TEST PAPER- MATHS

TEST PAPER - 2

SECTION A(40 Marks)

Answer All questions from this Section 

Question 1.

a) Solve the following Quadratic Equation: x²- 7x +3=0

Give your answer correct to two decimal places.     (3)

b) Given A= x    3 

                     y    3

If A²= 3I , where I is the identity matrix of order 2. Find x and y.      (3)

c) Using ruler and compass construct a triangle ABC where AB= 3cm. BC= 4cm and angle ABC= 90°. Hence constructed a circle circumscribing the triangle ABC . Measure and write down the radius of the circle.     (4)

Question 2

a) Use factor theorem to factorise 6x³+ 17x²+ 4x - 12 completely.     (3)

b) Solve the following inequation and represent the solution set on the number line.

3x/5  + 2< x + 4 ≤ x/2  + 5, x ∈R.    (3)

c) Draw a Histogram for given data, using a graph paper:

Weekly wages(Rs)  no of people 

3000-4000                 4

4000-5000                 9

5000-6000                 17

6000-7000                  6

7000-8000                  7

8000-9000                  2

9000-10000                4

Estimate the mode from the graph.     (4)

Question 3

a) In the figure given below,

O is the centre of the circle and AB is a diameter.

If AC= BD and angle AOC= 72, find: angle ABC, BAD, ABD.    (3)

b) Prove that: sinA/(1+ cotA)  - cosA/(1+ tanA)= sinA - cosA.    (3)

c) In what ratio is the line joining P(5,3) and Q(-5,3) divided by the y-axis? Also find the coordinates of the point of intersection.     (4)

Question 4

a) A solid spherical ball of radius 6cm is melted and recast into 64 identical spherical marbles.

Find the radius of each marble.    (3)

b) Each of the letters of the word AUTHORISE is written on identical circular disc and put in a bag. They are will suffered. If a disc is drawn at random from the bag, what is the probability that the letter is:

 (i) a vowel 

 ii) one of the first 9 letters of the English alphabet which appears in the given word.

 iii) one of the last 9 letter of the English alphabet which appears in the given word ?  (3)

c) Mr. Bedi visit the market and buys the following articles:

Medicine costing Rs 950, GST @ 5%

A pair of shoes costing Rs 3000, GST @ 18% 

A laptop bag costing Rs 1000 with a discount of 30%, GST  @ 18%.

  i)  Calculate the total amount of GST paid 

  ii) The total bill amount including GST paid by Mr. Bedi.    (4)

SECTION B(40 Marks)

Attempt any four questions from this Section.

Question 5

a) A company with 5000 shares of nominal value Rs 120 declares an annual dividend of 15%, calculate 

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

ii) annual income of Mr. Sharma who holds 80 shares of the company.

      If the return percentage of Mr. Sharma from his shares is 10%, find the market value of each share .    (3)

b) The mean of the following data is 16, Calculate the value of f.

Marks :       5     10    15    20     25

No of boys: 3     7      f       9       6.         (3)

c) The 4th, 6th and the last term of a geometric progression are 10, 40 and 640 respectively. If the common ratio is positive, find the first terms  , common ratio and the number of terms of the series.     (4)

Question 6

a) if A= 3     0  & B= -4     2 

              5     1.           1     0 

Find A²- 2AB + B².       (3)

b) In the given figure AB= 9cm, PA= 7.5cm and PC= 5cm

Chords AD and BC intersect at P

i) prove that ∆ PAB ~ ∆ PCD

ii) Find the length of CD

iii) Find area of ∆ PAB: area of ∆ PCD.     (4)

c) From the top of a cliff, the angle of depression of the top and bottom of a tower are observed to be 45° and 60° respectively. If the height of the tower is 20m. Find 

i) the height of the cliff .

ii) the distance between the Cliff and the tower.     (4)

Question 7

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

b) Using properties of proportion find x: y. Given (x²+ 2x)/(2x +4)= (y²+ 3y)/(3y +9).  (3(

c) In the given figure TP and TQ are two tangents to the circle with centre O,

touching at A and C respectively. If angle BCQ= 55° and angle BAP= 60°, find:

Angle OBA, OBC, AOC, ATC.      (3)

Question 8

a) What must be added to the polynomials 2x³- 3x²- 8x, so that it leaves a remainder 10 when divided by 2x +1.    (3)

b) Mr. Sonu has a recurring deposit account and deposits Rs 750 per month for 2 years. If he gets Rs19125 at the time of maturity, find the rate of interest.    (3)

c) Use graph paper for this question.

Take 1cm= 1 unit on both x and y axes.

i) Plot the following points on your graph sheets:

A(-4,0), B(-3,2), C(0,4), D(4,1) and E(7,3).

ii) Reflect the points B, C, D and E on the x-axis and name them as B',C', D', E'  respectively.

iii) join the points A,B, C, D, E, E', D', C', B' and A in order.

iv) Name the closed figure formed.      (4)

Question 9

a) 40 students enter for a game of shot-put competition. The distance thrown (in metres) is recorded below:

Distance (in m)  no of students 

12-13                     3

13-14                     9

14-15                    12

15-16                     9

16-17                     4

17-18                     2

18-19                      1

Use graph paper to draw on Ogive for the above distribution.

Use a scale of 2cm = 1m on one axis and 2cm= 5 students on the other axis.

