# Basic Maths Class 10 Question Paper

The following Questions of Basic Maths Class 10 Question Paper are given below.

## Maths sample paper | cbse sample paper 2021-22 class 10 maths standard with solution

### Maths Sample Paper 2

1. For any two positive integers a and b, HCF (a, b) x LCM (a, b) =

(a) 1

(c) a x b

(d) a/b

(b)(a×b)/2

Ans. c

2. The sum of two numbers is 15 and the sum of their squares is 113. The numbers are :

(a) 4, 11

(b) 5, 10

(c) 6,9

(d) 7, 8

Ans. d

3. Find the area of a triangle whose vertices are, (5, 2), (4, 7) and (7,- 4):

(a) 3 sq. units

(b) 4 sq. units

(c) 2 sq. units

(d) 5 sq. units

Ans.  c

4. The zeroes of the quadratic polynomial x2 + 7x + 10 are:

(a) -2 and -5

(b) 2 and 5

(c) 2 and -5

(d) -2 and 5

Ans.  a

5. If tan A+ sec A =x, then tan A =  and 5

(a) x2-1/x

(b) x2 ×1/2x

(c) x² +1/x

(d) x2+1/2x

Ans. b

6. The HCF of 336 and 54 is 6. Their LCM is:

(b) 2924

(a) 3024

(c) 3284

(d) 3098

Ans. a

7. The lines representing the following pair of linear equations, 9x + 3y + 12 = 0 and 18x + 6y + 24 = 0

(a) Intersect at a point

(b) Are parallel

(c) Are coincident

(d) None of these

Ans.  c

8. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q e from the centre is 25 cm. The radius of the circle is :

(a) 7 cm

(b) 12 cm

(c) 15 cm

(d) 24.5 cm

Ans. a

9. If one zero of the polynomial x2 + 3x+ k is 2, then the value of k is :

(a) 10

(b) –10

(c) -5

(d) 5

Ans. b

10. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, then the values of x and y are :

(a) x= 4, y = 3

(b) x= 6, y = 3

(c) x= 5, y = 4

(d) x = 7, y = 2

Ans. b

11. A tangent PQ at a point P of a circle of adius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :

(a) 12 cm

(b) 13 cm

(c) 8.5 cm

(d) √119 cm

Ans. d

12. If the LCM of 12 and 42 is 10m + 4, then m=

(a) 50

(b) 8

(c) 1/5

(d) 1

Ans. b

13. If a and Bare the roots of the polynomial x2- 16, then alphabeta(alhpa+ Beta) =.

(a) 0

(b) 4

(c) – 4

(d) 16

Ans. a

15. The cost of fencing a circular field at the. rate of rs.24 per metre is rs.5280. The field is to be ploughed at the rate of rs.0.50 per m2. The cost of ploughing the field is : (Takeπ n =22/7)

(a) 2000

(b) 1925

(c) 1800

(d) 1850

Ans. b

16. 1+ tan 45°/ 1- tan 45° =……..

(a) sin 90°

(b) sin 30°

(c) sin 45°

(d) 0

Ans. d

17. Find the area of a triangle whose vertices  are : (2, 3), (-1, 0) and (2, 4)

(a) 11.5 sq. units

(b) 12.5 sq. units

(c) 10.5 sq. units

(d) 8 sq. units

Ans. c

18. A dice is thrown once. What is the probability of getting a number greater than 4?

(a) 1/3

(b) 1/2

(c) 2/3

(d) 3/4

Ans. a

19. For which value of k will the following pair of linear equations have no solution ? 3x +y = 1 (2k – 1) x + (k- 1) y 2k + 1

(a) -2

(b) 4

(c) 2

(d) -4

Ans. c

20. Two coins are thrown in the air. The probability of getting tail on both of them is :

(a)1/2

(b) 1/4

(d) 2

(c) 4

Ans. b

21. A chord of a circle of radius 12 cm subtends  an angle of 120° at the centre. The area of the corresponding segment of the circle is :

(a) 82.84 cm2

(b) 80.84 cm2

(c) 83.84 cm2

(d) 88.44 cm2

Ans. d

22. Which of the following can not be the probability of an event ?

(a) 2/3

(b) -1.5

(c) 15%

(d) 0.7

Ans. b

23. Find the area of the triangle formed by the points P(-1.5, 3), Q (6, -2) and R (-3, 4):

(a) 0 sq. units

(b) 2 sq. units

(c) 3 sq. units

(d) 4 sq. units

Ans. a

24. 5 tan2 A- 5 sec2 A +1 =

(a) 1

(b) -5

(c) – 4

(d) 1

Ans. c

25. Which of the following number is divisible by 11 ?

(a) 1516

(b) 1452

(c) 1011

(d) 1121

Ans. b

26. The value of p for which of the polynomial x3 + 4×2 = px + 8 is exactly divisible by (x- 2) is :

(a) 0

(b) 3

(c) 5

(d) 16

Ans. d

27. If 7 sin? + 3 cos? 0 = 4, then tan 0 =

(b) 1/2.

