CBSE Previous Year Question Papers Class 10 Maths

CBSE Board Paper Solution-2020

Class : X

Subject : Mathematics (Standard) –

Theory

Set : 1

Code No : 30/5/1

Time allowed : 3 Hours

Maximum Marks : 80 Marks

General instructions:

Read the following instructions very carefully and strictly

follow them:

(i) This question paper comprises four sections – A, B, C

and D. This question paper carries 40 question All

questions are compulsory

(ii) Section A: Question Numbers 1 to 20 comprises of

20 question of one mark each.

(iii) Section B: Question Numbers 21 to 26 comprises of

6 question of two marks each.

(iv) Section C: Question Numbers 27 to 34 comprises of

8 question of three marks each.

(v) Section D: Question Numbers 35 to 40 comprises of

6 question of four marks each.

(vi) There is no overall choice in the question paper.

However, an internal choice has been provided in 2

question of the mark, 2 question of one mark, 2

questions of two marks. 3 question of three marks

and 3 question of four marks. You have to attempt

only one of the choices in such questions.

(vii) In addition to this. Separate instructions are given

with each section and question, wherever necessary.

(viii) Use of calculations is not permitted.

Section A

Question numbers 1 to 20 carry 1 mark each.

Question numbers 1 to 10 are multiple choice questions.

Choose the correct option.

1. On dividing a polynomial p(x) by x2 – 4, quotient

and remainder are found to be x and 3

respectively. The polynomial p(x) is

(A) 3×2 + x – 12

(B) x

3 -4x + 3

(C) x

2 + 3x – 4

(D) x

2 – 4x – 3

Answer:

2) In Figure-1, ABC is an isosceles triangle, right

angled at C. Therefore

(A) AB2 = 2AC2

(B) BC2 = 2AB2

(C) AC2 = 2AB2

(D) AB2 = 4AC2

Answer:

3) The point on the x-axis which is equidistant from

(─ 4, 0) and 10, 0) is

(A) (7, 0)

(B) (5, 0) (C) (0, 0)

(D) (3, 0)

OR

The centre of a circle whose end points of a

diameter are (─ 6, 3) and 6, 4) is

(A) (8, ─ 1)

(B) (4, 7)

7

(C) 0, 2

7

(D) 4, 2

Answer:

4) The value(s) of k for which the quadratic

equation 2×2 + kx + 2 = 0 has equal roots, is

(A) 4

(B) 4

(C) ─ 4

(D) 0

Answer:

5) Which of the following is not an A.P.?

(A) ─ 1.2, 0.8, 2.8 ….

(B) 3, 3 + 2, 3 + 2 2, 3 + 3 2, ….

4 7 9 12

(C) , , , ,…

3 3 3 3

-1 -2 -3

(D) , , ,…

5 5 5

Answer:

6) The pair of linear equations

3x 5y

+ =7 and 9x + 10y = 14 is

2 3

(A) consistent

(B) inconsistent

(C) consistent with one solution

(D) consistent with many solutions

Answer:

7) In Figure-2 PQ is tangent to the circle with

centre at O, at the point B. If

∠AOB = 100°, then ∠ABP is equal to

(A) 50°

(B) 40°

(C) 60°

(D) 80°

Answer:

8) The radius of a sphere (in cm) whose volume is

12Л cm3, is

(A) 3

(B) 3 3

(C) 32/3

(D) 31/3

Answer:

9) The distance between the points (m,–n) and

(–m, n) is

(A) m

2 + n2

(B) m + n

(C) 2 m

2 + n2

(D) 2m2+ 2n2

Answer:

10) In Figure-3. From an external point P, two

tangents PQ and PR are drawn to a circle of

radius 4 cm with centre O. If QPR = 90°, then

length of PQ is

(A) 3cm

(B) 4cm

Fill in the blanks in question number 11 to 15

11) The probability of an event that is sure to

happen is __.

Answer:

1 tan A2

12) Simplest form of 1 cot A2

is ______.

Answer:

13) AOBC is a rectangle whose three vertices are

A(0, –3), O(0, 0) and B (4, 0). The length of its

diagonal is ____.

Answer:

14)In the formula x a fi i

Answer:

(C) 2cm

(D) 2 2 cm

Answer:

15) All concentric circles are ______ to each other.

Answer:

Answer the following question numbers 16 to 20.

