RAW- 1 (X) CBSE

4/10/24

FILL IN THE BLANKS

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

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

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

4) if the sum and product of two quadratic conditions is a fundamental number, then both the conditions are____.

5) 7x²- 12x +18=0. The ratio of the sum and the product of the roots of the equations_____. 

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

7) ax²+ bx + c=0 (a≠ 0) if both the roots of the are mutually inverse and negative, then a+ c=____. 

8) If sum of two angles is ___, then they are called supplementary angles. 

9) If the bases of two triangles are situated on same line and the other vertex of the two triangles are common, then the ratio of the areas of two triangles are ____ to the ratio of their bases. 

10) if ABCD is a cyclic parallelogram then angle A is____. 

11) If the length of the sides of two Triangles are in proportion, then two Triangles are _____. 

12) If both the angles made by an arc in the same arc are equal, then the length of both the arcs is ____. 

13) A contagious Parallelogram is a_____. 

14) The vertices of a square figure are ____.

15) If a straight line intersects a cut at two points, then the straight line is called the ___ of the cut.

16) Due to the ratio of the length of the two chords PQ and RS in the O central circle, 1:1 angle POQ: angle ROS= ____ .

17) the perpendicular bisector of a chord of a chord is____. 

18) Angles lying in the same verse are ____. 

19) If the line segment joining two points makes equal opposite angles to the other two points on the same side, then the four points will be____. 

20) Two Triangles are similar if their____ 

21) If a straight line intersects the circle at two points, then the straight line is called ____ of circle. 

22) Two circles touch each other externally at the point A. A common tangent drawn to the two circles at the point A is ____ common tangent (direct/ transverse). 

23) if AOB is the diameter of a circle and C and D are two different points on the circumference not on the same side of AB, such that angle AOC=130°, then the value of angle CDB will be____.

24) The line segment parallel to any side of a triangle divides other two sides or the extended two sides ___. 

25) The perpendicular bisector of any chord of a circle is____ of that circle. 

26) The angle in the segment of a circle which is less than the semicircle is an ____angle. 

27) three circles can intersect each other at more than ____point/s. 

28) The distance between the centres of two circles with radii 9cm and 16cm is 25cm. The length of the segment of the tangent between them is____cm.

29) In ∆ ABC , angle A= angle B= 60°, AC=8cm. The lines AD and BD intersect at D with D= 90°. If DB= 2cm then the length of AD is ____cm. 

30) If an exterior angle of a cyclic quadrilateral be 50°, then the interior opposite angle is____. 

31) If PQ is the diameter of a circle with centre O and R is a point on the circumference such that angle ROQ= 120°, then the value of angle ORP is ____. 

32) The circle drawn with the hypotenuse of a right angled triangle as diameter passes through the ____. 

33) The straight lines parallel to the parallel sides of a trapezium divides____ other two sides. 

34)  If cos²x - sin²x = 1/x (x > 1), then cos⁴x - sin⁴x = ____. 

35) If the sun's angle of elevation increases from 30° to 60°, the length of the shadow of a post____. (decreases/ increases). 

36) if the angle of elevation of the sun is 45°, then the length of shadow and length of post ate____.

37) The value of tan 15 tan 45 tan 60 tan 75 is ____.

38) if tanx = 4/5, then x = ____.

39) If sinx =1/2, then cos2x =_____. 

40) If the opposite angles of a quadrilateral be supplement then the vertices of the quadrilateral will be_____.

41) cosx= √3/2, then sin2x=_____. 

42) The value of (4/sec²x + 1/(1+ cot²x) + 3 sin²x) is ____. 

43) The vertical of a cyclic squares are _____. 

44) If sinx =1/2, then tan2x =___.

45) If sin(x - 30°)= 1/2, then the value of cosx is_____. 

46) One solid sphere is melted and a solid right circular cylinder is made, then _____ of sphere and the cylinder will be equal.

47) number of surfaces of the solid right circular cylinder is____. 

48) The shape of a pencil with one end sarpend is the combination of a cylinder and a ____.

48) The numbers are plane surface of a solid hemisphere are____. 

49) ABC is the hypotenuse of the right angle AC triangle. Considering the side AB as an axis, the diameter of the right circular cone that will be formed in full circle of the triangle will be____. 

50) if the volume of a right circular cone is V cubic units and the area of the base being A square units, the height will be_____.

51) If the radius of the base of a right circular cylinder and a right circular cone are the same and their heights are also be same, then the ratio of their volumes will be ____. 

52) A solid sphere is melted to form a solid right circular cylinder. The volume of the sphere and the cylinder is____. 

53) The number of diagonals of a rectangular solid is____. 

54) The length of the diagonal of a plane of a cube= ____ x length of one side. 

55) A rectangular paper has unit length and unit width . A rectangular paper is folded into cylinder whose circumference is equal to the length of the paper____ curve of cylinder. 

56) The length of the radius of the base of a solid right circular cylinder and two hemisphere are equal. If tor hemisphere are placed side by side with the plane of the cylinder, then what is the shape of the new solid object = area of the plane of a hemisphere + ____ area of the curve of+ The area of the curve of second hemisphere.

57) If the diameter of a circular pipe is 3 cm and height is 4cm, then the length of the longest pole that will be placed inside the pipe is_____ cm. 

58) If the volume of a right circular cylinder and the area of the curved plane have the same number of values, then the length of the diameter of the cylinder is____. 

59) The variable x₁, x₂,.......x₁₀₀ are in ascending order of their magnitude, then the median of the variable is____. 

60) The measured of central tendency are mean, median and____. 

61) if the mean x₁, x₂, x₃....xₙ be bar x, then the mean of kx₁, kx₂, kx₃....kxₙ is _____(k≠0). 

62) The median of the data 8, 9, 6, 7, 5, 6, 7, 8, 9, 10 is____. 

63) If the mean of the number 6, 7, x, 8, y, 14 is 9, then x + y=____. 

64) The relation between x and y is 2x + 3y=7. If the median of y is 2; then the median of x is _____. 

65) The median of 2, 3, 4, 3, 6, 7, 8 is ____. 

66) The following are the marks obtained by 10 students in physics test: 65, 52, 71, 47, 49, 51, 37, 29, 77, 62; then the mean mark is____. 

67) The mode of 2, 3, 5, 6, 2, 4, 2, 8, 6, 9 will be____. 

68) The mode of the data 1,1,2,2,2,3,3,3,4,4,5,6,7 is____.

CHOOSE THE CORRECT OPTION:

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 quadric 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 0. 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 roots of the equation x²= 6² is/are

a) 0 b) 6 c) 0 and 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 the roots of the equation ax²+ bx + c=0(c ≠ 0) are real and unequal then b²- 4ax will be 

a) >0 b) =0 c) <0  d) none.     

12) The number of roots in a quadratic equation is

a) 1 b) 2 c) 3 d) none.     

13) If ax²+ bx + c=0 is a quadratic equation then

a) b≠ 0 b) c≠ 0 c) a≠ 0 d) none.   

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

a) 1 b) 2 c) 3  d) none     

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

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

16) The length of the two chords AB and CD cycle of a circle of centre O are equal and angle AOB= 60°,

then angle COD= is 

a) 40° b) 30° c) 60° d) 90°     

17) O is the centre of a circle and AB is a diameter, ABCD is a the cyclic quadrilateral.

Angle ABC=65°, angle DAC= 40°, then the measure of angle BCD is 

a) 75° b) 105° c) 115° d) 80°      

18) If Angle A =100° of a cyclic quadrilateral ABCD, then the value of angle C is 

a) 50° b) 80° c) 180° d) 200°       

19) The number of common tangents of two circles when they do not touch or intersect each other is :

a) 2 b) 1 c) 3 d) 2      

20) The length of the radius of 6 circle is 13cm and the length of a chord of the circle is 10cm, the distance of the coord from the centre of the circle is 

a) 12.5cm b) 12 cm c) √69cm d) 24 cm      

21) The centre of two concentric circles is O; a straight line intersects a circle at point A and B and the other circle at point C and D. If AC= 5 cm, then the length of BD is

a) 2.5cm b) 5cm c) 10 cm d) none.     

