35 and the sum of first 16 terms is 392. Find the sum of its first 28 terms .      1190

3) The n-th term of an AP is (2n + 1). Find the sum of first n terms of the AP.     n²+ 2n

4) The sum of the first n terms of an AP is n²+ 3n. Which term of it is 162 ?    80th

5) The sum of the first n terms of a series is pn²+ qn. Prove that the series is an AP .

6) if the sum of the first p terms of an AP is 4p²+ p, find the common difference of AP.      8

7) Show that the sum of n terms of the sequence (4, 12, 20, 28,...) is the square of an even number.      

8) At least how much should be added with the sum of n terms of the series 8+16+24+ 32+.... to make the result a perfect square?      1

9) The middle term of an AP consisting of 11 terms is 12, find the sum of 11 terms of that series.       132

10) The first term of an AP is 9, last term is 96 and sum of the terms is 1575. Find the number of terms and common difference of the AP.     30,3

11) If the n-th term of an AP is p, then show that the sum of first (2n -1) terms is (2n -1)p.

12) If the sum of first P terms of an AP is equals to to the sum of the first Q terms , then show that the sum of the first (P+ Q) term is zero.

14) The sum of the first n terms of an AP is q, and the n-th term is p; show that the first term is (2q - pn)/n.

15) The p-th term of an AP is 1/q and q-th term is 1/p. Show that the sum of pq number of terms is  (pq+1)/2.

17) The sum of the first p-terms of an AP and the sum of the first q terms of the same AP is p. Find the sum of the first (p + q) terms of the AP.          -(p+ q)

18) How many terms of the series (9+ 12+ 15+....) must be added to get the sum 306?             12

19) How many terms of the series 27+24+21+18+..... must be added to get the sum 126?.             7 or 12

R. N - 4

1)  How many numbers are there between 20 and 200 which are multiple of 6 ? Find the sum of thost numbers.        30, 3330

2) Find the sum of all the multiples of 13 between 750 and 1000.      16549

3) Calculate the sum of the integers from 1 to 100, which are not divisible by 3 or 5.                2632

5) The sum of the three numbers in AP is 15 and their product is 80, find the numbers.    2,5,8 or 8,5,2

6) Divide 36 in to three parts such that the parts are in AP and the sum and the squares of the parts is 450.     9,12,15

7) The sum of three number in AP is 12 and sum of their cubes is 288, find the numbers.       2,4,6 or 6,4,2

8) Four numbers are in AP. If the sum of the extremes be 10 and the product of the mean be 24, find the numbers.      2,4,6,8 or 8,6,4,2

9) 4 integers are in AP, if the sum is zero and product is 9, then find the integers .                    -3,-1,1,3 or 3,1,-1,-3

10) Five numbers are in AP. If their sum be 30 and the sum of their squares be 220, find the numbers.       2,4,6,8,10 or 10,8,6,4,2

11) The digits of a 3 digited number are in AP and the sum of the digits is 15. If 594 be added to this number the digits will be reversed . Find the original number.     258

19) The 3 sides of a right angler triangle are in AP. Show that the ratios of the sides are 3:4:5.

20) The three sides of a right angled triangle are in AP, if the length of the shortest side is 15cm, find the length of the longest side.     25cm

R. N - 5

3) The sum of first 50 terms of an AP is 200 and the sum of the next 50 terms 50 terms is 2700; find the common difference and the first term.     1, -41/2

5) Find the least value of n for which the sum of the first n terms of the series 12 + 20+ 28+..... is greater than 1020.      16

6) Which term of the series 19 + 91/5+ 87/5+.... is the first negative term ? Find also the least number of terms for which the sum of the series is negative.     25th

7) The sum of the first three of an AP consisting of n terms is p and the sum of the last three terms is q. Show that the sum of all terms is n(p +q)/6.

