# CBSE Class 10 Mathematics Previous Year Question Paper Term 1 2021 JSK-1-Set-4

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SECTION A

Question numbers 1 to 20 are multiple choice questions of 1 mark each.

Select the correct option.

Question 1.

If HCF (39, 91) = 13, then LCM (39, 91) is :

1. 91
2. 273
3. 39
4. 3549

Question 2.

is a/an :

1. integer
2. rational number
3. natural number
4. irrational number

Question 3.

The line represented by 4x - 3y = 9 intersects the y-axis at :

1. (0, - 3)
2. (-3,0)

Question 4.

The point on x-axis equidistant from the points P(5, 0) and Q(- 1, 0) is :

1. (2, 0)
2. (- 2, 0)
3. (3, 0)
4. (2, 2)

Question 5.

If ΔABC and ΔPQR are similar triangles such that ∠A = 31° and ∠R = 69°, then ∠Q is:

1. 70°
2. 100°
3. 90°
4. 80°

Question 6.

1. - 1

Question 7.

The area swept by 7 cm long minute hand of a clock in 10 minutes is:

1. 77 cm2

Question 8.

The probability of getting two heads when two fair coins are tossed together, is:

1.
2. 1

Question 9.

Two positive numbers have their HCF as 12 and their product as 6336. The number of pairs possible for the numbers, is :

1. 2
2. 4

Question 10.

The pair of equations y = 2 and y = -3 has

1. one solution
2. Two solutions
3. infinitely many solutions
4. no solutions

Question 11.

In the figure given below, what value of x will make PQ || AB?

1. 2
2. 3
3. 4
4. 5

Question 12.

1. 0

Question 13.

In a single throw of a die, the probability of getting a composite number is :

Question 14.

The decimal expansion of the rational number  will terminate after

1. One decimal place
2. two decimal places
3. three decimal places
4. four decimal places

Question 15.

The pair of lines represented by the linear equations 3x + 2y = 7 and 4x + 8y - 11 = 0 are

1. perpendicular
2. parallel
3. intersecting
4. coincident

Question 16.

In an equilateral triangle with length of side p, the length of the altitude is :

Question 17.

Given that sin θ =  , tan θ is equal to :

Question 18.

A vertical pole of length 19 m casts a shadow 57 m long on the ground and at the same time a tower casts a shadow 51 m long. The a height of the tower is:

1. 171m
2. 13 m
3. 17 m
4. 117 m

Question 19.

The simplest form of  is

1. cos θ
2. sin θ
3. cot θ
4. tan θ

Question 20.

In the given figure, ∠ABC and ∠ ACB are complementary to each other and AD ⊥ BC. Then,

1. BD.CD = BC2
2. AB.BC = BC2

SECTION B

Questions no. 21 to 40 are of 1 mark each. Answer any 16 questions from Q. No. 21 - 40.

Question 21.

If one of the zeroes of a quadratic polynomial (k - 1) x2 + kx + 1 is -3, then the value of k is:

Question 22.

If the lengths of diagonals of a rhombus are 10 cm and 24 cm, then the perimeter of the rhombus is:

1. 13 cm
2. 26 cm
3. 39 cm
4. 52 cm

Question 23.

In the given figure, x expressed in terms of a, b, c, is :

Question 24.

1. 0
2. 1
3. sin θ + cos θ
4. sin θ – cos θ

Question 25.

If ‘n' is any natural number, then (12)n cannot end with the digit:

1. 2
2. 4
3. 8
4. 0

Question 26.

A wire can be bent in the form of a circle of radius 56 cm. If the same wire is bent in the form of square, then the area of the square will be:

1. 8800 cm2
2. 7744 cm2
3. 6400 cm2
4. 3520 cm2

Question 27.

The probability that a non-leap year has 53 Wednesday, is :

Question 28.

If the given figure, points A, B, C and D are concyclic and ∠CBE = 130°. Then ∠FDC is :

1. 130°
2. 80°
3. 50°
4. 30°

Question 29.
The x – coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, -5) and R(-3, 6), then the coordinates of P are :
1. (8, 16)
2. (10, 20)
3. (20, 10)
4. (16, 8)

Question 30.

If the point (x, 4) lies on a circle whose centre is at origin and radius is 5 cm, then the value of x is :

1. 0
2. ±4
3. ±5
4. ±3

Question 31.

The value of θ for which 2 sin 2θ = 1, is :

1. 15°
2. 30°
3. 45°
4. 60°

Question 32.

The number 385 can be expressed as the product of prime factors as

1. 5×11×13
2. 5×7×11
3. 5×7×13
4. 5×11×17

Question 33.

The difference between circumference and radius of a circle is 111 cm. The area of the circle is

1. 1366 cm2
2. 1386 cm2
3. 1376 cm2
4. 1396 cm2

Question 34.

From the letters of word ‘MANGO’, a letter is selected at random. The probability that the letter is a vowel, is :

1.

Question 35.

If 17x – 19y = 53 and 19x – 17y = 55, then the value of (x + y) is :

1. 1
2. -1
3. 3
4. -3

Question 36.