Hence using your graph find:

i) the median 

ii) Upper quartile

iii) Number of students who cover a distance which is above 33/2 m.   (6)

b) If x= {√(2a +1) + √(2a -1)}/{√(2a +1) - √(2a -1)} , prove that x²- 4ax +1=0.   (4)

Question 10

a) if the 6th term of an AP is equals 4 times its first term and the sum of first six terms is 75, find the first term and the common difference.   (3)

b) The difference of two natural numbers is 7 and their product is 450. Find the numbers.    (3)

c) Use ruler and compass for this question. Construct a circle of radius 4.5cm.  (4)

Question 11.

a) A model of a high rise building is made to a scale of 1:50.

i) If the height of the model is 0.8m, find the height of the actual building.

ii) if the floor area of a flat in the building is 20m², find the floor area of that in the model.     (3)

b) From a solid wooden cylinder of height 28cm and diameter 6cm, two conical cavities are hollowed out.

The diameter of the cones are also 6cm and height 10.5cm.   (3) find the volume of the remaining solid prove The Identity

TEST PAPER - 1

Section - A (Attempt all questions)

Question 1:  Choose the correct answers to the question from the given options: (15)

i) A Dealer in Mumbai sold a washing machine to a consumer in Mumbai for Rs18000.  If the rate of GST is 18%, then SGST is 

a) Rs1620  b) Rs3240 c) nil  d) none 

ii) Roots of the equation 3x²- 2√6x + 2=0 are:

a) ±√(2/3) b) √(2/3), √(2/3)  c) - √(2/3) , -√(2/3) d) -√(2/3) , -√(3/2) 

iii) if x - 2 is a factor of x²- 7x + 2m, then the value of m is 

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

iv) The transpose of the matrix 

 1    5    4 

-2    1    6  is

a) 1  -2 b) -2  1  6 c) 1  -2 d) 4  5  1 

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

    -2   6                      4   6

v) 21% Rs 100 shares at Rs 140 gives rate of return as:

a) 10%  b) 120% c) 15%  d) 25% 

vi) The Reflection of the point P(0,3) in the y-axis is:

a) (0,-3) b) (3,0) c) (0, 3) d) (0,0)

vii) In the figure,

all dimensions are in cm.

 The length of AD is:

a) 12cm  b) 14cm c) 16 cm d) 18 cm

viii) Richa attaches a conical attachment to one side of the coin. The radius of coin and conical attachment is same. Which of the following is the surface area of the combined solid ?

a) coin base area + coin CSA

b) coin base area + coin CSA + cone CSA 

c) total surface area of coin + total surface area cone.

d) total surface area of cone.

ix) Which term of the GP 18, 12, 8, ...., is 512/729 ?

a) 9th b) 10th c) 11th d) 12th

x) if a coin is tossed 3 times, what is the probability of getting a tail each time ?

a) 1/8 b) 1/4 c) 1/16 d) 1/6

xi) Two similar jugs have heights of 4cm and 6cm respectively. If the capacity of the smaller jug is 48 cm³, then the capacity of the larger jug is:

a) 100 cm⅔ b) 130cm³ c) 152cm³ d)  162cm²

xii) x-axis divides the line segment joining the points (2,-3) and (5,6) in the ratio.

a) 1:2  b) 2:1  c) 3:5  d) 2:3

xiii) In the given figure,

O is the centre of the circle. If Angle OAB=40°, then angle ACB is equal to 

a) 50° b) 40° c) 60° d)  70°

xiv) The sum of the first 16 terms of the AP is 10, 6, 2,.... is 

a) -320 b) 320 c) -350 d) -300

xv) Assertion (A): The median of the following: 12.5, 12, 13, 15, 11, 12, 14, 16, 10, 12, 13

Reason (R): The value of the middle most observation obtained after arranging the data in an ascending and descending order is called the medium of the data 

a) A is true, R is false 

b) A is false, R is true 

c) both A and R are true 

d) both A and R are false 

Question 2:

i) A conical tent is to accommodate 77 perso. Each person must have 16 m³ of air to breathe. Given the radius of the tent as 7m, find the height of the tent and also its curved surface area.     (4)

ii) Amit Kumar invests Rs 36000 in buying Rs100 shares at Rs20 premium. The dividend is 15% per annum. Find :

a) the number of shares he buys.

b) his yearly dividend.

c) the percentage return on his investment.      (4)

iii) The sum of three numbers in GP is 35 and their product is 1000. Find the numbers .          (4)

Question 3:

i) Pawan deposituRs 150 every month in a bank for 8 months under the recurring deposit scheme. Find the maturity value of his deposit, if the interest is calculated every month and the rate of the interest is 8% per annum.      (4)

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

iii) Use graph paper to solve this question.

a) Plot the points P(0,3), Q(3,-2) and O(0,0) .

b) Plot R, the image of Q, when reflected in the y-axis and write its coordinates.

c) What is the geometrical name of the figure PQOR ?         (5)

SECTION - B

 (Attempt any four questions from this section)

Question 4:

i) A dealer is Patna (Bihar) supplies goods worth Rs 15000 to a dealer in Sonipat (Haryana). The dealer in Sonepat supplies the same goods to a dealer in Rohtak (Haryana) at a profit of Rs3000. If the rate GST is 18%. calculate:

a)  The cost of goods to the dealer in Rohtak.

b) Net GST paid by the dealer in Sonepat .       (3)

ii) Solve the equation 4x²- 5x -3=0 and give your answer to correct to two decimal places.     (3)

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

a) the actual length of AB in km.

b) the area of the plot in km².         (4)