22) The distance between two parallel chords of length 8cm each in a circle of diameter 10 cm is

a) 6cm b) 7cm c) 8cm d) 5.5 cm     

23) In the adjoining figure, if O is the centre of the circle, then the value of angle X is

a)  70° b) 60° c) 40° d) 200°     

24) In the adjoining figure,

if O is the centre of the circle and the BC is the diameter then the value of x is 

a) 60° b) 50° c) 100° d) 80°     

25) In the adjoining figure,

O is the centre of the circle; if ang ACB =30°, angle ABC= 60°, angle DAB= 35° and DBX= x°, then the value of x is 

a) 35 b) 70 c) 65 d) 55      

26) If AB is a diameter of a circle with Centre O and C is a point on the circumference such that angle BOC=60°, then the value of angle AOC is

a)  60° b) 30° c) 120° d) 90°      

27) In the adjoining figure,

O is the centre of the circle and AB is the diameter. If AB || CD, angle ABC=25°, then the value of angle CED is 

a) 80° b) 50° c) 25° d) 40°    

28) In the adjoining figure,

O is the centre of the circle, id angle BCD= 28°, angle AEC= 38°, then the value of angle AXB= ?

a) 56° b) 86° c) 38° d) 28°           

29) In the diagram

besides O is the centre of the circle and AB is a diameter. ABCD is a cyclic quadrilateral. Angle BAC is

a) 50° b) 60° c) 30° d) 40°       

30) In the diagram

besides ABCD is a cyclic quadrilateral. BA is produced to the point F. If AE|| CD, angle ABC= 92° and angle FAE= 20°, then the value of angle BCD is 

a) 20° b) 88° c) 108° d) 72°      

31) I is the centre of ∆ ABC, angle ABC= 60° and angle ACB= 50°. Then angle BIC is

a) 55° b) 125° c) 70° d) 65°         

32) In the adjoining figure,

O is the centre of the cirle, if Angle BAD= 65°, angle BCD= 45°, then the value of angle BCD is 

a) 65° b) 45° c) 40° d) 20°       

33) If tanx + cotx =2, then the value of (tan¹³x + cot¹³x) is 

a) 1 b) 0 c) 2 d) none      

34) If tanx = 4/5, then cosx =

a) 4/5 b) 3/5 c) 3/4 d) 5/√41     

35) If sinx = 1/√2, then sec2x =

a) 0 b) 1 c) 2 d) none     

36)  Height of tower is 100√3 metres. The angle of elevation of the top of the tower from a point at a distance 100metres from the foot of the tower is

a) 30° b)  45° c) 60° d) none       

37) If the ratio of the volume of two right circular cones is 1:4 and the ratio of radii of their bases is 4:5, then the ratio of their height is:

a) 1:5  b) 5:4 c) 25: 16 d) 25 :64       

38) If two cubes of length of each side 2√6 are placed side by side, then the length of the diagonal of the cuboid so produce is

a) 10cm b) 6cm c)  2cm d) 12cm     

39) If side of a cube is a unit and the diagonal of the cube is d unit then the relation between a and d will be:

a) √2 a= d b) √3 a = d c) a= √3 d d) a= √2 d       

40) If each of radius of the base and height of a cone be doubled, then the volume of it will be

a) 3 times  b) 4 times c) 6 times d) 8 times      

41) If the height of a cone is h unit, slant height I units and the diameter of the base is d unit, then (l²- h²)/d²= ?

a) 1/2  b) 1/3  c) 1/4 d) 1/5     

42) The volume inside a rectangular box is 440 cubic cm and the area of the inner base is 88 sq cm, then the inner height of the box is

a) 4cm b) 5cm c) 3cm d) 6 cm    

43) A rectangular pit is 40m long , 12m wide and 16m deep. In this pit a plank 5m long, 4 m wide and 2 m high will be placed ?

a) 190 b) 192 c) 184 d) 180     

44) The area of the lateral plane of a cube is 256 sq.m volume of cube 

a) 64cune m b) 216 cube m c) 256 cube m d)  51 cube m    

45) If the ratio of the volumes of two cubes is 1:27, then the ratio of the area of the total surface of both the cubes is 

a) 1:3 b) 1 : 8 c) 1: 9 d)  1:18       

46) if the area of all the sides of a cube is 5 square unit and the length of the diagonal is d units, then the contact between S and d is

a) S= 6d² b) 3S= 7d c) S³= d² d) d²= S/2    

47) If the ratio of the radii of two circular solid cylinder 2 :3 and the ratio of their height is 5:3, then the ratio of the areas of their sides is 

a) 2:5 b) 8 : 7  c) 10:9 d) 16:9     

48) if the ratio of the radiu of two right circular solid cylinder is 2:3 and that of the height is 5:3, then the ratio of their volume is 

a) 27:20 b) 20: 27 c) 4 :9 d) 9 :4     

49) 2 right circular cylinders have equal volumes and the ratio of their heights is 1:2, then the ratio of their radii--

a) 1:√2 b) √2: 1 c) 1:2 d) 2:1     

50) If the radius of a right circular cylinder is half the length and twice the height, then the volume of the cylinder will be the volume of the initial cylinder.

a) equal  b) double c) half  d) four times     

51) when the radius of a right circular cylinder is doubled and the height is halved , the area of the circle is the area of the original cylinder.

a) equal  b) double c) half  d) four times.  

52) If the ratio of the volumes of two solid sphere is 1:8, then the ratio of the area of the sphere will be ---

a) 1:2 b) 1:4 c) 1: 8 d) 1:16    

53) The total surface area of a solid hemisphere of radius 7cm will be 

a) 588π sq.cm b) 392π sq.cm c) 147π sq.cm d) 98π sq.cm   

54) if the ratio of the areas of the sides of two solid sphere is 16:9, then the ratio of their volumes will be 

a) 64 :27 b) 4 :3  c) 27 :64  d) 3:4      

55) if the area of the circle of a solid sphere and three times the volume have the same numerical value, then the length of the radius of the sphere is

a) 1 unit b) 2 unit c) 3 units d) 4 units.  

56) If the slant height of a right circular cone is 15cm and the diameter of the base is 16cm, then the area of the lateral plane of the cone will be

a) 60π sq.cm b) 68π sq.cm c) 120π sq.cm d) 130 π sq.cm   

57) The ratio of the volumes of two right circular cones is 1:4 and the radius of their bases is 4:5 p, then the ratio of their heights will be 

a) 1:5 b) 5:4 c) 25:16 d) 25:64       

58) Keeping the radius of the base of a right circular cone the same and doubling its height, the increase in its volume will be

a) 100% b) 200% c) 300% d) 400%     

59) if the radius of a right circular cone is r/2 units and the slant height is 21 units , then the area of the total plane of the cone is

a) 2πr(l+ r) cu. unit 

b) πr(l+ r/4) cu. unit 

c) πr(l+ r) cu. unit 

d) 2πr cu. unit     

60) The median of the data 11 , 29, 17, 21, 13, 31, 39, 19 is

a) (19+29)/2 b) 19 c) 21 d) none    

61) Mode is the 

a) least frequent value 

b) middle most value

c) most frequent value

d) largest value      

62) The mode of the data 1, 2, 3, 4, 5, 6, 7 is 

a) 4 b) 6 c) 7 d) none       

63) median of a frequency distribution can be obtained from

a)  pie diagram 

b) histogram 

c) frequency polygon 

d) ogive    

64) The median of 1, 5, 9, 3, 8, 7 is

a) 5 b) 7 c) 8  d) 5 and 7 both     

65) if the median after arranging in ascending order the data 8, 9, 12, 17, x+ 2, x + 4, 30, 31, 34, 39 is 15, then the value of x is 

a) 22 b) 21 c) 20 d) 24     

1) If  2 cos x= 2/5, without using table, find sinx.      (2)

2) Calculate the length of the tangent drawn to a circle of diameter 8 cm from a point 5 cm away from the centre of the circle.     (2)

3) a) If 7 is the mean of 5, 3, 0.5, 4.5, b, 8.5, 9.5, find b.

b) If each observation is decreased in value by 1 unit, what would be the new mean be ?    (3)

4) In the figure below, AB is a chord of the circle with centre O and BT is standing to the circle at B.