RAW- 1

1) The three angles of a right angled triangle are in AP. Find the angles .    30,60,90

2) The sum of the first five terms of an AP is 20, find its third term.      4

3) The 10th term of an AP is 44 and common difference is 4; find the first term of the series.     8

4) The 15th term of an AP is 33 and the 32nd term is 67; find the first term and the common difference.     5, 2

5)  The first two terms of an AP are 5 and 8 and the last term is 80; find the number of terms.          26

6) 3k+1, 7k, and 10k +8 are in AP, what will be the common difference ?      35

7) The third term of an AP is twice that of its first term and the fourth term is 15; find the common difference of the AP.      3

8) Find one arithmetic mean between (-5) and 15.        5

9) Find the arithmetic mean between (x - y)² and (x + y)².      x²+ y²

10) 2, x, 8, y are in AP; find the values of x and y.       5,11

11) In an AP the first term is (-5), the last term is 25 and the number of terms is 10. What is the sum of the series ?      100

13) The sum of how many terms of the AP 21+ 18+ 15+ 12+....will be zero?    15 

14) Find the sum of the first hundred natural numbers .     5050

15) If each term of a series in AP be multiplied by 3, would the series so obtained be again in AP.        Yes

1) State the term - define by the following:

a)  The branch of chemistry dealing with carbon compounds.

b) Organic compounds containing carbon and hydrogen only.

c) The tendency of an element of form chains of identical atoms .

d) Organic compounds having the same molecular formula but different structural formula.

2) Give reasons -for the following:

a) Organic compounds cannot be included along with organic compounds.

b) Catenation and isomerism are unique properties exhibited by organic compounds only.

3) State which of the following organic compounds or inorganic compounds exhibit the following properties.

a) Are essentially covalent compounds.

b) Are noncombustible

c) Are soluble in organic solvents .

d) Are good conductors of electricity.

e) Show slow molecular reactions .

f) Have low boiling points .

4) Complete the sentence- by selecting the correct word from the brackets.

a) Hydrocarbon are example of____( aliphatic/ aromatic) compounds.

b) Carbon has the ability to form strong ____(ionic/ covalent) bonds.

c) The element which shows maximum tendency of catenation is____(H/C/O)

d) An example of a hydrocarbon is ____(CH₃COOH/C₂H₆/ H₂CO₃)

e) ____can be classified into a series called 'homologous series'. ( metallic carbonates/ alcohols/ ammonium compounds)

f) The main source of organic compounds is____( natural/synthetic)

g) Methanoic acid (HCOOH) is an example of a/an _____(inorganiccompound/ organic compound/hydrocarbon).

5) Complete the table pertaining to homologous series-

a) Homologous series are a family of organic compounds following a regular____ pattern, all members of the series sharing a _____ formula.

b) Methane and ethane are members of the homologous series of ______. They differ in in molecular formula by a _____group and in vapour density by____.

c) Members of the alkene series have the_____ elements and functional group.

d) The following point of butane is ____ than that of ethene.

6) Give reasons- for the following :

a) Homologous series are prevalent for organic compounds and not for inorganic compounds.

b) Methane, Ethane and propene have similar chemical properties but differ in physical properties.

c) Hydrocarbon of the same homolgous series have the same general formula.

7) Match the hydrocarbon in Column - I with its correct 

a) Homologous series b) IUPAC name c) General formula

Column -1 

A: C₂H₆

B: C₃H₆

C: C₂H₂

D: C₄H₁₀

E: C₃H₄

F: C₂H₄

G: CH₄

Homologous series 

1: Alkanes 

2: Alkenes 

3: Alkynes 

Name( IUPAC)

a: Butane 

b: Ethene 

c: Propene 

d: Propyne

e: Ethane 

f: Methane 

g: Ethyne

General Formula 

i: CₙH₂ₙ

ii: CₙH₂ₙ₋₂

iii: CₙH₂ₙ₊₂

8) Match the Column 

Column I 

A: The formula indicating the actual number of atoms in a molecule of an organic compound.

B: The formula which shows a full branched arrangement of various atoms in an organic compound.

C: A shorthand method of representing the structure formula.

D: The formula which represents the structural formula depicting the valence electrons .

Column II 

a: Condensed structural formula 

b: Electronic structural formula

c: Molecular formula 

d: Branched structural formula 

9)

Column I 

The molecular formula of:

A: Methane

B:  Ethane 

C: Ethene (ethylene)

D: Ethyne (acetylene)

F: Propane 

G: 1- Butene (1- butylene)

H: Butane 

The condensed structure formula of :

I: Ethane 

J: Ethene(thylene)

K:  Ethyne (acetyline)

L: Propyne (methyl acetylene)

M: Propane

N: Butane 

O: Propane 

The branched structural formula of:

P: Ethane 

Q: Ethene 

R: Propyne 

S: 1-Butyne(ethyl acetylene)