Question 5:

i) If A= 0  -1 B= 1  3  C= 1  0

            2   5       6  4       -3  -2

 find A(B + C).    (3)

ii) Two circles touch externally at P. a tangent touches the circles at A and B. Prove that the tangent at P bisects AB.       (3)

iii) The polynomial (px³+ 3x²-3) and (2x³- 5x +p) when divided by (x -4) leave the same reminder. Find the value of p.          (4)

Question 6:

i) Find the coordinates of the point of trisection of the line segment joining the points A(5,-3), and B( 2,-9).        (3)

ii) Prove that: cotA - tanA = (2cos²A -1)/(sinA cosA).         (3)

iii) How many terms of the AP 72, 66, 60,..... must be taken to give the sum 0 ?     (4)

Question  7:

i) The daily wages of 80 workers in a project ate given below:

Wages   No. Of workers

400-450       2

400-500       6

500-550      12

550-600      18 

600-650      24 

650-700      13 

700-750       5 

Use a graph paper to draw an ogive for the above distribution, (use a scale of 2cm = Rs50 on x-axis and 2cm= 10 workers on yaxr). Use your ogive to estimate :

a) the median wagy of the workers .

b) the lower quartile wage of workers.

c) the number of workers who earns more than Rs625 daily.      (5)

ii) A bus covers distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/hr and as such it takes two hours longer to cover the total distance. Assume the uniform speed to be x km/hr, form an equation and solve it to evaluate x.      (5)

Question 8:

i) In a lottery there are 5 prizes and 20 blanks. What is the probability getting a prize ?    (3)

ii) Construct a quadrilateral ABCD which AB= 5cm, BC= 4cm, angle B= 60°, AD= 5.5cm and D is equidistant from AB and BC.       (3)

iii) In the given figure,

PQ is a tangent to the circle at A. AB and AD are bisectors of angle CAQ and angle PAC. If Angle BAQ= 30°, show that 

a) BD is a diameter of the circle.

b) ABC is an isosceles triangle.        (4)

Question 9:

i) Solve the following inequation and graph the solution set on the number line:

-1/5 ≤ 3x/10 +1 < 2/5, x ∈ R.       (3)

ii) Calculate the mean of the following distribution using step deviation method.

Marks    no.of students 

00-10       10

10-20        9

20-30       25

30-40       30

40-50       16

50-60       10        (3)

iii) In the figure,

ABCD is a parallelogram. P is a point on BC such that BP: PC= 1:2. DP produced meets produced at Q. Given ar(∆CPQ) is 20 m², find 

a) ar(∆ DCP)

b) ar(|| gm ABCD).           (4)

Question 10:

i) using properties of proportion, solve for x. Given that x is positive:

{2x + √(4x²-1)}/{2x - √(4x²-1)}= 4.      (3)

ii) Draw a circle with centre O and radius 3.1cm.  Take a point P outside the circle at a distance of 6.2cm from its Centre. Draw two tangents to the circle from the point P.     (3)

iii) An aeroplane at an altitude of 1500 metres finds that two ships are selling towards it in the same direction. The angles of depression as observed from the aeroplane are 45° and 30° respectively. Find the distance between the two ships.     (4)

TEST PAPER(MATHS)

TEST PAPER - 1

Section - A (Attempt all questions)

Question 1:  Choose the correct answers to the question from the given options: (15)

i) A Dealer in Mumbai sold a washing machine to a consumer in Mumbai for Rs18000.  If the rate of GST is 18%, then SGST is 

a) Rs1620  b) Rs3240 c) nil  d) none 

ii) Roots of the equation 3x²- 2√6x + 2=0 are:

a) ±√(2/3) b) √(2/3), √(2/3)  c) - √(2/3) , -√(2/3) d) -√(2/3) , -√(3/2) 

iii) if x - 2 is a factor of x²- 7x + 2m, then the value of m is 

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

iv) The transpose of the matrix 

 1    5    4 

-2    1    6  is

a) 1  -2 b) -2  1  6 c) 1  -2 d) 4  5  1 

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

    -2   6                      4   6

v) 21% Rs 100 shares at Rs 140 gives rate of return as:

a) 10%  b) 120% c) 15%  d) 25% 

vi) The Reflection of the point P(0,3) in the y-axis is:

a) (0,-3) b) (3,0) c) (0, 3) d) (0,0)

vii) In the figure,

all dimensions are in cm.

 The length of AD is:

a) 12cm  b) 14cm c) 16 cm d) 18 cm

viii) Richa attaches a conical attachment to one side of the coin. The radius of coin and conical attachment is same. Which of the following is the surface area of the combined solid ?

a) coin base area + coin CSA

b) coin base area + coin CSA + cone CSA 

c) total surface area of coin + total surface area cone.

d) total surface area of cone.

ix) Which term of the GP 18, 12, 8, ...., is 512/729 ?

a) 9th b) 10th c) 11th d) 12th

x) if a coin is tossed 3 times, what is the probability of getting a tail each time ?

a) 1/8 b) 1/4 c) 1/16 d) 1/6

xi) Two similar jugs have heights of 4cm and 6cm respectively. If the capacity of the smaller jug is 48 cm³, then the capacity of the larger jug is:

a) 100 cm⅔ b) 130cm³ c) 152cm³ d)  162cm²

xii) x-axis divides the line segment joining the points (2,-3) and (5,6) in the ratio.