If angle AOB= 32°, find the value of x and y.    (3)

5) The volume of a cylinder 14cm long is equal to that of a cube having an age 11 cm. Find the radius of the cylinder.     (4)

6) A piece of butter 3 cm by 5cm by 12cm is placed in a hemispherical bowl of radius 3.25cm. Will the butter overflow when it melts completely ?      (4)

7) Solve graphically 2x + 3 y= - 5;  2y + 3x = 0.      (5)

8) In a ∆ABC, angle A is obtuse, PB perpendicular to AC and QC perpendicular to AB. Prove that: AQ x AB = AP x AC.      (4)

9) Taniya standing on a vertical cliff in a jungle observes two rest houses in line with her on opposite sides deep in the jungle below. If their angles of depression are 30° and 45° and the distance between them is 222m, find the height of the cliff.    (5)

10) AB is a fixed line. Write about the locus of the point P so that AB²= AP²+ BP².   (2)

11) The base of a triangle is 2cm greater than twice its altitude. If the area is 12cm², calculate the base and the altitude.     (4)

12) In the given figure, calculate:

a) angle APB

b) angle AOB.        (3)

13) The midpoint of the line joining A(2, p) and B(q, 4) is (3, 5). Find the numerical values of p and q.     (3)

14) From the following table, find:

a) average wage of a worker. Give your answer, to the nearest paise.

b) model class.     (4)

Wages inRs.      No of Workers 

Less than 10         15 

Less than 20         35 

Less than 30         60 

Less than 40         80

Less than 50         90

Less than 60         127 

Less than 70         190

Less than 80         200

 

15) Examine the ogive given below which shows the marks obtained out of 100 by a set of students in an examination and answer the following questions:

a) How many students are there in the set ?

b) How many students obtained 40% marks ?

c) How many students obtained 90% and above ?

d) What is the medium marks ?     (4)

16) Prove that √{(1+ cosx)/(1- cosx)= cosecx + cotx.       (3)

RAW- 1 (X) ICSE

1) Find the rate of GST levied on a car that was sold at a price three times its marked price.         (3)

2) When 7x² - 3 x + 8 is divided by (x-4), find the remainder (using remainder theorem).  (2)

3) If  2 cos x= 2/5, without using table, find sinx.      (2)

4) Calculate the length of the tangent drawn to a circle of diameter 8 cm from a point 5 cm away from the centre of the circle.     (2)

5) If x², 4 and 9 are in continued proportion, find the value of x.    (2)

6) If x ∈ Z, find the solution set for the inequation 5 < 2x -3≤ 14 and graph the solution on a number line.       (3)

7) Find p and q if g(x)= x +2 is a factor of f(x)= x³ - px + x+ q and f(2)= 4.     (3)

8) Given X= 1    -2 & Y= 0

                     -3    4          1

a) Find a matrix Z such that X + Z is a zero matrix.

b) Find the matrix M such that X + M = X.

c) Find XY.                 (3)

9) a) If 7 is the mean of 5, 3, 0.5, 4.5, b, 8.5, 9.5, find b.

b) If each observation is decreased in value by 1 unit, what would be the new mean be ?    (3)

10) In the figure below, AB is a chord of the circle with centre O and BT is standing to the circle at B.

If angle AOB= 32°, find the value of x and y.    (3)

11)  Construct a rectangular Pentagon of side 3cm. Draw the lines of symmetry.   (3)

12) The volume of a cylinder 14cm long is equal to that of a cube having an age 11 cm. Calculate the radius of the cylinder.     (4)

13) A piece of butter 3 cm by 5cm by 12cm is placed in a hemispherical bowl of radius 3.25cm. Will the butter overflow when it melts completely ?      (4)

14) A company with 10000 shares of Rs50 each, declares an annual dividend of 5%. 

i) What is the total amount of dividend paid by the company ?

ii) What would be the annual income of a man who has 72 shares in the company ?

iii) If he receives only 4% on his investment, find the price he paid for each share.    (5)

15)i) State the equation of the mirror line, if point A(5,0) on reflection is mapped as A'(-5,0).

ii) State the equation of the mirror line, if point B(4,-3) on reflection is mapped as B'(4,3).

iii) Point C(-3,5) on reflection in y= 2 is mapped as C'. Find the co-ordinates of C.  (3)

16) In a ∆ABC, angle A is obtuse, PB perpendicular to AC and QC perpendicular to AB. Prove that: AQ x AB = AP x AC.      (4)

17) Taniya standing on a vertical cliff in a jungle observes two rest houses in line with her on opposite sides deep in the jungle below. If their angles of depression are 30° and 45° and the distance between them is 222m, find the height of the cliff.    (5)

18) AB is a fixed line. Write about the locus of the point P so that AB²= AP²+ BP².   (2)

19) Find the equation of a line that passes through (1,3) and is parallel to the line y= -3x +2.    (3)

20) In the given figure, calculate:

a) angle APB

b) angle AOB.        (3)

21) The midpoint of the line joining A(2, p) and B(q, 4) is (3, 5). Find the numerical values of p and q.     (3)

22) From the following table, find:

a) average wage of a worker. Give your answer, to the nearest paise.

b) model class.     (4)

Wages inRs.      No of Workers 

Less than 10         15 

Less than 20         35 

Less than 30         60 

Less than 40         80

Less than 50         90

Less than 60         127 

Less than 70         190

Less than 80         200

 

23) Examine the ogive given below which shows the marks obtained out of 100 by a set of students in an examination and answer the following questions:

a) How many students are there in the set ?

b) How many students obtained 40% marks ?

c) How many students obtained 90% and above ?

d) What is the medium marks ?     (4)

24) Prove that √{(1+ cosx)/(1- cosx)= cosecx + cotx.       (3)

REVISION TEST (CBSCE)- X 24/25

22/9/24

SECTION & 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.

Day - 5(2/6/24)

1) In what ratio is the line joining (2, -3) and (5,6) divided by x-axis.    1:2

2) In what ratio is the line joining (2, -4) and (-3, 6) divided by x-axis.    2:3

3) Calculate the Co-ordinates of the point P which divides the line joining A(-1,3) and B(5,9) in the ratio 1:2.        (1,5)

4) The line joining the points A(-3, -10) and B(-2,6) is divided by the point P such that PB/AB = 1/5. Find the coordinate of P.    (-11/5, 14/5)

5) P is a point on the line joining A(4,3) and B(-2,6) such that 5AP/2BP. Find the coordinates of P.      (16/7,27/7)

6) In what ratio does the point P(3,3) divide the join of A (1,4) and B(7,1)?    1:2

7) In what ratio does the point (1,a) divide the join of (-1, 4) and (4,-1)? Also find the value of a.      2:3, 2

8) In what ratio does the point (a,6) divide the join of (-4,3) and (2,8)? Also find the value of a.    3:2, -2/5

9) In what ratio is the join of (4,3) and (2, -6) divided by x-axt. Also find the Co-ordinates of the point intersection.    1:2, (10/3,0)

10) Find the ratio in which the join of (-4,7) and (3,0) divided by y-axis. Also find the coordinates of the point of intersection.     4:3, (0,3)

11) Points A, B, C and D divide the line segment joining the point (5, -10) and origin in five equal parts. Find the coordinates of A, B , C and D.    (4,-8), (3,-6),(2,-4),(1,-2)

12) Find the Co-ordinates of the points of trisection of the line joining the points (-3,0) and (6,6).         (0,2),(3,4)

13) Show that the line segment joining the point (-5,8) and (10,-4) is trisected by coordinate axes.          