The ratio in which the point ( -4, 6) divides the line segment joining the points A (-6, 10) and B(3, -8) is :

1. 2:5
2. 7:2
3. 2:7
4. 5:2

Question 37.

If sin2θ + sinθ = 1, then the value of cos2θ + cos4θ is :

1. -1
2. 1
3. 0
4. 2

Question 38.

38.The decimal expression of :

1. is terminating
2. is non-terminating and non-recurring
3. is non-terminating and recurring
4. does not exist

Question 39.

If the circumference of a circle is tripled, then its area becomes:

1. three times
2. nine times
3. eight times
4. two times

Question 40.

A father is three times as old as his son. In 12 years time, he will be twice as old as his son. The sum of the present ages of the father and the son is:

1. 36 years
2. 48 years
3. 60 years
4. 42 years

SECTION C
(Case Study Based Questions)
Section C consists of 10 questions of 1 mark each. Attempt any 8 questions from Q. No. 4150.                8 × 1 = 8

(Case Study – I)

A car moves on a highway. The path it traces is given below:

Based on the above information, answer the following questions:

Question 41.

What is the shape of the curve EFG?

1. Parabola
2. Ellipse
3. Straight line
4. Circle

Question 42.

If the curve ABC is represented by the polynomial –(x2 + 4x + 3), then its zeroes are:

1. 1 and -3
2. -1 and 3
3. 1 and 3
4. -1 and -3

Question 43.

If the path traced by the car has zeroes at -1 and 2, then it is given by:

1. x2 + x + 2
2. x2 - x + 2
3. x2- x – 2
4. x2 + x – 2

Question 44.

The number of zeroes of the polynomial representing the whole curve, is:

1. 4
2. 3
3. 2
4. 1

Question 45.

The distance between C and G is:

1. 4 units
2. 6 units
3. 8 units
4. 7 units

(Case Study – II)

Shivani is an interior decorator. To design her own living room, she designed wall shelves. The graph of intersecting wall shelves is given below:
Based on the above information, answer the following questions:

Question 46.

If O is the origin, then what are the coordinates of S?

1. (-6, -4)
2. (6, 4)
3. (-6, 4)
4. (6, -4)

Question 47.

The coordinates of the mid-point of the line-segment joining D and H is:

1.
2. (3, -1)
3. (3, 1)
4.

Question 48.

The ratio in which the x-axis divides the line-segment joining the points A and C, is:

1. 2 : 3
2. 2 : 1
3. 1 : 2
4. 1 : 1

Question 49.

The distance between the points P and G is

1. 16 units
2. 3√74 units
3. 2√74 units
4. √74 units

Question 50.

The coordinates of the vertices of rectangle IJKL are:

1. I(2, 0), J(2, 6), K(8, 6), L(8, 2)
2. I(2,-2), J(2, -6), K(8, -6), L(8, -2)
3. I(-2, 0), J(-2, 6), K(-8, 6), L(-8, 2)
4. I(-2, 0), J(-2, -6), K(-8, -6), L(-8, -2)

SECTION A

Ans 1. Correct Option: B

Product of numbers = LCM×HCF

∴ 39×91=LCM×13

∴ LCM=273

Ans 2. Correct Option: D

The product of any rational number and any irrational number will always be an irrational number. Here   is irrational, hence is  an irrational number.

Ans 3. Correct Option: A

Substituting x = 0 in 4x - 3y = 9, we get y = -3, hence the point is (0,-3).

Ans 4. Correct Option: A

A point on x-axis will have coordinates (x,0).

Now let A(x,0) is equidistant from the points P(5, 0) and Q(- 1, 0), all of which lie on the x-axis, thus we can say that PA = QA and A is the midpoint.

Hence,

Ans 5. Correct Option: D

ΔABC and ΔPQR are similar triangles

Hence by c.p.c.t.

∠A = ∠P

∠B = ∠Q

∠C = ∠R

Also in ΔABC

∠A + ∠B + ∠C =180o

∴ ∠A + ∠Q + ∠R =180o

∴ ∠Q = 80o

Ans 6. Correct Option: C

Ans 7. Correct Option: D

60 mins of clock = 360o

10 mins of clock = 60o

Now for the sector,

Ans 8. Correct Option: B

Two coins are tossed, hence sample space S is

S = {HH, TT, HT, TH}, n(S)=4

A = {HH}, n(A)=1

P(A) = n(A)/n(S) = 1/4

Ans 9. Correct Option: A

Let the numbers be 12x and 12y, where x and y are co-primes.

Product of the numbers = 144xy

144xy = 6336

xy = 44

Hence two numbers can be 1 and 44, or 11 and 4.

Ans 10. Correct Option: D

The graph of y = 2 and y = -3 does not intersect, hence no solution.