a) 1:2  b) 2:1  c) 3:5  d) 2:3

xiii) In the given figure,

O is the centre of the circle. If Angle OAB=40°, then angle ACB is equal to 

a) 50° b) 40° c) 60° d)  70°

xiv) The sum of the first 16 terms of the AP is 10, 6, 2,.... is 

a) -320 b) 320 c) -350 d) -300

xv) Assertion (A): The median of the following: 12.5, 12, 13, 15, 11, 12, 14, 16, 10, 12, 13

Reason (R): The value of the middle most observation obtained after arranging the data in an ascending and descending order is called the medium of the data 

a) A is true, R is false 

b) A is false, R is true 

c) both A and R are true 

d) both A and R are false 

Question 2:

i) A conical tent is to accommodate 77 perso. Each person must have 16 m³ of air to breathe. Given the radius of the tent as 7m, find the height of the tent and also its curved surface area.     (4)

ii) Amit Kumar invests Rs 36000 in buying Rs100 shares at Rs20 premium. The dividend is 15% per annum. Find :

a) the number of shares he buys.

b) his yearly dividend.

c) the percentage return on his investment.      (4)

iii) The sum of three numbers in GP is 35 and their product is 1000. Find the numbers .          (4)

Question 3:

i) Pawan deposituRs 150 every month in a bank for 8 months under the recurring deposit scheme. Find the maturity value of his deposit, if the interest is calculated every month and the rate of the interest is 8% per annum.      (4)

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

iii) Use graph paper to solve this question.

a) Plot the points P(0,3), Q(3,-2) and O(0,0) .

b) Plot R, the image of Q, when reflected in the y-axis and write its coordinates.

c) What is the geometrical name of the figure PQOR ?         (5)

SECTION - B

 (Attempt any four questions from this section)

Question 4:

i) A dealer is Patna (Bihar) supplies goods worth Rs 15000 to a dealer in Sonipat (Haryana). The dealer in Sonepat supplies the same goods to a dealer in Rohtak (Haryana) at a profit of Rs3000. If the rate GST is 18%. calculate:

a)  The cost of goods to the dealer in Rohtak.

b) Net GST paid by the dealer in Sonepat .       (3)

ii) Solve the equation 4x²- 5x -3=0 and give your answer to correct to two decimal places.     (3)

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

a) the actual length of AB in km.

b) the area of the plot in km².         (4)

Question 5:

i) If A= 0  -1 B= 1  3  C= 1  0

            2   5       6  4       -3  -2

 find A(B + C).    (3)

ii) Two circles touch externally at P. a tangent touches the circles at A and B. Prove that the tangent at P bisects AB.       (3)

iii) The polynomial (px³+ 3x²-3) and (2x³- 5x +p) when divided by (x -4) leave the same reminder. Find the value of p.          (4)

Question 6:

i) Find the coordinates of the point of trisection of the line segment joining the points A(5,-3), and B( 2,-9).        (3)

ii) Prove that: cotA - tanA = (2cos²A -1)/(sinA cosA).         (3)

iii) How many terms of the AP 72, 66, 60,..... must be taken to give the sum 0 ?     (4)

Question  7:

i) The daily wages of 80 workers in a project ate given below:

Wages   No. Of workers

400-450       2

400-500       6

500-550      12

550-600      18 

600-650      24 

650-700      13 

700-750       5 

Use a graph paper to draw an ogive for the above distribution, (use a scale of 2cm = Rs50 on x-axis and 2cm= 10 workers on yaxr). Use your ogive to estimate :

a) the median wagy of the workers .

b) the lower quartile wage of workers.

c) the number of workers who earns more than Rs625 daily.      (5)

ii) A bus covers distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/hr and as such it takes two hours longer to cover the total distance. Assume the uniform speed to be x km/hr, form an equation and solve it to evaluate x.      (5)

Question 8:

i) In a lottery there are 5 prizes and 20 blanks. What is the probability getting a prize ?    (3)

ii) Construct a quadrilateral ABCD which AB= 5cm, BC= 4cm, angle B= 60°, AD= 5.5cm and D is equidistant from AB and BC.       (3)

iii) In the given figure,

PQ is a tangent to the circle at A. AB and AD are bisectors of angle CAQ and angle PAC. If Angle BAQ= 30°, show that 

a) BD is a diameter of the circle.

b) ABC is an isosceles triangle.        (4)

Question 9:

i) Solve the following inequation and graph the solution set on the number line:

-1/5 ≤ 3x/10 +1 < 2/5, x ∈ R.       (3)

ii) Calculate the mean of the following distribution using step deviation method.

Marks    no.of students 

00-10       10

10-20        9

20-30       25

30-40       30

40-50       16

50-60       10        (3)

iii) In the figure,

ABCD is a parallelogram. P is a point on BC such that BP: PC= 1:2. DP produced meets produced at Q. Given ar(∆CPQ) is 20 m², find 

a) ar(∆ DCP)

b) ar(|| gm ABCD).           (4)

Question 10:

i) using properties of proportion, solve for x. Given that x is positive:

{2x + √(4x²-1)}/{2x - √(4x²-1)}= 4.      (3)

ii) Draw a circle with centre O and radius 3.1cm.  Take a point P outside the circle at a distance of 6.2cm from its Centre. Draw two tangents to the circle from the point P.     (3)

iii) An aeroplane at an altitude of 1500 metres finds that two ships are selling towards it in the same direction. The angles of depression as observed from the aeroplane are 45° and 30° respectively. Find the distance between the two ships.     (4)

TEST PAPER - 2

(Attempt all questions from this section)

Question 1:               (15)

i) Dividend Is always paid on.

