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Maths Question Paper For Class 10 2018 2019 2020 CBSE Board NCERT Books

Here we are providing CBSE Previous Year Question Papers Class 6 to 12 solved with soutions Maths Question Paper For Class 10 2018 2019 2020 CBSE Board NCERT Books class 10 Maths sample paper 2020 solved, sample paper class 10 Maths, cbse class 10 Maths question paper 2018, sample paper class 10 Maths 2019, Maths question paper for class 10, cbse previous year question papers class 10 Maths, cbse sample paper f Practice of previous year question papers and sample papers protects each and every student to score bad marks in exams.If any student of CBSE Board continuously practices last year question paper student will easily score high marks in tests. Fortunately earlier year question papers can assist the understudies with scoring great in the tests. Unraveling previous year question paper class 10 Maths is significant for understudies who will show up for Class 10 Board tests.

Class 10 Subject Maths Paper Set 2 with Solutions

SECTION A

Question numbers 1 to 10 are multiple choice questions of 1 mark each. Select the correct option.


Question 1: (Marks 1)

HCF of two numbers is 27 and their LCM is 162. If one of the number is 54, then the other number is

(a) 36

(b) 35

(c) 9

(d) 81


Answer :

(d) 81


Question 2: (Marks 1)

The cumulative frequency table is useful in determining

(a) Mean

(b) Median

(c) Mode

(d) All of these


Answer :

(b) Median


Question 3: (Marks 1)

In Fig. 1, O is the centre of circle. PQ is a chord and PT is tangent at P which makes an angle of 50° with PQ. ?POQ is

(a) 130°

(b) 90°

(c) 100°

(d) 75°

In Fig. 1, O is the centre of circle. PQ is a chord and PT is tangent at P which makes an angle


Answer :

(c) 100°


Question 4: (Marks 1)

ncert solution 10th math basic 430-2-1 question 4

(a) an integer

(b) a rational number

(c) an irrational number

(d) a whole number


Answer :

(c) an irrational no.


Question 5: (marks 1)

ncert solution 10th math basic 430-2-1 question 5


Answer :

ncert solution 10th math basic 430-2-1 answer 5


Question 6: (Marks 1)

If one zero of the polynomial


Answer :

3


Question 7: (Marks 1)

The decimal expansion of

(a) 2

(b) 4

(c) 5

(d) 1


Answer :

(c) 5


Question 8: (Marks 1)

The maximum number of zeroes a cubic polynomial can have, is

(a) 1

(b) 4

(c) 2

(d) 3


Answer :

(d) 3

Question 9: (Marks 1)

The distance of the point (–12, 5) from the origin is

(a) 12

(b) 5

(c) 13

(d) 169


Answer :

(c) 13


Question 10: (Marks 1)

If the centre of a circle is (3, 5) and end points of a diameter are (4, 7) and (2, y), then the value of y is

(a) 3

(b) –3

(c) 7

(d) 4


Answer :

(a) 3

Question numbers 11 to 15, fill in the blanks:

Question 11: (Marks 1)

The area of triangle formed with the origin and the points (4, 0) and (0, 6) is ________.

OR

The co-ordinate of the point dividing the line segment joining the points A(1, 3) and B(4, 6) in the ratio 2 : 1 is ________.


Answer :

12 sq units

OR

(3, 5)


Question 12: (Marks 1)

Value of the roots of the quadratic equation, x2 – x – 6 = 0 are ________.


Answer :

3 and –2


Question 13: (Marks 1)

If sin ?


Answer :

If sin ?


Question 14: (Marks 1)

The value of (tan2 60° + sin2 45°) is ________.


Answer :

The value of


Question 15: (Marks 1)

The corresponding sides of two similar triangles are in the ratio 3 : 4, then the ratios of the area of triangles is _________.


Answer :

9 : 16

Question numbers 16 to 20, answer the following :

Question 16: (Marks 1)

Find the value of (cos 48° – sin 42°).

OR

Evaluate: (tan 23°) × (tan 67°)


Answer :

cos 48° – cos (90 – 42°)

cos 48° – cos 48° = 0

OR

tan (90 – 67°) × tan 67°

cot 67° × tan 67°

= 1


Question 17: (Marks 1)

In figure-2 PQ and AB are two arcs of concentric circles of radii 7 cm and 3.5 cm resp., with


Answer :

In figure-2 PQ and AB are two arcs of concentric circles of radii 7 cm and 3.5 cm resp., with


Question 18: (Marks 1)

A card is drawn at random from a well shuffled deck of 52 playing cards. What is the probability of getting a black king?


Answer :

A card is drawn at random from a well shuffled deck of 52 playing cards. What is the probability


Question 19: (Marks 1)

A ladder 25 m long just reaches the top of a building 24 m high from the ground. What is the distance of the foot of ladder from the base of the building?


Answer :

A ladder 25 m long just reaches the top of a building 24 m high from the ground. What is the


Question 20: (Marks 1)

If 3k – 2, 4k – 6 and k + 2 are three consecutive terms of A.P., then find the value of k.


Answer :

(4k – 6) – (3k – 2) = (k + 2) – (4k – 6)

⇒ k = 3

SECTION B

Question numbers 21 to 26 carry 2 marks each.


Question 21: (Marks 2)

In a lottery, there are 10 prizes and 25 blanks. What is the probability of getting a prize?


Answer :

In a lottery, there are 10 prizes and 25 blanks. What is the probability of getting a prize?


