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

SECTION A

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

Select the correct option.

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. (-3,0)
4. 

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 
2. 1 
3. 
4. 

Question 7.

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

1. 77 cm2
2. 
3. 
4. 

 

Question 8.

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

1.  
2. 
3. 
4. 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. 3 
3. 4
4. 1 

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. 
2. 
3. 0
4. 

Question 13.

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

1. 
2. 
3. 
4. 

 

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 :

1. 
2. 
3. 
4. 

Question 17.

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

1. 
2. 
3. 
4. 

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
3. BD.CD= AD²
4. AB.AC = AD²

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:

1. 
2. 
3. 
4. 

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 :

1. 
2. 
3. 
4. 

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 :

1. 
2. 
3. 
4. 

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 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. 
2. 
3. 
4.  

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

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

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 =180^o

∴ ∠A + ∠Q + ∠R =180^o

∴ ∠Q = 80^o

Ans 6. Correct Option: C

 

 

60 mins of clock = 360^o

10 mins of clock = 60^o

Now for the sector,

Radius = 7cm

 

 

Two coins are tossed, hence sample space S is

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

A: getting two heads

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.