a) the face value of share 

b) the market value of share 

c) the amount invested d) none

ii) The roots of the quadratic equation x²-5x +5=0 are

a)  real and equal

b) real and unequal 

c) rational  d) imaginary

iii) The remainder when x³- 2x²- 5x +6 is divided by x + 2 is

a)  -1 b) 1 c) 2 d) 0 

iv) For a GP with first term a, common ratio r and last term l, The n-th term from the end is :

a) lrⁿ⁻¹ b) rⁿ⁻¹/l c) lⁿ⁻¹/r d) l/ⁿ⁻¹

v) 30th term of the AP 10, 7, 4,.....is

a)  97 b) 77 c) - 77  d) -87 

vi) The reflection of the point A(4,-1) in the line x=2 is

a) ( 0,-1) b) (8,-1) c) (0,1) d) (-1,0)

vii) in the figure,

if AB || CD, then

a) ∆ AOB ~ ∆ COD 

b) ∆ AOB ~ ∆ DOC

c)  ∆ AOB ~ ∆ ODC

d) none 

viii) A shed of a workshr is of the given shape.

The volume of the air that the shed can hold is:

a) 200m³ b) 288.75cm³ c) 300m³ d) 3077.25m³

ix) If 8- x ≥ 6 - 2x, x ∈N, then the solution set is:

a) {-2,-1,0,1,....}

b) {1,2,3,....}

c) {0,1,2,3....}

d) {--1,0,1,2....}

x) A book has pages numbered from 1 to 85. What is the probability that the sum of the digits of the page number is 8, if a page is chosen at random.

a) 6/85  b) 7/85 c) 9/85  d) 8/85

xi) The order of a column matrix is of the form :

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

xii) Two vertices of ∆ ABC are (-1,4) and B(5,2) and its centroid yG(0,3). The co-ordinates of C are:

a) (4,3) b) (4,15) c) (-4,-15) d) (-15,-4)

xiii) In the given figure,

O is the centre of a circle. If the length of chord PQ is equal to the radius of the circle, then and PRQ is:

a) 15° b) 30°  c) 45°  d) 60°

xiv) In a size transformation, if the scale factor k is equal to 1, then it is:

a) an enlargement b) a reduction 

c) an identity transformation d) none 

xv) Assertion (A): Daily wages of the workers of a factory are as below :

Daily wages (in Rs)  No of workers

131-136                        5 

137-142                       27 

143-148                       20

149-154                       18 

155-160                       12 

The lower limit of the modal class of the above data is 137.

Reason (R): The observation which occurs maximum number of times is called the mode of the data. 

a) A is true, R is false 

b) A is false, R is true 

c) Both A and R are true 

d) both A and R are false 

Question -2: 

i) Anupama has a recurring deposit account in a bank for 7/2 years. if the bank pays the interest at the rate of 12% p.a. and Anupama gets Rs 3961.80 on maturity. Find the value of monthly installment.      (4)

ii) Rs8000 and Rs10000 were invested in Rs100 shares giving dividend 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 sale proceeds 

c) gain% on the whole transaction.         (4)

iii) Show: cosx/(cosecx +1) + cosx/(cosecx -1) = 2 tanx.     (4)

Question -3:

i) Find three numbers in GP whose sum is 52 and the sum of whose product in pairs is 624.      (4)

ii) A(2,-4), B(3,3) and C(-1,5) are the vertices of ∆ ABC. Find the equation of the altitude of the triangle through C.      (4)

iii) use graph paper for this question. (take 2cm=1 unit along both x and y axis). ABCD is a quadrilateral whose vertices are A(2,2), B(2,2-2), C(0,-1) and D(0,1).

a) reflect quadrilateral ABCD on the y-axis and name it as A'B'CD.

b) Write down the coordinates of A's and B '.

c) Name two points which are invariant under the above reflection.

d) Name the polygon A'B'CD.         (5)

Section - B (40 marks)

(attempt any four questions from this section)

Question 4:

i) a dealer marks a juicer-mixer for Rs2150. A customer requests the dealer to reduce the price so that he has to pay Rs2124 including GST. if the rate of GST is 18%, how much reduction is needed in the price of the juicer mixture ?      (3)

ii) Solve the following equation using quadratic formula: 6x²+ (12- 8a)x - 16a =0.    (3)

iii)  The daily profits in rupee of 100 shops in a department store are distributed us follows:

Profit (in Rs)    no.of shops

0-100                12

100-200            18

200-300            27

300-400            20

400-500            17

500-600             6

Draw a histogram of the data given above on a graph paper and estimate the mode.  (4)

Question 5:

i) If A= 3    2 & B= 14    3

            -1    1           2     4, find a matrix C such that AC= B.     (3)

ii) In ∆ PQR,

angle PQR= 90°, PQ= 24cm and QR=7 cm. Find the radius of the inscribed circle.      (3)

iii) Determine the value of k such that (x- 2) is a the factor of the polynomial x³+ kx²- 5x -6.       (4)

Question 6:

i) Find the equation the line parallel to 2x + 5y -9=0 and passing through the midpoint of the line segment joining A(2,7) and B(-4,1).      (3)

ii) The side of a triangle plot of land in a map were 6cm, 8cm and 10cm.  If the scale of the map was 1: 1000. Find the actual area of the plot in m².       (3)

iii) The 10th term of an AP is 52 and 16th term is 82. Find its general term.    (4)

Question 7:

i) Construct angle ABC=120°, where AB = BC=5cm.  Mark two points D, E which satisfy both the following conditions .

a) equidistant from BA and BC.

b) at a distance of 5cm from B, point E is on the side of reflex angle ABC. join AE and EC. Describe the figures AECD, ABD and ABE.        (5)

ii) use graph paper for the question.         (5)

 The following table shows the weight in gram of a sample of 100 potatoes taken from a large consignment.