(a)1/√2

(c) 1/3

(d)1/√3

Ans. d

29. A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. The probability that the marble taken out will be red is

(a) 5/17

(b) 4/17

(c) 8/17

(d) 9/17

Ans. a

30. If LCM of a and 18 is 36 and HCF of a and 18 is 2, then a =

(a) 2

(b) 3

(c) 4

(d) 1

Ans. c

31. If the area of a circle is 154 cm?, then 1is circumference is :

(a) 55 cm

(b) 44 cm

(c) 11 cm

(d) 22 cm

Ans. b

32. If p(x) = ax2+ bx + c, then

(a) 0

(b) 1

(c) Sum of zeroes

(d) Product of zeroes

Ans.  d

33. If tanθ=12/5, then: (1+ sin θ)/(1- sin θ)= ……

(a) 24

(b) 12/13

(c) 25

(d) 9

Ans.  c

34. The pair of linear equations : 3/2 x + 5/3 y =7 and 9x – 10y= 14 is :

(a) Consistent

(b) Inconsistent

(c) Both (a) as well as (b)

(d) None of these

Ans. a

35. A box contains 6 blue balls, 9 black balls and 5 red balls. A ball is drawn at random from the box. The probability that it is a red ball is :

(a) 3/10

(b) 9/20

(d) 3/4

(c) 1/4

Ans. c

36. The solution of the pair of linear equations given below is : 2/√x+ 3/√y = 2 and 4/√x – 9/√y =-1

(a) x = 3; y= 7

(b) x = 4; y=9

(c) x= 2; y=5

(d) x = 6; y= 3

Ans.  b

37. If the points (1, 2), (0, 0) and (a, b) are collinear, then :

(a) a = b

(b) 2a = b

(c) a =- b

(d) a= 2b

38. (5 cos2 60° + 4 sec2 30°- tan2 45°)/ (sin2 30° + cos2 30°) =

(a) 67/ 12

(b)65/ 12

(c) 63/12

(d) 61/12

Ans. b

39. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The area of the sector formed by the arc is :

(a) 241 cm2

(b) 235 cm2

(c) 221 cm2

(d) 231 cm2

Ans. d

40. A lot of 20 bulbs contains 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective ?

(a) 2/5

(b) 4/5

(d) 1/5

(c) 3/5

Ans. c

#### Maths Sample Paper 3

1. Which of the following numbers is not irrational ?

(a) 3 + √7

(b) 3- √7

(c) (3+ √7)(3- √7)

(d)3 √7

Ans. c

2. The product of two number is 120 and the sum of their squares is 289. The sum of these numbers is :

(a) 20

(b) 23

(c) 16

(d) None of these.

Ans. b

3. Find the coordinates of the point which divides the join of the points A (-1, 7) and B(4,-3) in the ratio 2:3:

(a) (1, 3)

(c) (2, 3)

(b) (3, 1)

(d) (3, 2)

Ans. a

4. The degree of the polynomial x4-x2 + 2 is :

(b) 4

(d) 0

(a) 2

(c) 1

Ans. b

5. If sin 3A = cos (A -26°), where 3A is an acute angle, then the value of A is :

(a) 29°

(b) 26°

(c) 64°

(d) None of these.

Ans. a

6. The decimal expansion 23/ (2352 )of

(a) Terminating

(b) Non-terminating

(c) Both (a) as well as (b)

(d) None of these

Ans. a

8. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle :

(a) 7 cm

(c) 9 cm

(b) 6 cm

(d) 8 cm

Ans. d

9. If a and B are the zeroes of the quadratic polynomial x2-4x + 1, then  (1 / alpha) + (1/ beta) – (alpha.beta)

(a) 3

(c) 5

(b) -5

(d)-3

Ans. a

10. Solve 2x + 3y = 11 and 2x 4y =- 24 and hence find the value of ‘m’ for which  y = mx +3 :

(a) x= 2, y =-5; m= 1

(b) x=- 2, y = – 5; m= 2

(c) x=- 2, y = 5; m=-1

(d) 3, y= 5; m=-2

Ans. c

11. A tangent to a circle passing through a point di lying inside the circle:

(a) Intersects the circle at two points

(b) Exists

(c) Does not exist

(d) None of these

Ans. c

12. If HCF (a, b) = 12 and a x b = 1800, then what will be LCM (a, b) ?

(a) 3600

(b) 900

(c) 150

(d) 90

Ans. c

13. If the zeroes of the quadratic polynomial ax + bx +c, where c z 0 are equal, then

(a) c and a have opposite signs

(b) c and b have opposite signs

(c) c and a have the same signs

(d) c and b have the same signs

Ans. c

14. If the length of the tangent drawn from a point outside a circle at a distance of 10cm from its centre is 8cm, then the radius of that circle is :