14) Show that A(3,-2) is a point of trisection of the line segment joining the point (2,1) and (5,-8).     

 Also, find the coordinates of other point of trisection .     (4,-5)

15) Given , two fixed points A(0,10) and B(-30 ,0). Calculate the coordinates of a point P which lies in the AB such that:

a) 2AP 3PB.      

b) 3AP = AB

c) 7PB = AB

16) Given two fixed points P(-3,4) and Q(5,-2). Calculate the coordinates of points A and B in PQ such that:

5PA= 3PQ and 3PB = 2PQ.     

17) The line segment joining A(2,3) and B(6,5) is  intersected by x-axis at point K. Write down the ordinate of K. Hence, find the ratio in which K divides AB.      

18) The line segment joining the points M(5,7) and N(-3,2) is interesting by y-axis at point L. Write down the absicca of L. Hence, find the ratio in which L divides MN.     

Also the Co-ordinates of L.

19) Calculate the coordinates of points which devide the join of (8, 6) and (2,.3) into 4 equal parts.     (13/2,21/4),(5,9/2) and (7/2,15/4)

20) A(2,5), B(-1,2) and C(5,8) are the coordinates of the vertices of the triangle ABC. Points P and Q lie on AB and AC respectively, such that :

AP: PB = AQ : QC= 1:2.

a) calculate the Co-ordinates of P and Q.        (1,4)

b) Show that PQ= (1/3)BC

21) A(-3,4) B(3,-1) and C(-2,4) are the vertices of a triangle ABC. Find the length of line segment AP, where point P lies in side BC, such that BP: PC = 2:3.

Day- 4 (17/5/24)

1) 2x²+ 3x-20= 0

2) 4x² - 12x + 9= 0.

3) 3x² -8x + 2= 0.

4) 2x + 2/x +5= 0

5) x + 96/x = 22.

6) x(2x +5) -3= 0

7) x(3x + 1/2) - 6 = 0

8) 3x(3x - 8)+ 16= 0

9) 4(x +2)(x +1)= 15.

10) One root of x² - 3x - c= 0 is -2, find the value of c and the other root.

11) One root of 2x²- 3(5x + c)= 0 is 3/2, find the value of c and other root.

Solve the following equations using formula 

Give your answer correct to 2 decimal places.

1) x²+ 4x + 2 = 0.

2) 5x²- 3x- 7= 0.

3) x - 10/x = -7.

4) 2x + 5 = 9/x.

5) 3x(2x -7)= 4.

6) 2(x -1)(x -5)= 5.

7) 5(x +1)²+ 10(x +1)+ 3= 0.

8) (x -1)² -6(x -1)= 11.

9) Find the values of k for which the given equation has real and equal roots:

a) 12x²+ 4kx +3= 0.

b) kx² - 2 √5 x + 4= 0.

c) 4x²- 3kx + 1 = 0.

d) (k+1) x² - 2(k -1)x + 1 = 0.

10) Find the values of k for which the given equation has real roots.

a) 2x² - 5x- k = 0.

b) kx²+ 6x +1 = 0.

Day - 3 (12/5/24)

Type -1

1) 2x²+ 2= 5x.  

2) x²+ 9x - 52= 0

3) 6x²+ 5x - 4= 0.

4) 3x²+ 14x +8= 0

5) 7x²= 8 - 10x.

6) x(x +1)+ (x +2)(x +3)= 42.

7) 6x(3x -7)= 7(7- 3x).

8) 3(x²- 4)= 5x.

9) √3 x²+ 10x + 7 √3 = 0.

10) x²+ 2 √2 x - 6= 0

Type - 2

1) (x +3)/(x +2)= (3x -7)/(2x -3).

2) (x +2)/(x +3)= (2x -3)/(3x -7).

3) (5x +1)/(7x +5)= (3x +1)/(7x +1).

4) (3x -7)/(2x -5)= (x +1)/(x -1).

5) (x +1)/(x - 2)+ (x +11)/(x +3)= 4.

6) x/(x +1)+ (x +1)/x = 34/15, x≠ 0, x≠ -1

7) 6/(x +1 )+ 5/(2x +1)= 3

8) 4/(x -1)- 5/(x +2)= 3/x.

9) 5/(x -2)- 4/x = 3//(x +6).

10) (x +2)/6 - 1/(x +2)= 1/6.

11) x⁴- 10x² + 9= 0

12) x⁴- 25x² + 25= 0

13) 11/(5x -4) - 10/(4 - 5x)= 1

Type -3

1) Find the value of p in the following:

a) If (k+2)= 0 and 4k²+ kp²+ 82= 0.

b) If (2k -1)= 0 and k²+ 8kp²+ 2p= 0.

Type - 4

For each of the following solution set, find the quadric equation:

a) x= 2,3

b) x= 3, -4

c) x = 2, 2

d) x= 1/2, 1/3

Miscellaneous 

1) Solve: x - 10/x = 9, if x= (a, b), then find 

a) a+ b 

b) ab

2) Find solution set of 2x² - 5 x - 3= 0, where x= (α, β). if the above quadratic equation is identical equal to ac²+ bx + c= 0, find a, b and c. Hence show that 

a) α+ β = -b/a

b) α β = c/a

3) Find the solution set of 2x - 5/x = 3, x= (α, β). If the above quadratic equation is identical equal to ax² + bx + c= 0, find a, b and c. Hence show that

a) α + β = -b/a 

b) α β = c/a

Day -2 7/5/24

1) 4 sin²60° + 3 tan²30° - 8 sin45° cos45°

2) 4 sin45° cos45° - sin²30° + tan²60°

3) 4/tan²60° + 1/cos²30° -  sin²45°.

4) 4 cos²60° + 4 tan²45° - sin²30° 

5) (cos90° + sinn²30° - sin45°)(sin0° + cos60°sin45°)

6) (sin90° + sin²45° cos45° - tan30°)(4sin²30° + cos60° + 1/tan60°)

7) Given cosA = 1/3, A is an acute angle, find tan²A.

8) Given 7 tanA = 24, A is an acute angle, find tan²A.

9) Given 5 tanA = 4, find the value of (5 sinA - 3 cosA)/(5sinA + 2 cosA)

10) Given 5 sinA = 3, A is an acute angle, find (cosA - 1/tanA)/2/tanA.

Day -1 5/5/24

1) If 2 cosx = 3/5, find the value of tanx + sin²x.    (2)

2) Solve graphically: 2x + 3y = -5; 2y + 3x = 0.     (3)

3) The midpoint of the line joining A(2, p) and B(q, 4) is (3,5). Find the numerical value of p and q.     (1)

4) Find the value of 3 cos45 cosec30+ 2 cos60 cosec 30.   (2)

5) Show 1/(sinx + cosx) + 1/(sinx - cosx)= 2 sinx/(2sin²x -1).    (3)

6) P(2,4), Q(3,3) and R(7,5) are the vertices of a ∆PQR. Find 

a) The coordinates of the centroid G of ∆PQR.       (2)

7) Solve: x/(x +1) + (x +1)/x = 34/15.      (2)

REVISION TEST MATHS -(W.B) 24/25

21/8/24

(The Answers of the questions 1, 2, 3 are to be written at the beginning of the answer scripts mentioning the question numbers in the serial order. Necessary calculation and drawing must be given on the right and side by the drawing margins on the first few pages on answer script. Table and calculator for any type are not allowed. Approximate value of π may be taken 22/7, if necessary . Graph paper will be supplied, if required. Arithmatic problems may be solved by algebraic method)

__________________________________

1) Choose the correct answer:     1x6 = 6

i) if the ratio of the principle and yearly amount be in the ratio 25:28, then the yearly rate of interest is 

a) 3%  b) 12%  c) 75/7%  d) 8%    

ii) 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  

iii) The number of common Tangents of two circles when they do not touch or intersect each other Is-

a) 2 b) 1 c) 3 d) 4   

iv) if sinx = cosx then the value of 2x will be 

a) 30° b) 60° c) 45° d) 90°.     

v) If  each of radius of the base and height of a cone be doubled , then the volume it will be--

a) three times  b) four times c) six times d) eight times     

vi) The medians of the number 2, 8, 2, 3, 8, 5, 9, 5, 6 is

a) 8  b) 6.5  c) 5.5 d) 5.   