Column II 

a: C₂H₄

b: C₃H₈

c: H₃C - CH₂ - CH₂ - CH₃

d: H - C ≡ C- H

e: C₄H₁₀

f: H₂C = CH₂

g:          H    H

              |      |

       H - C -  C - H

             |      |

            H     H

h) H - C = C - H

           |      |

          H    H

i) H₃C - CH₃

j) H₃C - CH = CH₂

k) C₂H₂

l)        H    H

           |      |

    H - C -  C - C ≡ C - H

          |      |

         H     H

m) C₂H₆

n) H₃C - C ≡ CH

o) H₃C - CH₂ - CH₃

p) C₄H₈

q) CH₄

r)    H

       |

 H - C - C ≡ C - H

       |

      H

10) Complete the following:

a) Isomers are organic compounds having the same _____formula, but differing from each other in____ arrangement. (structural /molecular/empirical )

b) Isomers, n- butane and Iso-butane have____ chemical properties and ____physical properties, while Isomers n-butane and 1-butane have _____ physical and chemical properties.  (Dissimilar/similar)

c) The number of isomers possible of the Alkane, hexane are ____ than the Isomers possible of the alkane, pentane. (Less/more)

ORGANIC Chemistry 

R- 1

1) By reaction of aqueous NaHCO₃ with which of the following compound CO₂ is produced? 

a) CH₃CH₂OH b) CH₃CHO c) CH₃COCH₃ d) CH₃COOH.     

2) Which of the following is the alkyl group containing two carbon atoms ?

a) methyl  b) ethyl c) propyle d) isopropyl         

3) Which of the following is a saturated hydrocarbon ?

a) C₃H₆ b) C₂H₄ c) C₂H₂ d) C₂H₆       

4) Which of the following is the functional group of aldehydes ?

a) -OH b) -CHO c) > C = O d) - COOH

5) When zinc dust is added to a mixture of 95% ethyl alcohol and 5 percent 1,1,2,2 -tetrabromoethane, the gaseous hydrocarbon liberated is-

a) Ethene  b) ethyne  c) Ethane d) Methane  

6) The main constituent of LPG is

a)  n-butane b) iso- butane  c) propane d) Ethane   

7) Functional group of acetone is 

a) > C = O b) - CH₂ c) -OH d) -COOH          

8) The enzyme which breaks down start solution (C₅H₁₀O₅) into maltose is 

a) maltas b) zymase c) diastase d) none       

9) The number of hydrogen atoms in an alkene with two carbon atoms is 

a) 2 b) 4 c) 6 d) 7        

10) C₃H₈ is the formula of gaseous hydrocarbon. The formula of another gaseous hydrocarbon of the same series, having five carbon atoms is

a) C₅H₁₂ b) C₅H₁₀ c) C₅H₈ d) C₅H₅.          

11) Which one among the following is not hydrocarbon ?

a) CH₄ b) C₂H₅OH c) C₆H₆ d) C₆H₁₂  

12) Bromoethene can be prepared by treating ethyne gas with:

a) HBr vapour  b) bromine  c) Conc. HBr d) none   

13) Which one of the following is not a biodegradable polymer ?

a) starch b) teflon c) protein d) cellulose.      

14) Bond angle of H---C---H in CH₄ is 

a) 120° b) 180° c) 98°05 d) 109°28.           

15) Which one among the following is a hydrocarbon of Alkene series ?

a) C₄H₈ b) C₄H₁₀ c) C₄H₆ d) C₆H₁₆.  

16) When methanol is treated with acidified potassium dichromate the new organic compound formed is:

a) acetic Acid 

b) formaldehyde 

c) Formic acid 

d) acetaldehyde          

17) The first member of Homologous series of hydrocarbon having -C= C- bond, which can exist p, is:

a)  Methene b) Methane c) Ethene  d) ethyne        

18) The difference in molecular mass between two successive compounds in a homologous series is 

a) 18  b) 14  c) 10 d) 4 

19) Each member of the homologous series of an organic compound differs from the next member by:

a) -CH₃ b) -C₂H₂ c) -CH₂ d) -C₂H    

20) The hydrocarbon which can form substitution compounds only is

a) C₂H₄ b) C₃H₆ c) C₃H₇ d) C₃H₈     

21) Equal volumes of ethene and hydrogen at same temperature and pressure are passed through a catalyst maintained at 300°C, when an addition reaction takes place. The catalyst used is

a) platinum  b) iron(II) oxide c) Vanadium pentoxide  d) none      

22) Which of the following is obtained by dehydration of Ethanol ?

a) acetylene  b) hydrogen c) ethylene  d) ethane     

23) When sodium propionate is heated with soda lime, the gas evolved is 

a) Methane b) propane  c) ethene  d) Ethane      

24) The main constitution of CNG is

a) Methane  b) Ethane c) ethylene  d) acetylene.   