Ans 11. Correct Option: A

By converse of Basic proportionality theorem,

PQ || AB if,

Ans 12. Correct Option: A

Ans 13. Correct Option: A

A die is thrown, hence sample space S is given by

S= {1, 2, 3, 4, 5, 6}, n(S) = 6

A: number is composite

A= {4,6}, n(A) = 2

P(A) = 2/6 = 1/3

Ans 14. Correct Option: C

The denominator 250 can be expressed as 2×53 (powers of 2 and 5 only), here highest power is 3, and thus decimal will terminate after 3 places.

Ans 15. Correct Option: C

For 3x + 2y = 7 and 4x + 8y = 11

3/4 ≠ 2/8

So, intersecting.

Ans 16. Correct Option: A

Let ∆ABC be equilateral, with AD altitude

Ans 17. Correct Option: C

Ans 18. Correct Option: C

Ans 19. Correct Option: D

Ans 20. Correct Option: C

∠ABC and ∠ ACB are complementary

Hence, ∠ABC + ∠ ACB = 90o

In ∆ABC

∠ABC + ∠ ACB + ∠BAC = 180o …(sum of angles of triangle)

∴ ∠BAC = 90o

So in right angled triangle BAC, a perpendicular is drawn to the hypotenuse from the 90o vertex, hence we have

SECTION B

Questions no. 21 to 40 are of 1 mark each. Answer any 16 questions from Q. No. 21 - 40.

Ans 21. Correct Option: A

(k - 1)x2 + kx + 1

One of the zeros is -3

∴ (k - 1)9 - 3k + 1 = 0

∴ 9k – 9 - 3k + 1 = 0

∴ k=4/3

Ans 22. Correct Option: D

Diagonals of rhombus bisect each other perpendicularly

Hence,

Ans 23. Correct Option: B

Ans 24. Correct Option: C

Ans 25. Correct Option: D

(12)n = (22 × 3)n

Now, to get 0 in the unit’s place, you will need 2 as well as 5 in its prime factors.

Thus (12)n cannot end with 0.

Ans 26. Correct Option: B

Circumference of circle = perimeter of square

Ans 27. Correct Option: A

A non-leap year has 52 weeks and 1 day, hence the sample space S will be

S = {M, T, W, Th, F, Sa, S}, n(A) =7

A: getting extra Wednesday

A = {W}, n(A)=1

P(A) = 1/7

Ans 28. Correct Option: C

∠ABC + ∠CBE = 180o…(linear pair)

∴ ∠ABC = 50o

∠ABC + ∠CDA = 180o…(opposite angles are supplementary)

∴ ∠CDA = 130o

∠CDA + ∠CDF = 180o…(linear pair)

Ans 29. Correct Option: D

Let the coordinates of P be (2t,t).

If P is equidistant from Q(2, -5) and R(-3, 6), hence

PQ = PR

∴ (2t- 2)2 + (t + 5)2 = (2t + 3)2 + (t - 6)2

∴ 4t2 - 8t + 4 + t2 + 10t + 25 = 4t2 + 12t + 9 + t2 - 12t + 36

∴ -8t + 4 + 10t + 25 = 9 + 36

∴ 2t = 16

∴ t = 8

∴ P(16, 8)

Ans 30. Correct Option: D

Radius of a circle is the distance between a point on its circumference and its center

Ans 31. Correct Option: A

2 sin 2θ = 1

∴ sin 2θ = 1/2

But sin 30 = 1/2

∴ 2θ = 30o

∴ θ = 15o

Ans 32. Correct Option: B

385 can be expressed as 5×7×11

Ans 33. Correct Option: B

Ans 34. Correct Option: C

S: Selecting letters of word ‘MANGO’

S = {M, A, N, G, O}, n(S) = 5

A: Selecting a vowel from letters of word ‘MANGO’

A = {A, O}, n(A) = 2

P(A) = 2/5

Ans 35. Correct Option: A

17x – 19y = 53 …(1)

19x – 17y = 55 …(2)

Eqn.(2) – eqn.(1) gives

∴ 2x + 2y = 2

∴ x + y = 1

Ans 36. Correct Option: C

Let point T(-4, 6) divides the line segment joining the points A(-6, 10) and B(3, -8) in the ratio k:1

Hence by section formula

Ans 37. Correct Option: B

sin2 θ + sin θ = 1...(1)

sin θ = 1 - sinθ

sin θ = cos2 θ

Substitute in (1)

∴ cosθ + cos2 θ = 1

Ans 38. Correct Option: B

Hence, non-terminating and non-recurring.

Ans 39. Correct Option: B
Circumference = 2𝜋r
New circumference = 2𝜋R
∴ 3 x 2𝜋r = 2𝜋R
∴ R = 3r
Area = 𝜋r2
∴ New area = 𝜋R2 = 9𝜋r2

Ans 40. Correct Option: B

Let father’s present age be x and son’s present age be y

Given,

x = 3y

After 12 years

x + 12 = 2(y + 12)

x – 2y = 12

∴ 3y – 2y = 12

∴ y = 12 and x = 36

∴ Sum = 48

SECTION C
(Case Study Based Questions)
Section C consists of 10 questions of 1 mark each. Attempt any 8 questions from Q. No. 4150.         8 × 1 = 8

(Case Study – I)

Ans 41. Correct Option: A