2) Fill in the blanks(any five ):     1x 5= 5

i) At same rate percent per annum, the simple interest and compound interest of same principal are same in _____year.     

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

iii) if the length of the sides of two triangles are in the proportion, then two triangles are _____.       

iv) if cos²x - sin²x = 1/x  (x > 1), then cos⁴x - sin⁴x= ____.     

v) The numbers of plane surface of a solid hemisphere are____.        

vi) if the mean of x₁ , x₂ , x₃ ,.....xₙ be bar x, then the mean of kx₁ , kx₂, kx₃,....kxₙ is ____(k≠ 0).      

3) Write true or false( any five):    1x5= 5

i) A starts a business with Rs10000 and B gives Rs20000 after 6 months. At the end of the year their profit be equal.     

ii) If x= 2+√3, the value of x+ 1/x is 2√3.      

iii) If two circles of radius 7cm and 3cm touch each other externally, then the distance between the centres will be 4cm.      

iv) If 0°< xx < 90°, then sinx > sin²x.     

v) If the total surface area of a hemisphere be 36π sq.cm, then its radius will be 3cm.   

vi) If the perpendicular drawn on x-axis from the point of intersection of both ogives, the abscissa of the point of intersection of this perpendicular with the x-axis will be median.     

4) Answer the following questions (any ten): 2x10= 20

i) A sum of money is double in 8 years at r% rate of compound interest per annum. At the same rate in how many years it will be 4 times at the sum ?    

ii) A invests 3/2 times more than B invests in a business. At the end of the years B receives Rs1500 as profit. How much profit A will get at the end of that year ?    

iii) Without solving, find the values of p for which the equation x²+ (p -3)x + p= 0 has a real and equal roots.nn.  

iv) if x ∞ yz and y ∞ zx, show that z is a non zero constant.

v) The perimeter of two similar triangles are 20cm and 16cm respectively. if the length of one side of the first triangle is 9cm, then find the length of the corresponding side of second triangle.      

vi) In ∆ ABC , angle ABC=90°, AB= 5cm, BC= 12cm. Find the the length of the circumradius of ∆ abcd.      

vii) In ∆ ABC , if AB= (2a -1), AC = 2 √(2a) cm BC = (2a+1)cm, then write down the value of angle BAC.      

viii) If x= a seck and y= b tan k then find the relation between x and y free from x and y.    

ix) If tan(x +15°)=√3, find the value of sinx + cosx.    

x) the diameter of one sphere is double the diameter of another sphere . if the numerical value of total surface area of large sphere is equal to the volume of smaller sphere , then find the radius of the smaller sphere.   

xi) If the number of surfaces of a cuboid is x, the number of edges is y, the number of vertices is z and the number of diagonals is P, then find the value of x- y + z+ p.  

xii) if 11, 12, 14, x - 2, x + 4, x + 9, 32, 38, 47 are arranged in ascending order and their medians is 24, find x.   

5) Answer any one: 5

i)The difference between simple interest and compound interest for 2 years of a sum of money becomes Rs80 at 4% intrest per annum. Calculate the sum of money.  

ii) A, B, C start a business jointly investing Rs180000 in together . A gives Rs20000 more than that of B and B gives 20000 more than that of C. Distribute the profit of Rs10800 among them.      

6) Solve any one: 3

i) 1/(a+ b + x) = 1/a + 1/b + 1/x, (x≠ 0, -(a+ b)).     

ii) If 5 times of a positive whole number is less than by 3 than twice of its square, then find the number.    

7) Answer any one :   3

i) Simplify : 7/(√2+ √3)  - (√3 +1)/(2+ √3) + (√2+ 1)/(3+ 2√2).    

ii) The total expenses of a hostel partly constant and partly vary directly as the number of boarders. When the number of boarders are 120 and 100 the total expenses are Rs2000 and Rs1700 respectively. What will be the number of boarders when the total expenses is Rs1880 ?        

8) answer any one question :   3

i) if a/(b + c) = b/(c + a) = c/(a+ b), then prove that each ratio is equals to 1/2 or -1.   

ii) if (b + c - a)x = (c + a - b)y = (a+ b - c)z = 2,  then show that (1/x + 1/y)(1/y + 1/z)(1/z + 1/x)= abc.

8) answer any one question:    5

i) if in a triangle, the area of the square drawn on one side is equal to the sum of the areas of the squares drawn on other two sides, then and prove that angle opposite to the first side will be a right angle.

ii) if two tangents are drawn to a circle from a point outside it, then the line segments joining the point of contracts and the exterior point are equal.

10) answer any one question :    3

i) prove that the quadrilateral formed by the internal bisectors of the four angles of a quadrilateral is cyclic.

ii) O is the circumcentre of ∆ ABC and OD perpendicular BC; prove that angle BOD = Angle BAC.

11) Answer any one question:    5

i) Draw an equalateral triangle of side 6cm and draw the incircle of the triangle. (Only traces of construction are required)

ii) Construct a rectangle with sides 8cm and 6cm and construct a square equal in area to that of the rectangle.(only traces of constructions are required)

12) answer any two questions:    2x3= 6

i) if the measure of 3 angles of a quadrilateral are π/3, 5π/6, and 90°, then determine the fourth angle in sexagesimal and circular measure.     

ii) If (sink)/x = (cosx)/y then prove that sinx - cosx = (x - y)/√(x²+ y²).

iii) If tan 9°= a/b , then show that sec²81/(1+ cot² 81)= b²/a².

13) answer any one question:   5

i) The distance between two pillars is 150m. Height of one is thrice the other. From the midpoint of the line segment joining the foot of the pillars ,the angle of elevation of the top of the pillars are complementary to each other. Find the height of the shorter pillar.    

ii) If the angle of depression from a lighthouse of two ships situated in the same line with the lighthouse are 60° and 30° and if the nearer ship is 150m away from the light house, then find the distance of the other ship from the lighthouse.   

14) Answer any two questions:    4x2=8

i) Determine the volume of a solid right circular cone which can be made from a solid wooden cube of 4.2dcm edge by wasting minimum quantity of wood.   

ii) A hemispherical bowl with radius 9cm is completely filled with water. How many cylinderical bottles of diameter 3cm and height 4 cm can be filled up with the water in the bowl.     

iii) Area of the base of a closed cylinderical water tank is 616 sq.m and height is 21 m. Find the total surface area of the tank.   

15)i) Answer any two questions:  2x4= 8

i) If the median of the following data is. 32, find the values of x and y when the sum of the frequency is 100.

Class interval     frequency 

00-10                    10 

10-20                     x

20-30                    25

30-40                    30

40-50                     y

50-60                   10          

ii) Find the mode from the following distribution table:

Class interval       frequency 

00-05                      5

05-10                     12

10-15                     18

15-20                     28 

20-25                     17 

25-30                     12

30-35                      8     

iii) by preparing a cumulative frequency(greater than type) table from the following data, draw an ogive in a graph paper.