(a) 6 cm

(c) 5 cm

(b) 7 cm

(d) 4 cm

Ans. a

15. Which of the following is equal to t ?

(b) Circumference x Diameter

(c) Circumference/Diameter

Ans. c

16.  (sin 30° + tan 45° – cosec 60°) /(sec 30° + cos 60° + cot 45°) =……

(a) (40-20√3)/11

(b) (43-24√3)/11

(c) (42+20√2)/11

(d) (42-20√2)/11

Ans.  b

17. Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9) :

(a) (-5, 0)

(c) (-4, 0)

(b) (-6, 0)

(d) (-7, 0)

Ans.  d

18. The probability of getting at least one head on tossing two coins simultaneously is:

(a) 1/2

(b) 1/3

(c) 2/3

(d) 3/4

Ans.  d

19. Half the perimeter of a rectangular garden, whose length is 4m more than its width 34m. Find the length and breadth of the garden :

(a) 20m and 15m

(c) 20m and 12m

(b) 20m and 16m

(d) 18m and 16m

Ans. b

20. The probability of getting an even number in a single throw of a dice is :

(d) 2/3

(c) 5/6

(b) 1

(a) 1/2

Ans. a

21. A chord of a circle of radius 10 cm subtends a right angle at the centre. The area of the corresponding minor segment will be :

(a) 27.5 cm2

(c) 28.5 cm2

(b) 22.5 cm2

(d) 24.5 cm2

Ans.  c

22. Two players, Sangeeta and Reshma, play tennis match. It is known that the probability of Sangeeta winning the match is 0.62. What is the probability of Reshma winning the match ?

(a) 1.62

(b) 0.5

(d) 0.38

(c) 0.8

Ans. d

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

(c) 5

(d) 7

(a) 6

(b) 8

Ans. d

24. If cos x = a/b, then sin x= …..

(a) (b2-a2)/b

(b) (b-a)/b

(c) √(b2-a2)/b

(d) √(b-a)/b

Ans. c

25. If HCF (26, 169)= 13, then LCM (26, 169)=

(a) 26

(b) 52

(c) 338

(d) 13

Ans. c

26. Find the quadratic polynomial, the sum and product of whose zeroes are √2 and 1/3 respectively:

(a) 3x2 – 3√2 x +1

(b) x2 + 3√2 x -1

(c) 3x2 – √2 x +1

(d) 3x2 + 3√2 x -1

Ans. a

27. If cos (40° +A) = sin 30°, then A .

(a) 30°

(b) 40°

(c) 60°

(d) 20°

Ans. d

28.  The perpendicular, at the point of contact, to the tangent to a circle :

(a) Does not pass through the centre of the circle

(b) Passes through the centre of the circle

(c) Both (a) as well as (b)

(d) None of these probability ?

Ans. b

30. If the HCF of 55 and 99 is expressible in the form 55m-99, then the value of m is :

(c) 1

(d) 3

(a) 4

(b) 2

Ans. b

31. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The length of the arc is :

(a) 20 cm

(b) 18 cm

(c) 22 cm

(d)24 cm

Ans. c

32.  Both the zeroes of the quadratic polynomial, x2 + kx + k, k not equal to 0:

(a) Can not be positive

(b) Can not be negative

(c) Are always unequal

(d) Are always equal

Ans. a

33.  If √3, If 3 tan θ = 3 sin θ, then: sin2 θ – cos2 0 = ….

(a) 0

(b) 1

(c) 1/2

(d) 1/3

34.  Solve the following pair of equations: 2/x+ 3/y =13 and 5/x- 4/y = – 2

(a) x = 1/2 ;y =1/3

(b) x =- 1/2 ;y =1/3

(c) x = 1/2 ;y=-1/3

(d) x=-1/2 :y=-1/ 3

Ans. a

35. A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

(a)1/4

(b)3/4

(c)1/2

(d) 2/3

Ans. b

36. The following pair of linear equations : 5x- 15y = 8 and 3x – 9y = 24/5

(a) Has a unique solution

(b) Has two solutions

(c) Has infinitely many solutions

(d) Has no solution.