R-2

1) Write the structural formula of propanone.

2) Wohler first prepared an organic compound from an inorganic compound in the laboratory, What is the organic compound ?

3) Give an example of a biodegradable natural polymer.

4) Write one use of Urea.

5) What is the value of H---C---H bond angle in methane ?

6) Write the IUPAC name of CH₃CH₂COOH.

7) What is the industrial source of CNG ?

8) Write the IUPAC name of CH₃CH₂CHO.

9) Write the structural formula of the positional isomer of CH₃CH₂CH₂OH.

10) Mention one use of poly(tetrafluoroethylene).

11) Mention one use of poly vinyl chloride.

12) Write down the constitutional formula of isomer of CH₃CH₂OH.

13) Name and essential Amino acid.

14) Define rectified spirit.

15) Name and non-biodegradable polymer.

16) What is the formula of the functional group of ketone compounds ?

17) Which organic compound is used for ripening fruits ?

18) Give an example of addition reaction.

19) What is the black coating you find in the interior of cooking utensils at your home?

20) Name the first member of the homologous series of the carboxylic acid.

21) Name the first homologous of alkanes which exhibits isomerism

22) Name the homologous organic compound with functional group - O-

23) Give the chemical equation of hydrogenation of Ethylene.

24) Name two bio-inorganic molecules.

25) Write down the name of the monomer of Teflon .

26) Name the simplest gaseous saturated hydrocarbon.

27) How is Methane prepared in the laboratory ?

Current Electricity 

R-1

1) Charge of an electrons is:

a) - 3.2x 10⁻¹⁹C

b) - 1.6 x 10⁻¹⁹C

c) 1.6 x 10⁻¹⁹C

d) 3.2x 10⁻¹⁹C 

2) if the resistance(R) of the conductor and time of flow of current in the conductor(t) remain unchanged , the relation between the heat produced(H) in the conductor and flow of current(I) is 

a) H ∞ I b) H ∞ 1/I² c) H ∞ I² d) H ∞ 1/I. 

3) If 12C of charge flows through a conductor for 2 minutes, the electric current is

a) 6 ampere 0.1ampere c) 24 ampere d) 10 amperes 

4) Coulomb's law related to electric charges is applicable when of the two charges

a) one is point, one is Spherical 

b) both the spherical 

c) one is point, one is extended 

d) both are points 

5) The characteristics of a fuse wire are 

a) high resistance, high melting point 

b) low resistance, low melting point

c) low resistance, high melting point

d) high resistance, Low melting point 

6) Temperature remaining unchanged, if the potential difference between the two ends of a conductor is V and the current through the conductor is I, which of the following is true ?

a) V ∞ I b) V ∞ I² c) V ∞ I⁻¹ d) V ∞ I⁻² 

7) The relation among the electromotive force(V), work (W) and charge(Q) is 

a) Q= WV b) Q= V/W c) Q= V/W² d) Q= W/V 

8) Which of the units given below is the SI unit of resistance ?

a) volt b) ampere c) coulumb d) ohm 

9) In domestic electric circuit the fuse wire is connected to which is the following ?

a) earth line b) live line c) neutral line d) both live and neutral lines. 

10) Which of the following physical quantity represent ampere ?

a) coulumb second 

b) volt. ohm⁻¹ c) voly. ohm d) volt⁻¹ ohm 

11) Resistivity of which of the following decreases with increase in temperature ?

a) conductor

b) semiconductor

c) superconductor 

d) insulator 

12) With increase in temperature, the resistivity of a metallic conductor -

a) does not increase 

b) increases 

c) does not increase

d) decreases. 

13) Which principle is abided by Lenz's law ?

a) conservation of energy 

b) conservation of mass 

c) conservation of momentum 

d) conservation of charge. 