Class interval       frequency 

00-05                      4

05-10                     10 

10-15                     15

15-20                      8

20-25                      3

25-30                      5        

2/8/24

MULTIPLE CHOICE QUESTIONS (1 MARK)

1) If a principal becomes twice of it n years, then the rate of simple interest per annum is:

a) 5% b) 10% c) 15% c) 22% 

2) In a partnership business, the ratio of share of profit of two friends in 1/2 : 1/3, then the ratio of their principals is 

a) 2: 3  b) 3:2  c) 1:1  d) 5:3 

3) Interest on Rs a at the simple interest 10% per annum for b months is:

a) Rs ab/100  b) Rsab/120 c) Rs ab/1200  d) Rs ab/10

4) If the ratio of principle and the yearly amount be in the ratio 25: 28, then the rate of yearly rate of interest is

a) 3%  b) 12% c) 75 /7%  d) 8%

5) if the total interest becomes Rs x for any principal having the rate of simple interest of x% per annum for x years then the principle will be 

a) Rs x  b) Rs100 x c) Rs100/x d) Rs100/x²

6) The total interest of a principal in n years at the rate of simple interest of r% per annum is p/25, the principal will be

a) Rs 2p b) Rs4p c) Rsn/2 d) n/4 e) none

7) if the interest on Rs p at the rate of simple interest of r% per annum in t years is I, then

a) I= prt b) prt I= 100 x I c) prt= 100 x I d) none 

8) A principal becomes twice of its amount in 20 years at a certain rate of simple interest. At that same rate of simple interest, that principal becomes thrice of its amount in 

a) 30 years b) 35 years c) 40 years  d) 45 years 

9) A sum of Rs400 amounts to Rs480 in 4 years. What will it amount to if the rate of re

interest is increased by 2% ?

a) Rs484 b) Rs560 c) Rs512 d) none 

10) At what rate of percent per annum will Rs2304 amount to Rs2500 in 2 years at compound interest ?

a) 9/2% b) 21/4% c) 25/6% d) 13/3%

11) An amount doubles itself in 5 years with simple interest. What is the amount of interest percent per annum?

a) 10% b) 20% c) 25% d) 30%

12) Three partners shared in a business in the ratio 5:7: 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their Investments ?

a) 5:7 : 8 b) 20:49 : 64  d) 38:28 :21 d) none

13) A person deposited Rs100 in a bank and got the amount Rs121 for 2 years. The rate of compound interest is:

a) 10%  b) 20% c) 5% d) 21/2% 

14) in case of compound interest , the rate of compound interest per annum is 

a) equal b) unequal c) both equal or unequal d) none

15) in case of compound interest

a) the principal remains unchanged each year

b) principal changes in each year 

c) principal may be equal or unequal in each year

d) none 

16) The capital of three friends in a partnership business are Rs200, Rs 150, Rs 250 respectively. After sometime the ratio of their profit share will be 

a) 5:3:4 b) 4:3:5 c) 3:5:4 d) 5:4:3

17) Surendra and Naushad started business with capital Rs 1500 and Rs1000. After a year there was a loss of Rs75, then the loss of Surendra 

a) Rs 45  b) Rs30  c) Rs25  d) Rs40

18) Amal and Bimal started a business. Amal invested Rs500 for 9 months and Vimal invested some money for 6 months. They make a profit of Rs69 in a year, Bimal gets profit of Rs46. The capital of Vimal in the business is

a) Rs1500 b) Rs3000 c) Rs4500 d) Rs6000

19) Pallavi invested Rs500 for 9 months and Rajiv invested Rs600 for 5 months in a business. The ratio of their profit shares will be 

a) 3:2 b) 5:6 c) 6:5 d) 9:5

5/5/24 (DAY -1)

1) The salary of a man increases every year by 8%. 2 years ago his salary was Rs18750.

a) What was his salary last year ?

b) What is his present salary ?       (2)

2) Solve: 21x²- 8x -4= 0.      (2)

3) A largest possible circle is drawn in a rectangle with sides 24cm and 20cm. Find 

a) area of the circle.

b) area of the remaining part of the rectangle if the circle is cut off from it. (π=3.14).   (2)

4) A man borrows Rs25000 at compound interest and repays Rs33275 at the end of 3 years. Find the rate of interest per annum charged.     (3)

5) In the figure, I is the incentre of the circle. AI produce to meet the circle in D.

Calculate:

a) angle DCB

b) angle IBC

c) angle BID

d) Given angle BAC= 50° and angle ABC= 64°.      (4)

6) 

In the figure AB is a common tangent to two circles intersecting at C and D. Write down the measure of (angle ACB + angle ADB).

Justify your answer.      (3)

7) The compound interest for the third year on a certain sum is Rs726. If the simple interest on the same sum is Rs1800, find the rate and the sum.       (4)

Daily Test - XI(24/25)

28/10/24

SET THEORY (1)

1) For any Set A, (A')' is equals to 

a) A' b) A c) θ d) none

2) Let A and B be two sets in the same universal set, then, A - B=

a) A ∩B b) A' ∩B c) A ∩ B' d) none 

3) The number of subsets of a set containing n elements is

a) n b) 2ⁿ -1 c) n² d) 2ⁿ

4) For any two sets A and B, A∩( A∪ B)=

a) A B) B c) θ d) none 

5) if A={1, 3, 5}, B={2,4}, then 

a) 4 ∈ A B) {4}⊂ A c) B ⊂ A d) none 

6) The symmetric difference of A and B is 

a) (A - B) ∩ (B - A)

b) (A - B) ∪ (B - A)

c) (A ∪ B) - (A ∩ B)

d) {(A ∪B) - A} ∪ {(A ∪ B) - B}

7) The symmetric difference of A={1,2,3} and B={3, 4,5} is 

a) {1,2} b) {1,2,4,5} c) {4,3} d) {2,5, 1, 4, 3}

8) For any two sets A and B, (A - B) ∪ (B - A) =

a) (A - B) ∪ A

b) (B - A) ∪ B

c) (A ∪B) - (A ∩B)

d) (A ∪B) ∩(A ∩ B)

9) Which of the following statement is false:

a) A - B= A ∩ B'

b) A - B = A - (A ∩B)

c) A - B = A - B'

d) A - B = (A ∪B) - B

10) For any three sets A, B and C 

a) A ∩(B - C)= (A ∩B) - (A ∩C)

b) A ∩(B - C)= (A ∩B) - C

c) A ∪(B - C) = (A∪B) ∩ (A ∪C')

d) A ∪(B - C) = (A ∪ B) - (A ∪ C)

11) Let a={x: x ∈ R, x ≥ 4} and B={x ∈ R; x < 5}. Then, A ∩ B=

a) (4,5) b) (4,5) c) (4,5) d) (4,5)

12) Let U be the universal set containing 700 elements. if A and B are sub-sets of U such that n(A)= 200, n(B)= 300 and n(A∩B)= 100. Then , n (A' ∩ B')=

a) 400 b) 600 c) 300 d) none 

13) Let A and B be two sets such that n(A)= 16, n(B)= 14, n(A∪B)= 25. Then n(A∩B) is equal to 

a) 30 b) 50 c) 5 d) none

14) If A={1,2,3,4,5}, then the number of proper subsets of A is 

a) 120 b) 30 c) 31 d) 32 

15) In set builder method the null set is represented by 

a) { } b) ∅ c) {x : x ≠ x} d) {x : x=x}

16) If A and B are two disjoint sets, then n(A∪B) is equals to 

a) n(A)+ n(B)

b) n(A)+ n(B) - n(A ∩ B)

c) n(A)+ n(B)+ n(A ∩B)

d) n(A) n(B)

e) n(A) - n(B)

17) For two sets A ∪ B= A iff

a) B ⊆ A B) A ⊆ B c) A≠ B d) A= B

18) If A and B are two set such that n(A)= 70, n(B)= 60, n(A∪B)= 110 , then n(A ∩B) is equal to 

a) 240 b) 50 c) 40 d) 20

19) If A and B are two apgiven sets , then A ∩ (A∩ B)ᶜ is equals to

a) A b) B c) ∅ d) Aᶜ ∩ Bᶜ  

20) If A={x : x is a multiple of 3} and, B={x: x is a multiple of 5}, then A - B is

a) A ∩B b) A∩B' c) A' ∩B' d) (A ∩B)'