Ans. c

37. If A(1, 3), B (-1, 2), C (2, 5) and D (x, 4) are the vertices of a parallelogram, then x= ……..

(a) 0

(b) 3

(c) 3/2

(d) 4

Ans. d

38. If tan 2A = cot (A – 18°), then : A=………

(d) 18°

(a) 27°

(b) 24°

(c) 36°

Ans. c

39. The area of a square inscribed in a circle of radius 8 cm will be :

(a) 64 cm2

(c) 442 cm2

(b) 128 cm2

(d) 256 cm2

Ans. b

40. One card is drawn from a well-shuffled deck of 52 cards. What is the probability of getting a spade ?

(a) 1/13

(b) 4/13

(c) 1/4

(d) 9/52

Ans. b

#### Maths Sample Paper 4

1. The decimal expansion of is: 13/3125 is

(a) Terminating

(b) Non-terminating repeating

(c) Both (a) as well as (b)

(d) None of these

Ans. a

2. Look at the equations given below: 4x + 3y = 41 x+3y = 26 The correct method of solving these equations is :

(a) 4x -x+ 3y – 3y= 41- 26

(b) 4 (x+ 3y) + 3y = 41

(c) 4x +x+ 3y- 3y 41 – 26

(d) 4x + 3y+ 3y = 41-26

Ans. a

3. Points (1, 2), (4, y), (x, 6) and (3, 5) form rhombus. The values of x and y are :

(a) (2, 3)

(b) (4, 3)

(c) (6, 3)

(d) (2, 5)

Ans. c

4. The value of the polynomial p(z)=z4-2z3+3 at z =- 1 is :

(a) 2

(b) 3

(c) 5

(d) 6

Ans. x

5. If tan A = 3/4, then the value of (4sin A – cos A) / (4 sin A + cos A) is:

(a)1/2

(b)3/4

(c)1/3

(d)2/3

Ans. a

6. LCM of 17, 23 and 29 is:

(a) 11339

(b) 12339

(c) 15339

(d) 14449

Ans. a

7. The pair of linear equations x+ 3y = 6 and 2x – 3y = 12 is :

(a) consistent

(b) Inconsistent

(c) Both (a) as well as (b)

(d) None of these

Ans.  a

8. If the angle between two radii of a circle is 110°, then the angle between the tangents at the ends of these radii is

(a) 90°

(b) 50°

(c) 70°

(d) 40°

Ans. c

9. The quadratic polynomial, the sum and product of whose zeroes are 4 and 1 respectively is :

(a) x2 + 4x – 1

(c) x2 4x-1

(b) x2 + 4x+1

(d) x2– 4x + 1

Ans. d

10. The distance between the points (2, 3) and (4, 1) is :

(b) 2√2

(a) √2

(d) 4√2

(c) 3 √2

Ans b

12. There is a circular path around a sports field. Rimpi takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point ?

(a) 37

(b) 28

(c) 36

(d) 21

Ans. c

13. The product of zeroes of the cubic polynomial ax3 + bx2 + cx +d is :

(b) c/a

(a) – b/a

(c)-d/a

(d)-c/ a

Ans. c

14. If two tangents inclined at an angle of 6o are drawn to a circle of radius 3 cm from an external point, then the length of each tangent will be:

(b) 4 cm

(a) 6 cm

(c) 3√3 cm

(d) 3 cm

Ans. c

15. Raman draws a circle of diameter 6 units Then he draws another circle with a radius four times that of the first circle. If he divides the circumference of the new circle with its diameter, then the quotient so obtained will be:

(a) Pi

(b) 2pi

(c) 8

(d) 12

Ans. a

16. sin 25° cos 65° + cos 25° sin 65°……

(a) 2

(b) 0

(c) 1

(d) 3

Ans. c

17. The points (-4, 0); (4, 0) and (0, 3) are  the vertices of a ……triangle.

(a) Right angled

(b) Isosceles

(c) Equilateral

(d) None of these

Ans.  b

18. In a lottery, there are 10 prizes and 25″ blanks. A lottery is drawn at random. What is the probability of getting a prize ?