Weight (in gm).   Frequency 

50-60                       8 

60-70                      10

70-80                      12

80-90                      16

90-100                    18

100-110                  14

110-120                  12

120-130                  10

a) calculate the cumulative frequencies .

b) draw the cumulative frequency curve and from it determine the median weight of the potatoes.

Question 8:

i) What is the probability that an ordinary year has 53 Sundays ?     (3)

ii) A spherical metallic ball of radius 3cm is melted and recast into three spherical balls . The radii of two of these balls are 2.5cm and 2cm respectively. Find the radius of the third ball.      (3)

iii) In the figure,

O is the centre of the circle and angle AOC= 100°.

Calculate angle ADC and ABC.      (4)

Question 9:

i) Solve the following inequation and represent the solution set on the number line:

-2/3 < 1 + x/3 ≤ 2/3, x ∈ R.      (3)

ii) Find the mean of the following distribution .

X: 5      6    7    8     9 

f:  3      7    5    9     1      (3)

iii) In ∆ ABC,

D is a point on bcrsuch that angle ABC= angle CAD, AB= 20cm, AD= 10cm and AC = 14cm. Find 

a) DC b) BD c) ar(∆ ADC): ar(∆ ABC).       (4)

Question 10:

i) using properties of proportion find x : y, given: 

(x²+ 2x)/(2x +4) = (y²+ 3y)/(3y +9).     (3)

ii) Construct a regular hexagon of side 2.8 cm. Inscribe a circle in it.     (3)

iii) The angle of elevate of an aeroplane from a point P on the ground is 60°. After a flight of 15 seconds , the angle of elevation changes to 30°. if the aeroplane is flying at a constant height of 1500√3 m, find the speed of the aeroplane.       (4)

TEST PAPER-3

TEST PAPER -3

SECTION - A(40) MARKS

(Attempt all questions from this section)

1) Choose the correct answers to the questions from the given options.  (15)

i) A dealer in Rohtak(Haryana) sold a table for Rs16000 to a consumer in Sonpat (Haryana). If the GST rate is 18%, then IGST is:

a) Rs1440 b) Rs2880 c) Rs3000 d) nil

ii) The roots of x²- 5x +1=0 are:

a) real and unequal  

b) real and equal 

c) imaginary  d) none 

iii) On dividing x²- 4x + m by (x -2), the remainder is  -1. The value of m is 

a) 1 b) 2 c) -2 d) 3 

iv) An identity matrix is always:

a) a square Matrix

b)  rectangular Matrix 

c) a row matrix 

d) a null matrix 

v) The sum of 1+ 3+ 7+....199 is:

a) 10000 b) 9000 c) 8000 d) 8500

vi) Which of the following points is invariant with respect to the line y=-2?

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

vii) In the figure,

the product AB is equal to :

a) c + x b) cx c) bc d) b + c

viii) A right circular cylinder of radius r and height h (h > 2r) just encloses a sphere of diameter:

a) r b) 2r c) h d) 2h

ix) if Disha invests Rs15500 on Rs100 shares at a premium of Rs25, then the number of shares she buys is:

a) 124  b) 155 c) 160 d) 180 

x) What is the probability of not picking a face card when you draw a card at random from a deck of playing cards ?

a) 3/13 b) 10/13 c) 1  d) 2/13 

xi) 12th term of the GP 4, 8, 16, 32,..... is

a) 8000 b) 8050 c) 8120 d) 8192

xii) The y-axis divides the line segment joining the points (-4,5) and (3,-7) in the ratio:

a) 2: 7  b) 3 : 7  c) 4: 3  d) 3:4 

xiii) in the figure,

if Ang ACB=50°, then angle AOB is

a) 40 b) 50 c) 60 d) 70

xiv) A replica of a cone is made. if their surface areas are in the ratio 4:25, then the ratio of the radius is:

a) 4 :25 b) 8 125 c) 2:5  d) 1:5

xv) Assertion (A) : For a data, if mean=20 and  mode= 22, then the value of median will 20.7.

Reason (R): The emperical relationship between mean, mode and median is given by:  mean = 3 median  - 2 mode

a) A is true, R is false 

b) A is false, R is true 

c) both A and R are true 

d) both A and R are false 

Question 2:

i) Shalini has a cumulative time deposit account of Rs340 per month at 6% . if she gets Rs7157 at the time of maturity, find the total time for which the account was held.   (4)

ii) A man bought 1000 shares, each of face value Rs5 at 7 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.      (4)

iii) Prove (1+ cosA)/(1- cosA)= (cosecA + cotA)².     (4)

Question 3:

i) The n-th term of a sequence is (4ⁿ + 7n). Find the sum of first n terms of this sequence.     (4)

ii) A(2,7) and (-3,5) are two given points . Find 

a) the gradient of AB 

b) the equation of AB.     (4)

iii) Use graph paper for this question.