21) In the city 20% of the population travels by car, 50% travels by bus and 10% travels by both car and bus. Then, Person travelling by car or bus is 

a) 80% b) 40% c) 60% d) 70%

22) An investigator interviewed 100 students to determine the performance of three drinks; milk, coffee and tea. The investigator reported the 10 students take all the three drinks milk, coffee and tea; 20 students take milk and coffee; 25 students take milk and tea; 12 students take milk only; 5 student take coffee only and 8 students take tea only; then the number of students who did not take any of three drinks is

a) 10 b) 20 c) 25 d) 30

23) Two finite sets have m and n elements . The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second set. Then, the values of m and n are:

a) 7, 6 b) 6, 3 c) 6, 4 d) 7, 4 e) 3, 7

24) In a class of 175 students the following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70, Chemistry 40; mathematics and physics 30; mathematics and chemistry 28; physics and chemistry 23; mathematics, physics, chemistry 18. How many students have offered mathematics alone ?

a) 35 b) 48 c) 60 c) 22 d) 30

26/10/24

1)  If α , β be the roots of the equation ax²+ bx+ c= 0 and γ, δ those of the equation px²+ qx + r= 0, show that ac/pr = b²/q², if αδ = βγ .

2) If the sum of the first 2n terms of a GP is twice the sum of the reciprocals of the terms, then show that the continued product of the terms is equal to 2ⁿ.

3) How many numbers of four digits can be formed from the numbers 1,2,3, 4? Find the sum of all such numbers (digits being used once only). 24, 66660

4) If 9α=π, find the value of sinα sin2α sin3α sin4α. 3/16

5) If tan θ = (tanα - tan β)/(1- tanα tan β), then show that sin2θ = (sin2α - sin2 β)/(1- sin2α sin2β).

6) If 8R²= a²+ b²+ c² (or, cos²A+ cos²B + cos²C= 1), then show that the triangle ABC is right angled.

7) Solve: cos³ θ cos3 θ+ sin³ θsin3 θ = 1/8. nπ± π/6

8) If {m tan (x- y)}/cos²y= n tan y/cos²(x - y), show that y= (1/2)[x - tan⁻¹{n - m)/(n+ m)} tan x].

30/4/24

1) T

he rth term of an AP is n and it's nth term is r; show that its mth term is r+ n- m.

2) If the 1st term of an AP is 34 and 6th term is 48, then find 2nd, 3rd, 4th and 5th term of the AP.    36.8,39.6,42.4,45.2

3) Find the middle term (or terms) and the sum of the following arithmetic series:

3+7+11+15+....+95.       1176

4) The fifth term of an AP is 30 and its twelfth term is 65, find the sum of its 20 terms.    1150

5) The sum of n terms of an AP is 3n²+ 5n. Find the number of the term which is equal to 152.        25

6) How many terms of the series {22+ 18+ 14+ 10 +....} must be added to get the sum 64 ? Explain the double answer.    4 or 8

7) The nth term of an AP is p; show that , the sum of its first (2n -1) terms is (2n -1)p.

8) Insert 7 arithmetic mean between 1 and 41.     6,11,16,21,26,31,36

9) Find the sum of all natural number between 500 and 1000 divisible by 13.     28405

10) a,b,c,d be respectively the sums of p, q, r terms of an AP , show that, a/p (q -r)+ b/q (r - p)+ c/r (p - q)=0

TEST 

(TOTAL 62 MARKS).        Time 1:30 minutes 

(Attempt all: 1x 10)= 1)

1) There are ____ method of describing a set

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

2) If A ⊆ B, then B is called a ____ of A.

a) subset b) superset c) proper subset d) equal 

3) A relation which is reflexible, symmetric and transitive, is called an ___

a) Domain b) range c) co-domain d) equivalence 

4) Let f(x)= x² and g(x)=(3x+2) be two real functions. Then, find f/g)(x)

5) simplify: iⁿ + iⁿ⁺¹ + iⁿ⁺² + iⁿ⁺³

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

6) if x²+5=0 then x is

a) ±√5 b) 5 c) ±√5 d) none

7) If (n+2)!= 2550 (n!) then n is 

a) 4 b) 9 c) 49 d) 94

8) Which term of the AP 64,60,56,.......is 0?

a) 15th b) 16th c) 17th d) 18th

9) Which term of the GP 1/4, -1/2, 1, .....is -128?

a) 10th b) 11th c) 12th d) 13th

10) Value of sin(31π/3)

a) √3 b) 1/2 c) √3/2 d) 1

Attempt any 6: 6 x 2= 12)

11) Find the conjugate of 1/(4+ 3i).

12) (x +7)/(x+4) > 1, x ∈ R

13) solve graphically: 2y + 5> 0

14) Find the sum of 32 terms of an AP whose third term is 1 and the 6th term is -11.

15) The 5th, 8th and 11th terms of a GP are a, b c, c respectively. Show that b²= ac.

16) Prove sin(40+x) cos(10+x) - cos(40+ x) sin(10+ x)=1/2

17) Show that sin10 sin50 sin60 sin70= √3/16

Attempt any 10 : 10x 4= 40

18) In an Examination, 56% of the candidates failed in English and 48% failed in science. If 18% failed in both English and science, find the percentage of those who passed in both the subjects.

19) Let A={1,2,3,4,5} and B={1,4,5}.

Let R be a relation 'is less than ' from A to B.

a) List the elements of R

b) Find the domain, co-domain and range of R.

c) Depict the above relation by an arrow diagram.

20) Find the domain and range of f(x)= √(x²-4).

21) If ³√(x + iy)= (a + ib), show that (x/a + y/b)= 4(a²- b²).

22) In how many ways can 5 children be arranged in a line such that 

a) two of them, Ram and Shyam, are always together;

b) two of them, Ram and Shyam, are never together ?

23) How many numbers greater than a million can be formed with the digits 2,3,0,3,4,2,3?

24) Prove that: ²ⁿCₙ = {2ⁿ. (1.3.5........(2n-1))}/n!

25) Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

26) The sum of n terms of two Arithmetic progression are in the ratio (7n -5): (5n +17). Show their 6th terms are equal.

27) Find the sum of the series 0.7+ 0.77+ 0.777+......to n terms.

28) Show that √[2+ √{2+ 2 cos4x}]= 2 cosx.

29) sin(π/5) sin(2π/5) sin(3π/5) sin(4π/5)= 16

Test-1 (24/6/24)

1) Find the value of

a) sin 1755°.          

b) cot(-870).             

c) cot 660+ tan(-1050).         

2) Value sec(-1680) sin330

a) 0 b) 1 c) -1 d) none

3) Value of tan130 tan 140 

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

4) value of m² sin(π/2)- n² sin(3π/2)+ 2mn secπ.       

a) m-  b) m+ n c) (m+n)²  d) (m - n)²

5) If 6k=11π, the value of 2 cosk + 3 tank is

a) 1 b) 0 c) √3 d) 2√3

6) If cotx= cos60+ sin30, the value of cosx + cos(x - 90) is

a) 1 b) √2 c) 1/√2 d) 0

7) If 3sin²x+ 5 cos²x = 4 and π/2< x <π, value of sin2x.       

a) 0 b) 1 c) -1 d) none

8) If tanx= -4/3, find the value of sinx.  

a) 4 b) 5 c) ±5/4  d)  ±4/5

9) If sinx= -2/3 and 270< x <360, then find the value of sin(x -270) tan(360- x).     

a) 2 b) 3 c) 3/2 d)  2/3

10) If A,B,C,D are four angles of a quadrilateral, show that, sin(A+ B)+ sin(C+ D)= 0.

12) If A,B,C are the angles of a triangle, show that tan (C- A)/2= cot(A+ B/2).