(a) 1/10

(b) 2/5

(c)2/7

(d) 5/7

Ans. c

19. Solve the following pair of equations,  5/(X-1) + 1/(y-2)=2  And 6/(x-1) -3/(y-2)=1

(a) x=-4; y = 5

(c) x= 4:y =- 5

(b) x=4: y= 5

(d) x= -4 y=-5

Ans. b

20. One card is drawn from a well-shuffled  deck of 52 cards. The probability that the card will not be an ace is :

(b) 12/13

(a) 1/13

(d) 4/13

(c) 2/13

Ans. b

21. The length of the minute hand of a clock js 14 cm. The area swept by this hand in 5 minutes is :

(a) 158/3 cm2

(b) 154/3 cm2

(c) 150/3 cm2

(d) 152/3 cm2

Ans. b

22. It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday ?

(a) 0.008

(b) 0.08

(c) 0.004

(d) 0.006

Ans. a

23. If A and B are (-2, -2) and (2, -4), respectively, find the coordinates of P such that AP=3/7 AB and P lies on the line segment AB.

(a) (2/7,20/7)

(b) (-2/7, -20/7)

(c) (3/7, 19/7)

(d) (-3/7, -19/7)

Ans.  b

24.  sin 18°/cos 72° =…..

(a) 1

(b) 2

(c) 3

(d) 4

Ans. a

25. The LCM of two numbers is 1200. Which of the following can not be their HCF ?

(a) 600

(b) 500

(c) 400

(d) 200

Ans. b

26. Find the polynomial whose zeroes are 1, – I and I :

(a) x3 – x2 -x +1

(c) x3 +x2 + x -1

(b) x3 + x2 -x+ 1

(d) x3– x2 +x +1

Ans. a

27. If sin A = , then 8/ 17 sec A cos A + cosec A cos A= .. .

(a) 23/8

(b) 15/ 8

(c) 8/15

(d) 6/23

Ans.  a

28. Two concentric circles are of radii 5 cm and 3 cm. The length of the chord of the larger circle which touches the smaller circle is :

(a) 10 cm

(b) 8 cm

(c) 18 cm

(d) 12 cm

Ans. B

29. A child has a die whose six faces show the letters as given below : A D C D E A The die is thrown once. What is the probability of getting A ? 1

(a) 1/6

(b)1/2

(d)1/3

(c) 3/4

Ans. d

30. The product of two irrational numbers:

(a) Is always a rational number

(b) Is always an irrational number

(c) Can be a rational or an irrational number

(d) None of these

Ans. c

32. If the zeroes of the quadratic polynomial x2 + (a+1) x+ b are 2 and 3, then :

(a) a= -7; b=-1

(b) a = 5; b=-1

(c) a=2; b=-6

(d) a= 0; b=-6

Ans.  d

33. 3 sin2 20°-2 tan2 45°+3 sin2 70° =

(a) 0

(b) 1

(d) -1

(c) 2

Ans.  b

34. For what value of k will the following pair of linear equations have infinitely many  solutions : kx + 3y – (k-3)= 0 and 12x + ky –k=0

(a) 4

(b) 3

(c) 6

(d) 2

Ans. c

35. A die is thrown twice. What is the probability that 5 will come up at least once ?

(a) 11/36

(b) 25/36

(c)1/6

(d) 2/6

Ans. a 4

36. The linear pair of equations: 5x-8y+ 1 =0 3x-(24/5)y + 3/5= 0  has:

(a) A unique solution

(b) No solution

(c) Infinitely many solutions

(d) None of these

Ans.  c

37. Find the area of a triangle ABC formed by the points A(5, 2), B(4, 7) and C(7,-4):

(a) 4 square units

(b) 3 square units

(c) 2 square units

(d) 5 square units

Ans. c

38. If cos (40° + A) = sin 30°, then A =…….

(a) 60°

(b) 20°

(c) 40°

(d) 30°

Ans.  b

39. The area of a circle that can be inscribed in a square of side 8 cm is :

(a) 12 pi cm2

(b) 9 pi cm2

(c) 16 pi cm2

(d) 36 pi cm2

Ans. c

40. A piggy bank contains hundred 50p coins. fifty Rs 1 coins, twenty Rs 2 coins and ten3 Rs 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin will be a 50 p coin ?

(a)5/9

(b)6/9

(c) 8/9

(d) 7/9

Ans. a

#### Maths Sample Paper 5

1. The largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 is :

(a) 11

(b) 17

(c) 34

(d) 45

Ans. b

2. 5 pencils and 7 pens together cost rs. 50, whereas 7 pencils and 5 pens together cost rs. 46. The cost of one pencil and that of one pen is :

(a) rs.5, rs 3

(b) rs.3, rs.5

(c) rs.4, rs. 4

(d) None of these

Ans. b

3. The area of a triangle whose vertices are (2, 3), (-1,0) and (2, -4) is :

(a) 21/2 Square units

(b) 21 Square units

(c) 42 Square units

(d) None of these

Ans. a

4. Find the quadratic polynomial, the sum and product of whose zeroes are -3 and 2 respectively :

(a) x2 -3x – 2

(c) x2 – 3x + 2

(b) x2 + 3x + 2

(d) x² + 3x – 2

Ans. b

5. (1+ tan2 A) / (1+ cot2 )=…..