14) A potential difference of 20 volts applied across the ends of a conductor enables 20 coulumbs charge flow through it in 5 seconds . What is the resistance of the conductor.

a) 3 ohms b) 4ohms c) 5ohms d) 6 ohms 

15) The emf of a sample voltage cell is

a) 1.08 b) 2.36 c) 3.46 d) 7.78 

16) Commercial unit of electrical energy is 

a) BOT b) volt c) coulumb d) ampere 

17) The core of an electromagnet is made of 

a) alnicu b) steel c) soft iron d) none 

18) Material of a fuse wire is 

a) Copper b) an alloy c) semiconductor d) an insulator 

19) In electric motor electric energy is converted to____ energy.

a) mechanical b) sound c) heat d) chemical 

20) The SI unit of potential is 

a) ampere b) volt c) gauss d) siemens 

21) The product of the total number of tuns in a solenoid aystrength of current in ampere is called

a) reverse ampere 

b) ampere turn 

c) pole strength d) none 

22) Chemical energy Converts to___ energy into a voltaic cell.

a) sound b) electrical c) heat d) nuclear 

23) The unit of potential difference is

a) joule b) volt c) ampere d) coulumb. 

24) Same current flows through conductor. If the resistance of one is 4 times than that of the other, then the ratio of potential difference established in the two is

a) 4:1 b) 1:4 c) 8:1 d) 1:16 

25) What magnitude of the current flow through a conductor of resistance 8 Ohm's when it is connected to a battery of emf 2 volts ?

a) 16 ampere 

b) 0.25 ampere

c) 5 ampere

d) 10 ampere 

26) What is the effective resistance of the resistance 2 Ω,4Ω and 5 Ω connected in parallel

a) 11 Ω b) 2Ω c) 4 Ω d) 1.05Ω 

27) in a Circuit, 2 Ω and 3Ω resistors are connected in series to the parallel arrangement of 2 Ω and 3Ω resistors. What is the resistance in the circuit ?

a) 10Ω b) 6.2Ω c) 6.2 Ω d) 15Ω 

28) The colour of the earthing wire is 

a) black or green 

b) green or yellow 

c) yellow or blue 

d) green or black 

27) Which quantity expresses the work done by an electrical instrument ?

a) I²R b) I²Rt c) I²Rt/J d) VI 

28) 1 volt is equals to 

a) 1C/1J b) 1J/1C c) 1A/1J d) 1J/1A 

29) With increase in temperature, the resistance of a semiconductor 

a) increases b) decreases c) remains the same d) becomes half of its value 

30) I₁, I₂, I₃ are amounts of current flowing through three resistance R₁, R₂ and R₃ (R₁ > R₂ > R₃) connected in parallel. The relation among I₁, I₂ and I₃ is 

a) I₁= I₂> I₃

b) I₁> I₂> I₃

c) I₁< I₂< I₃

d) I₁> I₂< I₃ 

31) The filament in an electric lamp has____ resistance.

a) high 

b) medium 

c) low

d) none 

32) 1Hp is 

a) 476W b) 746W c) 764 W d) 647 W

33) 1 BOT is 

a) 1W-h b) 1kW-h c) 1MW-h d) 1mW-h 

34) Equivalent resistance of two resistances 3 Ω and 6Ω connected in parallel will be 

a) 3Ω b) 6Ω c) 4.5Ω d) 2Ω 

35) Electric power is expressed by 

a) VI b) V²I c) VI² d) VIT 

36) The unit of current is 

a) joule b) volt c) ampere d) coulumb 

37) Unit of charge in SI system is 

a) coulumb 

b) ampere 

c) Henry 

d) Ohm 

38) 0.55 ampere current flow through an electric bulb of 400 ohm resistance when it is connected in a line of electric supply. What is the emf of the line ?

a) 550 volts b) 440 volts c) 220 volts d) 1320 volts 

R-2

1) What is the SI unit of electric charge ?

2) What is the unit of electrical conductance ?

3) What are the constituents of fuse wire ?

4) Kilowatt -hour is the unit of which physical quantity ?

5) Name a machine where electrical energy is convert to mechanical energy

6) Apart from the live wire, what are the two other wires in the household circuit ?

7) A thin wire and a thick wire of the same conducting material have the same length, Which one of them will carry more current when connected to the same potential difference ?

8) Give an example of semiconductor 

9) How does the resistance of a semiconductor change with increase of temperature ?

10) Which type of energy transformed to electrical energy in a Dynamo ?

11) What will be the change in the motion of a Barlow's wheel if the direction of the current is reversed?