Question 22: (Marks 2)

In a family of three children, find the probability of having at least two boys.

OR

Two dice are tossed simultaneously. Find the probability of getting

(i) an even number on both dice.

(ii) the sum of two numbers more than 9.


Answer :

In a family of three children, find the probability of having at least two boys


Question 23: (Marks 2)

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


Answer :

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of larger circle


Question 24: (Marks 2)

ncert solution 10th math basic 430-2-1 question 24


Answer :

ncert solution 10th math basic 430-2-1 answer 24


Question 25: (Marks 2)

The wheel of a motorcycle is of radius 35 cm. How many revolutions are required to travel a distance of 11 m?


Answer :

The wheel of a motorcycle is of radius 35 cm. How many revolutions are required to travel a


Question 26: (Marks 2)

Divide (2x2 – x + 3) by (2 – x) and write the quotient and the remainder


Answer :

Divide (2x2


Question 27: (Marks 3)

If a and ß are the zeroes of the polynomial


Answer :

If a and ß are the zeroes of the polynomial


Question 28: (Marks 3)

Draw a line segment of length 7 cm and divide it in the ratio 2 : 3.

OR

Draw a circle of radius 4 cm and construct the pair of tangents to the circle from an external point, which is at a distance of 7 cm from its centre.


Answer :

Correct construction

OR

Correct construction


Question 29: (Marks 3)

The minute hand of a clock is 21 cm long. Calculate the area swept by it and the distance travelled by its tip in 20 minutes.


Answer :

The minute hand of a clock is 21 cm long. Calculate the area swept by it and the distance


Question 30: (Marks 3)

If x = 3 sin θ + 4 cos θ and y = 3 cos θ – 4 sin θ then prove that x2 + y2 = 25

OR

If sin θ + sin2 θ = 1; then prove that cos2 θ + cos4 θ = 1.


Answer :

x2 = 9 sin2 θ + 16 cos2 θ + 24 sin θ cos θ

y2 = 9 cos2 θ + 16 sin2 θ – 24 sin θ cos θ

x2 + y2 = 25

OR

sin θ = 1 – sin2 θ = cos2 θ

L.H.S = cos2 θ + (cos2 θ) 2 = cos2 θ + sin2 θ

= 1 = R.H.S


Question 31: (Marks 3)

Prove that 3 is an irrational number

OR

Using Euclid’s algorithm, find the HCF of 272 and 1032.


Answer :

 Prove that 3 is an irrational number.

OR

1032 = 272 × 3 + 216

272 = 216 × 1 + 56

216 = 56 × 3 + 48

56 = 48 × 1 + 8

48 = 8 × 6 + 0 HCF(1032, 272) = 8


Question 32: (marks 3)

In a rectangle ABCD, P is any interior point. Then prove that PA2 + PC2 = PB2 + PD2 .


Answer :

In a rectangle ABCD, P is any interior point. Then prove that


Question 33: (Marks 3)

In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 3. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is correct.

In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 3. Champa


Answer :

In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 3. Champa


Question 34: (Marks 3)

Solve graphically:

2x – 3y + 13 = 0; 3x – 2y + 12 = 0


Answer :

Correct graph of 2x – 3y + 13 = 0, 3x – 2y + 12 = 0

Solution x = –2, y = 3

SECTION D

Question numbers 35 to 40 carry 4 marks each.


Question 35: (Marks 4)

The product of two consecutive positive integers is 306. Find the integers


Answer :

Let two consecutive integers x, x + 1

x(x + 1) = 306 ⇒ x2 + x – 306 = 0

⇒ (x + 18) (x – 17) = 0

⇒ x = –18, (Rejected), 17

∴ Two consecutive integers 17, 18


Question 36: (Marks 4)

The 17th term of an A.P. is 5 more than twice its 8th term. If 11th term of A.P. is 43; then find its nth term.

OR

How many terms of A.P. 3, 5, 7, 9, ... must be taken to get the sum 120?


Answer :

a17 = 2a8 + 5 ⇒ a + 16d = 2(a + 7d) + 5

⇒ 2d – a = 15 ...(1)

a11 = 43 ⇒ a + 10d = 43 ...(2)

Solving (1) & (2) a = 3 d = 4

an = 4n – 1

OR

How many terms of A.P. 3, 5, 7, 9, ... must be taken to get the sum 120?


Question 37: (Marks 4)

A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on opposite bank is 60°. When he moves 30 m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and width of the river. [Take 3 = 1.732]


Answer :

A person standing on the bank of a river observes that the angle of elevation of the top of a


Question 38: (Marks 4)

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

OR

Prove that the length of tangents drawn from an external point to a circle are equal.


Answer :

Correct Fig., given, to prove, construction

Correct proof given, to prove, construction,

OR

Correct Fig., given, to prove, construction

Correct proof given, to prove, construction,


Question 39: (Marks 4)

From a solid cylinder whose height is 15 cm and the diameter is 16 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of remaining solid. (Give your answer in terms of π).

OR

The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height. Find the ratio of the volumes of the two parts.


Answer :

The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to it


Question 40: (Marks 4)

The mode of the following frequency distribution is 36. Find the missing frequency (f).

The mode of the following frequency distribution is 36. Find the missing frequency (f).


Answer :

The mode of the following frequency distribution is 36. Find the missing frequency (f).

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Maths Question Paper For Class 10 2018 2019 2020 CBSE Board NCERT Books

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