13) If A+ B= 60°, show that, sin(120°- A)= cos(30° - B).

14) Find the value of tan(nπ+ π/4).          

15) If x= 100, determine the sign of the expression sinx + cosx.      

a) Positive b) negative c) both a and b d) either a or b

16) If sin(A - B)=√3/2 and sin A= 1/√2, find the least value of B.    

a) 75° b) 60° c) 30° d) 15°

17) Show that: tan1+ tan2 + tan3.........tan87 tan88 tan89= 1.

REVISION MATHS- XI(24/25)

Day - 3(15/6/24)

1) The diagram represents a relation from set A to set B.

Rwpresent the relation in roster form.

2) 

Write the relation denoted by the adjacent arrow diagram by listing its elements and also write the domain and range of the relation.

3) if pth, qth and rth terms of an AP are respectively a⁻¹, b⁻¹, and c⁻¹, show that, (q - r)bc + (r - p)ca + (p - q)ab = 0.

4) How many terms of the series 1/2 + 1/3 + 1/6+ ....must be taken so that the sum may be -3/2)?

5) Find the sum of 1- 3 +5 - 7 +9 -11+ .... to n terms.

6) How many even numbers are there between 15 and 115?  Find the sum of all these numbers.

7) Find the sum of all numbers between 200 and 300 which are multiples 7.

8) If (p+1)th term of an AP be a, find the sum of first (2p+1) terms of the AP.

9) If the 11th term of an AP be 25, find the sum of first 21 terms of the AP.

10) There are (2n +1) terms in an AP. Show that the ratio of the sum of odd terms and the sum of even terms is (n+1): n.

11) find the 99th term of the series 2+7+14+23+34+......

12) How many terms are there in the series 1+ 3+ 6 + 10+ 15 + 21+ ......+ 5050?

Day -2 (13/6/24)

1) The sum of four numbers in AP is 20 and sum of their squares is 120; Find the numbers.

2) The sum of 6 numbers in AP is 345 and difference between the first and the sixth is 55; find the numbers.

3) The fourth term of an AP is thrice the first term and the 7th term exceeds twice the third term by 2. Find the sum of the first 10 terms of the AP.

4) If the sum of the first n terms of an AP is 40, the common differences 2 and the last term is 13, find the value of n.

5) If A={a,b,c,d,e,f}, B={c,e,g,h} and C={a,e,m,n}, find:

a) A∪B b) B ∪C c) A ∪C d) B∩C e) C∩A f) A∩B

6) If A={1,2,3,4,5}, B={4,5,6,7,8}, C={7,8,9,10,11} and D={10,11,12,13,14}, find

a) A∪B b) B∪C c) A∪C d) B∪D e) (A∪B)∪C f) (A∪B)∩C g) (A∩B)∪D h) (A∩B)∪(B∩C) i) (A∪C)∩(C∪D)

7) If A and B are two sets such that n(A)= 27, n(B)= 35 and n(A U B)= 50, find n(A∩B).

8) If A={1,3,5} and B={2,3}, find (A x B) and (B x A). Show that (A x B) ≠ (B x A). 

9) If P={a,b,c} and Q={q}, find (P x Q) and (Q x P). Show that (P x Q) ≠ (Q x P). 

10) let A ={1,2,3} and B={2,4,6}.

Show that R={(1,2),(1,4),(3,2), (3,4)} is a relation from A to B. Find 

a) domain (R)

b) codomain(R)

c) range (R)

Depict the above relation by an arrow diagram.

11) let A={1,2,3,4,5} and B={1, 4, 5}.

Let R be a relation 'is less than' from A to B.

a) List the element of R.

b) Find the domain, co-domain and the range of R.

c) depict the above relation by an narrow diagram.

Day - 1 (10/6/24)

1) Express in the form of A+ iB, where A and B are real: (i+ i²+ i³+ i⁴)/((1+ i).   (1)

2) Express (1+ 3i)/(2- 5i) in the form of a+ ib.        (1)

3) Find the conjugate of 1/(3+ i).     (1)

4) find the modulus of (1+ 2i)/(2- i).   (1)

5) Are the numbers (2+ 3i) and (-2+ 3i) conjugate to each other ?     (1)

6) If |x + 4/i|= 5, find the value of x.  (1)

7) Find the modulus of (x + iy)/(x - iy). (2)

Day- 1

REVISION MATHS- XII(24/25)

Day -3

1) Without expanding at any stage , find the value of the determinant:

∆= 2    x      y+ z 

      2    y      z + x 

      2    z      x + y

2) If M= 1     2 

               2     3 and M² - kM - I₂= 0, then find the value of k.

3) Find dy/dx , if x= at² and y= 2at.

4) Using properties of determinants, prove 

x    x²      1+ px³

y    y²      1+ py³

z    z²      1+ pz³ =

(1+ pxyz)(x - y)(y - z) (z - x) Where p is any scalar.

5) Prove that the function f(x)= |x -1|, x∈R, is continuous at x= 1.

6) If A= 3   -2   3 & B= -1  -5   -1

              2    1  -1          -8  -6    9

              4   -3   2         -10  1    7

Evaluate. Hence, solve the system of equations, 3x - 2y + 3z= 8; 2x + y - z = 1; 4x - 3y + 2z = 4.

7) Using elementary transformation, find the inverse of the matrix 

 1     3     -2

-3     0     -1

 2     1      0

Day- 2

1) If y= (cosx - since)/(cosx + since), then find dy/dx 

2) If x = a sin2t, y= a(cos2t + log tan t) then find dy/dx.

3) If A= 1.  4     x

              z   2     y

             -3  -1   3 is a symmetric Matrix, then the value of x+ y+ z is

4) If A= 3     2

              5    -7, then find inverse of A.

5) Evaluate the determinant:

 x -1         1

 x³       x²+ x +1

6) If 2     2 = 3x      1

        2     3    4x      2 then find x

7) f(x= (since)/x  + cosx,  if x≠ 0

                2                         If x= 0

Show that it continuous at x= 2.

8) If A= 2    -3      5

             3     2      -4

             1     1      -2 then find inverse of A. 

Using the inverse of A solve the following system of equations:

2x - 3y + 5z= 11

3x + 2y - 4z= -5

x + y -2z= -3.

Day-1

A) Using properties of determinants. Prove that:

a) x²    y²     z²

    x³     y³    z³

   xyz  xyz  xyz

= xyz(x - y)(y - z)(z - x)(xy+ yz+ zx)

b) y+ z    x+ y    x

    z + x   y+ x     y = x³+ y³+ z³- 3xyz

    x+ y    z + x    z 

c)    a       b - c      c- b

      a- c      b          c- a

      a - b   b - a        c

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

d) (b+ c)²      a²       a²

        b²      (c +a)²    b²

        c²           c²    (a +b)²

= 2abc(a+ b+ c)³

B) If X is a 2x2 matrix given that 

1) A= 1     3 & B= 1     -1

          0     1          0      1 with the relation AX= B, find the matrix X.

2) If A= 1  2  3 B= 1   0   2 & C= 4   4   10

             -1 -3  2      3   4   5          4   2   14 with the relation 2A + kB= C find the value of k (given k≠ 0).

3) If A= 4    2

              1    1 find (A - 2I)(A - 3I), where I is a unit matrix.

4) Solve by matrix method: 5x - 12y = -9; 7x - 6y = -8.

C)1) f(x)= (1- cosx)/(x sinx), when x≠ 0

              = 2, When x=0

Find the value of m such that f(x) is continuous at x= 0.

2) Given f(x)= x²+4, x≤2 & €(x)= 2x, x ≤2

                      = x+6, x>2            = 4, x> 2.

Show that f(x) x €(x) is continuous at x= 2.

3) f(x)= {log(1+ax) - log(1- bx)}/x is not defined at x= 0; find the value of f(0) so that f(x) is continuous at x= 0.