12) How much work has to be done when1 coulumb of charge is taken against a potential difference of 1 volt ?

13) Mention one use of ammeter.

14) How much charges has flown through a circuit if a current of 0.2A flows for 2 seconds in that circuit ?

15) Write the name of one nonmetal which is a good conductor of electricity.

16) State the energy transformation in Barlow's wheel 

17) What is electric cell ?

18) What type of transformation of energy takes place in an electric cell?

19) What is the practical unit of electric power ?

20) What transformation of energy takes place in the Electric motor ?

21) Which one of the two bulb 60W and 100 W will glow better when connected to parallel under the same potential difference ?

22) Name the instrument used for detecting current in an electric circuit. 

23) What is the colour of the live wire ?

24) What material of wire is used in electric heater ?

25) Define temperature of co-efficient

26) narme two substances which are good conductors of electricity.

27) What is a Rheostat 

28) What will happen to Barlow's wheel if the amount of current is increased ?

29) Write the full form of LED

30) How can energy of a motor be increased ?

31) What type of combination is used in domestic circuit ?

32) Name two non-omic resistances 

33) What is a non-ohmic circuit ?

34) Name two devices in which heating effect of current is utilised.

35) Write the full form of CFL 

R- 3

1) Mention one similarity and one dissimilarity between electromotive force and potential difference.

2) Two resistance a and b, when connected separately to the same potential difference, it was seen that the current flowing through a was six times the current flowing through b. Determine the ratio of a and b.

3) A bulb is marked with '220 V-50W'. Explain its significance.

4) What is Osteroids experiment ?

5) Describe Fleming's left hand rule.

6) How can the strength of an electromagnet be increased ?

7) What is 3-pin plug?

8) Why is the earthing pin of a 3-pin plug long and thick ?

9) What do you mean by the potential difference ?

10) On what factors does the resistance of a conductor depend ?

11) Why is fuse wire used in electric circuit.

12) What is electric Motor ?

13) What is solenoid ?

14) Define BOT.

15) Why is nichrome wire used in electric heater ?

16) Define coulumb 

17) What is earthing ? How is a person saved from electric shock even if the live wire accidentally touches the metal body of an electric iron the person is working with ?

18) Define Ampere 

19) Define Ohm?

20) Define eyquivalent resistance.

21) What is internal resistance of a cell ?

22) Find the current flow through a metallic conductor having resistance 10 ohm when potential difference across two ends is 220 volt.

23) State Ohm's law 

24) Calculate the electrical energy used when a 60 watt bulb is used for 50 hours.

25) Find the number of electrons in a charge of 1 Coulumb .

26) Write down the dimension of emf or pd and charge.

27) What is specific resistance ?

Quadratic Equation 

1) The product of two roots of the equation x²- 7x +3=0 is

a) 7 b) -7 c) 3 d) -3

2) Under what condition one root of the quadratic equation ax²+ bx + c=0 is zero ?

a) a=0 b) b=0 c) c

 =0 d) none

3) 2x²- 3x - k +2=0 one root of the equation is zero. The value of k is 

a) 2 b) -2 c) 1/2 d) -1/2

4) If two roots of equation x²+ 4x + k =0 are equal, then the value of k is 

a) 1 b) 2 c) 3 d) 4

5) If two roots of equation x²- 6x + k=0 are real and unequal then what is the value of k.

a) more than 6

b) less than 6

c) more than 9

d) less than 9

6) The sum of two roots of the equation x²- 6x +2=0

a) 2 b) -2 c) 6 d) -6

7) If the product of two roots of the equation is x²- 3x + k = 10 is -2, what is the value of k ?

a) -2 b) -8 c) 8 d) 12

8) If two roots of the equation ax²+ bx + c=0 (a= 0) be equal, then 

a) c= -b/2a b) c= b/2a  c) c= -b²/4a  d) c= b²/4a 

9) The root/s of the equation x²= 36 is

a) 0 b) 6 c) 0and 6  d) -6

10) If two roots of the equation (k +1)x²+ 2kx + (k +2)= 0 are equal and negative then the value of k is 

a) 1 b) -1 c) 0 d) -2

11) If roots of the equation ax²+ bx + c =0 (c ≠ 0) are real and unequal then b²- 4ac will be 

a) >0 b) =0 c) <0  d) none

12) If ax²+ bx + c is a quadratic equation then 

a) b=0 b) c≠ 0 c) a≠ 0 d) none 

13) The highest power of the variable of a quadratic equation is 

a) 1 b) 2 c) 3 d) none

14) The equation 4(5x²- 7x +2)= 5(4x²- 6x +3) is 

a) linear b) quadratic c) 3rd degree d) none

15) The roots of the equation ax²+ 2bx + c=0 (a≠ 0) are real and equal, then b²= ____.