( take 2 centimetre= 1 unit along with x and y axis)

Plot the points O(0,0), A(-4,4), B(-3,0) and C(0,-3)

a) Reflect points A and B on the y-axis and name them A' and B' respectively. Write down their coordinates.

b) Name the figure OABCB'A'.

c) State the line of symmetry of this figure.       (5)

SECTION - B(40 MARKS)

(Attempt any four questions from this section)

Question 4:

i) Three friends X, Y and Z live in Ghaziabad (U. P) X sells medicine worth Rs50000 to Y. Y sells the same medicine to Z at a profit of Rs60000. if the rate of GST is 12%, find:

a) SGST paid by Y

b) total CGST 

c) the amount paid by Z for the medicines.    (3)

ii) The scale of a model ship was 1:300

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

b) if the deck area of the model is 1 m², find the deck area of the ship.

c) If the volume of the ship is 108000000 m³, find the volume of the model.    (3)

iii) A mathematics aptitude test of 50 students were recorded as follows :

Marks      no.of students 

50-60           4

60-70           8 

70-80          14

80-90          19

90-100         5

Draw a histogram for the above data and locate the mode.    (4)

Question 5:

i) If A= 1  -3 B= 2  -1 & C= 2   0

             0   4      2    1          0   3 

Find the 2x2 matrix X such that A+ X = 2B - C.    (3)

ii) In the figure,

AP , AQ and BC are tangent to the circle. If AB = 5cm, AC= 6cm and BC= 4cm, then find the length of AP .     (3)

iii) If (2x +1) is a factor of (3k +2)x³ + (k -1), find the value of k.     (4)

Question 6:

i) Find slope of the line passing through the point (2,4) and (-2,-3).   (3)

ii) Draw two intersecting lines to include an angle of 30°. Use ruler and compasses to locate points which are equidistano from these lines and also 2cm away from their point of intersection. How many such points exist ?    (3)

iii) Which term of the AP 5, 12, 19, 26, 33.... will be 35 more than its 12th term?   (4)

Question 7:

i) The distance by road between two towns A and B is 216km and by rail it is 200km. A car travels at a speed of x km/h and the train travels at a speed which is 16 km/h faster than the car. Calculate :

a) The time taken by the car to reach town B from A, in terms of x.

b) The time taken by the train to reach town B from A in terms of x.

c) if the train takes 2 hours less than the car to reach town B, obtain an equation in x and solve it. find the speed of the train.      (5)

ii) The marks obtained by 200 students in an examination are given below:

Marks  No.of students 

0-10        5

10-20     10

20-30     11

30-40     20

40-50     27

50- 60    38

60-70     40

70-80     29

80-90      6

Draw an ogive for the above distribution. From the ogive, determine

a)  the median

b) the lower quartile.      (5)

Question 8:

i) A card is drawn at random from a well shuffled pack of playing cards. Find the probability that the card drawn is

a) a king or a Jack.

b) a non ace

c) a red card.      (3)

ii) From a solid cone of height 12cm and base radius 6cm, a cone of height 4cm has been removed. Find the total surface area of the remaining solid.     (3)

iii) In the given figure,

O is the centre of the circle.

If Angle EBC = 108° and angle AOB=92°

calculate the value of angle BDC.     (4)

Question 9:

i) Solve the following inequation and graph the solution set on the number line.

3 ≥ (x -4)/2 + x/3 ≥ 2; x ∈ R.      (3)

ii) Find the mean of the following frequency distribution:

Class   frequency 

0-100         6

100-200    9

200-300   15

300-400   12

400-500     8       (3)

iii) in the figure,

XY|| BC . If AX =3 cm, XB=1.5cm and BC= 6cm, find XY.      (4)

Question 10:

i) Using the properties of proportion, solve for x:

{√(3x) + √(2x -1)}/{√(3x) - √(2x -1)}= 5.     (3)

ii) Draw a circle of radius 3.2cm. Draw two tangents to it inclined at an angle of 45° to each other.     (3)

iii) At the foot of a mountain, the elevation of its summit is 45°. After ascending 500m, toward the mountain up an incline of 30°, the elevation change to 60°. Find the height of the mountain.     (4)

MATHS REVISION - IX

1) In case of compound interest, the rate of compound interest per annum is 

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

2) In case of compound interest 

a) The principals remains unchanged each year 

b) principal changes in each year

c) principal may be equal or unequal in each year d) none 

3) If p + q= √13 and p- q= √5 then the value of PQ is 

a) 2 b) 18 c) 9 d) 8 

4) If a + b= √5 and a - b=√3 then the value of a²+ b²

a) 8 b) 4 c) 2 d) 1 

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

a) b≠ 0 b) c≠ 0 c) a≠ 0 d) none. 

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

a) 1 b) 2 c) 3 d) none 

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

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

8) x = 2+ √3 then value of x+ 1/x 

a) 2 b) 2√3 c) 4 d) 2-√3 

9) A person goes 24m West from a place and then he goes 10m north. The distance of the person from the starting point is

a) 34m b) 17m c) 26m d) 25m 

10) Two rods of 13m length and 7m length are situated perpendicularly on the ground and the distance between their feet is 8m. The distance between their top parts is

a) 9m b) 10m c) 11m d) 12m. 