(a) sec2 A

(c) cot2 A

(b)-1

(d) tan2 A

Ans. d

6. The HCF of 306 and 657 is 9. Their LCM is :

(b) 22338

(a) 23338

(d) 26338

(c) 24338

Ans. b

7. Solve the following equations: x+y= 14 x-y= 4

(a) x= 5; y=9

(c) x=-5; y=-9

(d) x=-9, y=-5

(b) x=9; y=5

Ans. b

8. The number of tangents that can be drawn to a circle through a point outside it is:

(a) 1

(b) 2

(c) 3

(d) 4

Ans.  b

9. If one zero of the cubic polynomial x3+ax2+bx+c is 1, then what will be the  product of its other two zeroes ?

(a) b-a-1

(b) b-a+1

(d) a-b-1

(c) a-b+1

Ans.  b

10. If the point Q (0, 1) is equidistant from the points P (5, -3) and R(x, 6), then the value of x is :

(a) ±2

(b) ±3

(c) ±4

(d) ±5

Ans. c

11. A circle can have parallel tangents.

(a) three

(b) Four

(c) Two

(d) Infinite

Ans. c

12. The LCM of 23 x 32 and 22 x 33 is…..

(a) 23

(b) 33

(c) 23 x 33

(d) 22 x 32

Ans. c

13. The quadratic polynomial, the sum and product of whose zeroes are 1/4 and -1 respectively are :

(a) 4x2 – x – 4

(b) x2 – 4x + 1

(c) 4x2 + x+ 4

(d) x2 + 4x – 4

Ans.  a

15. Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60° :

(b) 136/7 cm2

(a) 132/7cm2

(c) 125/7cm2

(d) 122/7cm2

Ans. a

16. 9 sec2 A- 9 tan2 A =……

(b) 9

(a) 1

(d) 0

(c) 8

Ans. b

17. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2,-1):

(a) 20 square units

(b) 21 square units

(c) 22 square units

(d) 24 square units

Ans. d

18. A box contains 3 blue, 2 white, and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be red ?

(a) 3/9

(b) 5/9

(c) 4/9

(d) 2/9

Ans. c

19. The solution of the following pair of linear equations is : 6x + 3y = 6xy and 2x + 4y = 5xy

(a) x = 2; y= 3

(c) x=-1; y=-2

(b) x= 1; y=2

(d) x= 3; y=4

Ans. b

20. 12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one :

(a) 1/11

(b) 1/12

(c) 5/16

(d) 11/12

Ans. d

21. If the circumference of a circle is equal to the sum of the circumferences of two circles of diameters 36 cm and 20 cm, then its radius is :

(a) 28 cm

(b) 16 cm

(c) 56 cm

(d) 42 cm

Ans. a

22. Two dice are thrown together. The probability of getting 3 as the sum is :

(b) 1/18

(a) 1/36

(d) 3/18

(c) 2/18

Ans. b

23. A(4, 5). B (x, y), C(6, -3) and D (2,-3) are the vertices of rhombus. The value of x is:

(b) 5

(a) 2

(c) 6

(d) 8

Ans. d

24. If tan A = cot B, then, A + B= ?

(b) 90°

(a) 45°

(c) 60°

(d) 30°

Ans. b

25. The largest number that will divide 70 and 125 leaving remainders 5 and 8 is :

(a) 13

(b) 65

(c) 875

(d) 1750

Ans. a

26. If √(5/3) and -√(5/3) are the two zeroes of the polynomial 3x4+ 6x3-2x2-10x-5, then its other two zeroes are :

(a) 1, 1

(b) 1,-1

(c) -1, -1

(d) None of these

Ans. c

27. If sin A + sin2 A = 1, then cos2 A + cos4 A ……..

(a) 1

(b) 1/2

(c) 2

(d) 3

Ans.  a

28. In two concentric circles, the chord of the larger circle which touches the smaller circle is at the point of contact: ……

(a) Divided in the ratio 1: 2

(b) Bisected

(c) Divided in the ratio I: 3

(d) None of these

Ans. b

29. Five cards-the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. What is the probability that the card is the queen ?