16) If the product and sum of two quadratic surds is a rational number, then the surds are ___' surd.

17) The equation (a -2)x²+ 3x +5=0 will not be a quadratic equation for a= ____

18) If in a quadratic equation ax²+ bx + c=0(a≠ 0), b²= 4ac, then the roots of the equation will be real and ____.

19) If the sum and product of two quadratic equations is a fundamental number, then both the conditions are____:

20) (x -2) and (x -3) is proportional x to the mean of the x _____.

21) 7x²- 12x +18=0. The ratio of the sum and the product of the roots of the equation ____.

22) ax²+ bx + c=0 (a≠ 0) if both the roots of the equation are mutually inverse (reciprocal), then c=_____.

23) ax²+ bx + c=0 (a≠ 0) if both the roots of the equation are mutually inverse and negative, then a+ c= _____

24) x²+ x + 1=0 both the roots of the equation are real.   T/F

25) x²- x + 2 =0 both the roots of the equation are not real. T/F

26) x²= 25 the only root of the equation is 5.   T/F

27) 3x² - 2√6 x + 2=0 both the quadratic equation will be real and equal .   T/F

28) If the roots of the equation 5x²- 2x +3=0 be α , β,  find the value of (1/α + 1/β).

29) If the equation be 2 and -3, then write the equation.

30) Find the value of p for which the equation x²+ (p +3)x + p=0 has real and equal roots. 

31) If kx²+ 2x + 3k =0 (k≠ 0) the sum and product of the roots of the equation are same, find the value of k.

32) If x²- 22x + 105= 0 the equation has two roots α , β then determine the value of α - β

33) Solve:

a) 1/(x -3) - 1/(x +5) = 1/6.    

b) The product of two consecutive positive odd numbers is 143. Construct the equation and determine the number by applying Sridhara Acharya's formula.   

c) Determine the equation whose roots are the square of the roots of the equation x²+ x +1=0.         

d) If the price of 1 dozen pens is reduced by Rs6, then 3 more pens can be bought in Rs30. Calculate the price of 1 dozen pens before the reduction of price.  

e) {(x +4)/(x- 4)}² - 5{(x +4)/(x- 4)}+ 6 =0, (x≠ 4).    

f) The digit in the unit's place of a two digited number is 6 more than that at that the ten's place. th6e product of the digit is 12 less than the number. Find the possible values of the digit in the unit place.   

g) if 5 times a positive whole number is less by 3 than twice of its square, then find the number.      

h) 1/x - 1/(x - b) = 1/a - 1/(a - b).     

i) x² -(√3+ 2)x + 2√3=0.    

j) (x +3)/(x- 3) + 6{(x -3)/(x+3)}= 5.  

k) x/(x +1) + (x +1)/x = 25/12, x≠0,-1.   

l) (2x +1)+ 3/(2x +1) = 4.     

m) (x +1)/2 + 2/(x +1) = (x +1)/3 + 3/(x +1) - 5/6.  

n) {(x +a)/(x - a)}² - 5{(x + a)/(x - a)}+ 6 = 0, x≠ a.    

o) The tens digit of a number is 3 less than the unit. Subtracting their product from the number gives the distunction 15. Find the unit digit of the number.   

p) There are two taps in our school's cistern. A cistern is filled in a 1/x minute by both the drains. The second tap takes 5 minutes longer than the first. In how much time will each tap fill the cistern separately ?       

q) When a two digit positive number is multiplied by its unit digit, the product is 189. If the tens digit is twice the unit digit, then what is the unit digit ?       

r) (b - c)x²+ (c - a)x + (a - b)=0 if both the roots of a quadratic equation are equal, show that 2b = a+ c.

s) (a²+ b²)x² - 2(ac + bd)x + (c²+ d²)=0. If both the roots of equation are equal, then show that a/b = c/d.

t) ax²+ bx + c =0 if one root is twice the other, then show that 2b²= 9ac.