11) If sinx - cosx = 0 (0≤ x ≤ 90°) and sex + cosecx = y, then the value of y is 

a) 1 b) 2 c) √2 d) 2√2 

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

a) 1 b) 0 c) 2 d) none 

13) If cotx = 7/7.5, then cosecx is

a) 7.5/4 b) 8/17 c) 17/15 d) 15/17 

14) If 2x = secA and tanA= 2/x then the value of 2(x²- 1/x²)²= ?

a) 1/2 b) 1/4 c) 1/8 d) 1/16 

15) The value of (sin43° . cos47°+ cos43° sin47°) is 

a) 0 b) 1 c) sun4° d) cos4° 

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

a) 4/5 b) 3/5 c) 3/4 d) 5/√41 

17) If sinx = 1/√2, then sec2x =

a) 0 b) 1 c) 2 d) none 

18) The value of ( tan35/cot55 + cot78/tan12) is 

a) 0 b) 1 c) 2 d) none 

19) ABC is a triangle. Then sin{(B+ C)/2}=

a) sin(A/2) b) cos(A/2) c) sinA d) cosA 

20) 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 

21) 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 

22) 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 

23) 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 

24) 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 

25) 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 

26) 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 

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

a) (19+29)/2 b) 19 c) 21 d) none 

28) Mode is the 

a) least frequent value 

b) middle most value

c) most frequent value

d) largest value 

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

a) 4 b) 6 c) 7 d) none 

30) median of a frequency distribution can be obtained from

a) pie diagram 

b) histogram 

c) frequency polygon 

RATIONAL NUMBER

1) Every Rational number is 

a) a natural number 

b) an integer 

c) a real number

d) a whole number 

2) Decimal representation of a rational number cannot be

a) terminating 

b) non-terminating 

c) non-terminating repeating 

d) non-terminating non-repeating

3) π is an irrational number because its decimal expansion is

a) terminating 

b) non-terminating 

c) non-terminating repeating 

d) non-terminating non-repeating 

4) Every point on a number line represents

a) a unique real number 

b) a natural number 

c) a rational number

d) an irrational number 

5) Which of the following is a rational number?

a) -2/3 b) -1/√5  c) 13/√5 d) √2/3

6) Which of the following is irrational ?

a) 0.15 b) 0.1 5161616.... 

c)  0.151615161516....

d) 0.5015001500015....

7) A rational number equivalent to 3/17 is

a) 6/17  b) 6/34  c) 17/3 d) 3/34

8) A rational number between 2 and 3 is

a) 2.010010001.... b) √6 c) 5/2  d) 4 - √2 

9) Four rational numbers between 3 and 4 are 

a) 3.1, 3.2 , 3.8, 3.9 

b) 3/5, 4/5, 1, 6/5 

c) 3.1, 3.2, 4.1, 4.2

d) 13/5, 14/5, 16/5, 17/5

10) The smallest irrational number to be added to 3 + √2 to get a rational number is

a) -√ 2 b) 3 -√2  c) √2- 3  d) √3+2

11) The value of 0.3333....in the form p/q, where p and q are integers and q≠ 0 is

a) 33/100 b) 3/10 c) 1/3 d) 3/100

12) 0.322222.... Expressed in the form of p/q, where p and q are integers and q ≠0, is 

a) 8/25 b) 29/90 c) 32/99 d) 32/199

13) 0.437437437.... expressed in the form of p/q, where p and q are integers and q≠ 0, is

a) 437/9999 b) 394/999 c) 434/99  d) 437/99 

14) simplest rationalization factor of ³√40 is 

a) ³√25 b) ³√5  c) √40 d) √5

15) 2√5+ √5 is equals to 

a) 2√10  b) 10 c) 3√5 d) 3√10

16) The perimeter of the given figure is

a) 60√5  b) 12√5  c) 27√5  d) 32√5 

17) On simplification of (2√5/3  - √2/2 + 6√11)+ (√5/3 + 3√2/2 - √11), we get 

a) √5+ √2+ 5√11 

b) √5/2+ 2√2 +√11

c) √5+√2+ 6√11

d) √5+ 2√2+ 5√11

18) The product of ³√7 and √5 is 

a) ³√35 b) ⁶√35 c) ⁶√6125 d) ⁶√1225

19) The product of √18/6 and √18/3 is

a) 1 b) 1/12 c) 1/3  d) √2

20) √5 x √7 x √15 x √21 in simplification form is

a) √105 b) √210 c) 105 d) 210

21) (3+ √3)(3- √3) on simplification becomes equal to 

a) 18 b) 2√3 c) 6 d) 9 

22) The value of (3+ √5)²(3 - √5)² is 

a) 15 b) 16  c) 4 d) 14 

23) ³√250 ÷ ³√10 in simplified form is equals to

a) ³√25  b) 5 c) √5  d) ³√2500 

24) 30/(√20 + √5) is equals to 

a) 10/3√5  b) 30/√5 c) 10/√5  d) 12√5

25) 6/(√12 - √3) is equal to 

a) 1/√3 b) 2/√3  c) 2√3 d) 6√3 

Short Answer Questions 

1) Express 0.1233333..... in the form of p/q, where p and q are integers and q≠ 0.

2) Express 0.999999.... in the form of p /q, where p and q are integers and q≠ 0.

3) Arrange ³√4, √3 and ⁴√6 in descending order.

4) Find to rational numbers between -2/3 and 1/4.

5) Rationalize the denominators of (√7- √6)/(√7 + √6).

6) Two classmate Salma and Anil simplified two different expressions during the revision hour and explained to each other their simplifications. Salma explains simplification of √2/(√5+ √3) and Anil explains simplification of √28 + √98 + √147. Write both the simplification . What value does it depict ?

7) Varun was facing some difficulty in simplification and 1/(√7 - √3).  His classmate Priya gave him a clue to rationalize the denominator for simplification . Varun simplified the expression and thanked Priya for this goodwill. How did Varun Simplify 1/(√7 - √3)? What value does it indicate ? 

EXPONENTIAL