(b)4/5

(a) 3/5

(d)1/5

(c) 2/5

Ans. d

30. The sum of two numbers is 216 and their HCF is 27. The numbers are :

(b) 154, 162

(a) 27, 189

(d) 81, 189

Ans. a

31. A chord of a circle of radius 10 cm subtends a right angle at the centre. The area of the  corresponding major sector is :

(b) 235.5 cm²

(a) 230.5 cm2

(d) 245.5 cm²

(c) 228.5 cm2

Ans. b

32. If alpha and Beta are the zeroes of the quadratie polynomial x2– 6x +k and 3alpha + 2Beta= 20, then k = …….

(a) 8

(b) -16

(c)-8

(d) 2

Ans. b

33. [cos A/ (1+sin A)] + [(1+sin A)/cos A]=……

(a) 2 sec A

(b) 2 sin A

(c) 2 cos A

(d) 2 tan A

Ans.  a

34. The pair of linear equations,  5x-8y+1= 0 and 3x-(24/5)y+(3/5)=0 has:

(a) A unique solution

(b) No solution

(c) Infinitely many solutions

(d) None of these

Ans. c

35. There are 40 students in Class X of a school of whom 25 are girls and 15 are boys. The class teacher has to select one student as a class representative. She writes the name of each student on a separate card, the cards being identical. Then she puts cards in a bag and stirs them thoroughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of a girl ?

(b) 1/2

(a) 3/8

(c) 5/8

(d) 2/3

Ans. c

36. The following pair of linear equations: 5x- 3y =11 and -10x + 6y=-22 is :

(a) Consistent

(b) Inconsistent

(c) Both (a) as well as (b)

(d) None of these

Ans. a

37. If the distance between the points A (2, -2) and B (-1, x) is 5, then x=

(a) 1

(b) -1

(c) 2

(d) -2

Ans. c

38. Cos 45° /sec 30° +cosec 30°= 3

(a) 3 √2-√6/8

(b) 3√2-6/8

(c) 4√2+7 /8

(d) 4√2-7/8

Ans.  b

39. A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. The area of the corresponding minor sector is:

(a) 22.4 cm2

(b) 20.4 cm2

(c) 28.4 cm2

(d) 32.4 cm2

Ans. b

40. A die is thrown twice. What is the probability that 5 will not come up either time ?

(a) 11/36

(b)25/ 36

(d) 29/36

(c) 5/36

Ans. b

### Maths Sample Paper 1

1. Two numbers are in the ratio 15:11.  If their HCF is 13, then the numbers are:

(b) 105, 77

(a) 75, 55

(c) 15, 11

(d) 195, 143

Ans. d

2. Find the values of x and y from the equations : x-y= 3 and x/3+y/2=5

(a) x = 6, y = 9

(b) x= 9, y= 6

(c) x= 10, y = 5

(d) None of these

Ans.  b

3. If the points (a, 0), (0, b) and (1, 1) are collinear, then :

(a) 1/a+1/b=2

(b) 1/a+1/ b= 1

(c) 1/a+1/b = 0

(d) 1/a+1/b=4

Ans. b

4. Which of the following is a factor of the polynomial p(x) = (x)3 + 4x + 5 ?

(a) (x – 1)

(c) (x -2)

(d) (x + 2)

(b) (x+1)

Ans. b

6. The HCF of 6, 72 and 120 is:

(a) 4

(b) 8

(c) 16

(d) 6

Ans. d

7. The following pair of linear equations: 3x+2y = 5 and 2x – 3y = 7 is :

(a) Consistent

(b) Inconsistent

(c) Both (a) as well as (b)

(d) None of these

Ans.  a

8. The word ‘tangent’ was introduced by..

(a) Yulak

(b) Thomas Fineke

(c) Aryabhatta

(d) None of these.

Ans. b

9. The maximum number of zeroes of a quadratic polynomial is :

(a) 1 0

(b) 2

(c) 3

(d) 4

Ans. b

10. The area of a quadrilateral whose vertices taken in order, are (- 4, -2), (-3, -5), (3, -2) and (2, 3):

(a) 20 sq. units

(c) 26 sq. units

(b) 24 sq. units

(d) 28 sq. units

Ans. d

11. A line intersecting a circle in two points is called :

(a) Tangent

(c) Both (a) as well as (b)

(b) Chord

(d) None of these

Ans. b

12. Odd number for any positive integer n will be :

(b) n+1

(c) 2n + 1

(d) 2n

(a) n

Ans. c

13. The zeroes of the quadratic polynomial x2 + 99x + 127 are :

(a) Both positive

(b) Both negative

(c) One positive and one negative

(d) Equal

Ans.  b

14. If the distance between two parallel tangents of a circle is 18 cm, then its radius is :

(a) 10 cm

(b) 9 cm

(c) 8 cm

(d) 11 cm

Ans. b

15. The area of a circle is 2464 cm2. Its radius is :

(a) 14 cm

(c) 28 cm

(b) 21 cm

(d) 35 cm

Ans. c

16. If 5 tan θ  4, then : (5 sin θ – 4 cos θ)/(5 sin 0 +4 cos 0 )

(a) 5

(d)

(b) 0

(c)

Ans.  b

17. The distance between the points (0, 5) and (- 5, 0) is :

(b) 5sq2

(c) 10

(d) 2sq5

(a) 5

Ans. b

18. If P(E) = 0.08, then the value of P(E) is

(a) 0.92

(b) 0.95

(c) 0.90

(d) 0.85

Ans. a

19. The pair of linear equations : x- 3y – 3 = 0 and 3x – 9y – 2 = 0 has :

(a) A unique solution

(b) No solution

(c) Infinitely many solutions

(d) None of these

Ans. b

20. A dice is thrown once. The probability of getting an odd number is :

(a)

(b)

(c) 3

(d) 4

Ans. a

21. The area of the sector of a circle of radius R and central angle θ° is :

(a) 180°x 2π R

(b) θ/180° × 2πR?

(d) θ/720°× 2πR2

(c) θ/360° × 2πR

Ans.  d

22. A dice is thrown once. The probability of getting a prime number is :

(a) 2/3

(c) 1/2

(d) 1/4

(b) 1/3

Ans.  c

23. The distance between the points A (a + b, a – b) and B(a-b, a-b) is :

(a) √a2 +b2

(b) a + b

(c) √2/a2 +b2

(d) √a2-b2

Ans.  c

24. sin (45° + θ) cos (45° –θ )

(b) 0

(d) 1

(a) 2 cos θ

(c) 2 sin θ

Ans.  b

25. Given that LCM (306, 657) 22338, The HCF of these numbers is :

(b) 9

(a) 7

(c) 11

(d) 14

Ans. b

26. If a and B are the zeroes of the polynomial x2 + x+ 1, then 1/alpha+ 1/beta

(b) 1

(a) 0

(c) -1

(d) None of these

Ans.  c

27. tan 48° tan 23° tan 42° tan 67° = . ..

(c) 1

(d) 1/3

(b)1/2

(a) 0

Ans. c

29. One card is drawn from a well-shuffled deck of 52 cards. The probability of getting a face card is :

(a) 1/13

(b) 2/3

(c) 3/13

(d) 4/13

Ans. a

30. If A = 2n + 13 and B = n+ 7, where n is natural number, then HCF of A and B is

(a) 2

(b) 1

(c) 3

(d) 4

Ans. c

31. The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour ?

(a) 4275

(b) 4475

(c) 4575

(d) 4375

Ans. b

32. If p(x) = ax2 + bx + c, then – b/a =…….

(a) 0

(c) Product of zeroes

(d) Sum of zeroes

(b) 1

Ans.  d

33. If sin (A + B) = 1, then the value cos (A – B) is :

(b) 1

(a) sin 2B

(c) 0

(d) None of these

Ans. c

34. Which of the following pairs of linear equations is consistent ?

(a) x + y = 5; 2x+ 2y= 10

(b) x – y = 8; 3x – 3y = 16

(C) 2x-2y-2=0; 4x-4y-5 0

(d) 2y-3x-3 = 0; 4x – 5y- 4 = 0

Ans. a

35. The probability of getting a rotten egg from a lot of 400 eggs is 0.035. The number of rotten eggs in the lot is :

(a) 21

(b) 7

(c) 28

(d) 14

Ans. c

36. The solution of the following pair of linear  equations is : and 3x + 2y = 4 8x + 5y = 9

(a) x= 2; y=3

(b) x =-2; y=5

(c) x= 3; y=2

(d) x =-5; y=2

Ans.  b

37. The distance of the point (-6, 8) from the origin is :

(a) 6

(c) 5

(b) 10

(d) 5√ 2

Ans. b

38. 1+ tan2 A/ 1+ cot2 A =

(c) cot2 A

(a) sec2 A

(d) tan2A

(b) -1

Ans. a

39. Five cards- the ten, jack, queen, king and A ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. What is the probability that the card is the queen

(a)3/5

(b) 4/5

(c)2/5

(d) 1/5

Ans. d

40. A lot consists of 144 ball pens of which 20 are defective and the others are good. You will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to you. What la the probability that you will buy it ?

(a) 5/36

(b) 31/36

(c) 6/36

(d)9/36

Ans. c

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