16) Find the sum of the first 100 natural numbers.

Answer:

17) In Figure-4 the angle of elevation of the top of

a tower from a point C on the ground, which is

30 m away from the foot of the tower, is 30°.

Find the height of the tower.

Answer:

18) The LCM of two numbers is 182 and their HCF is

13. If one of the numbers is 26, Find the other.

Answer:

19) Form a quadratic polynomial, the sum and

product of whose zeroes are (-3) and 2

respectively.

OR

Can (x2 – 1) be a remainder while dividing x4 –

3×2 + 5x – 9 by (x2 +3)? Justify your answer

with reasons.

Answer:

20) Evaluate:

2 tan 450 cos 600

0

sin30

Answer:

SECTION B

Question number 21 to 26 carry 2 marks each. 21)

In the given Figure-5, DE ||AC and DF||AE.

Answer:

Prove that BF BE

= .

FE EC

22) Show that 5+2 7 is an irrational number, where

7 is given to be an irrational number.

OR

Check whether 12n can end with the digit 0 for any

natural number n.

Answer:

23) If A, B and C are interior angles of a ABC,

then show that

cos B+C2 =sin A2.

Answer:

24) In Figure 6, a quadrilateral ABCD is drawn to

circumscribe a circle.

Prove that

AB + CD = BC +AD.

OR

In Figure-7, find the perimeter of ABC, if AP =

12 cm.

Answer

25) Find the mode of the following distribution:

Marks 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60

Number

of

Students

4 6 7 12 5 6

Answer:

26) 2 cubes, each of volume 125 cm3, are joined

end to end. Find the surface area of the

resulting cuboid.

Answer:

Section C

27) A fraction becomes when 1 is subtracted

from the numerator and it becomes when 8 is

added to its denominator. Find the fraction.

OR

The present age of a father is three years more

than three times the age of his son. Three years

hence the father’s age will be 10 years more

than twice the age of the son. Determine their

present ages.

Answer:

28) Use Euclid Division Lemma to show that the

square of any positive integer is either of the

form 3q or 3q + 1 for some integer q.

Answer:

29) Find the ratio in which y-axis divides the line

segment joining the points (6, – 4) and (-2, -7).

Also find the point of intersection.

OR

Show that the points (7, 100, (-2, 5) and (3, -4)

are vertices of an isosceles right triangle.

Answer:

30) Prove that:

1 sinA

sec A + tan A

1 sinA

Answer:

31) For an A.P., it is given that the first term

(a) = 5, common difference (d) = 3, and the nth

term (an) = 50. Find n and sum of first n terms

(Sn) of the A.P.

Answer:

32) Construct a ΔABC with sides BC = 6 cm, AB = 5

cm and ABC= 60°. Then construct a triangle

whose sides are of the corresponding sides of

ΔABC.

OR

Draw a circle of radius 3.5 cm. Take a point P

outside the circle at a distance of 7 cm from the

centre of the circle and construct a pair of tangents

to the circle from that point.

33) Read the following passage and answer the

question given at the end:

Diwali Fair.

A game in a booth at a Diwali Fair involves using

a spinner first. Then, if the spinner stops on an

even number, the player is allowed to pick a

marble from a bag. The spinner and the marbles

in the bag are represented in Figure – 8.

Prizes are given when a black marble is picked.

Shweta plays the game once.

(i) What is the probability that she will be

allowed to pick a marble from the bag?

(ii) (ii) Suppose she is allowed to pick a

marble from the bag, what is the

probability of getting a prize, when it is

given that the bag contains 20 balls out

of which 6 are black?

Answer:

34. In figure – 9, a square OPQR is inscribed in a

quadrant OAQB of a circle. If the radius of circle

Answer:

SECTION D

Obtain other zeroes of the polynomial

35) p(x) = 2x – x – 11x + 5x + 54 3 2 if two

of its zeroes are 5 and- 5.

OR

What minimum must be added to

2x -3x + 6x +7 so that resulting polynomi3 2

al will be divisible by x – 4x +8 ?2

Answer:

36) Prove that the ratio of the areas of two similar

triangles is equal to the square of the ratio of

their corresponding sides.

Answer:

37) Sum of the areas of two squares is 544m2. If

the difference of their perimeters is 32 m, find

the sides of the two squares.

is 6 2 cm, find the area of the shaded region.

OR

A motorboat whose speed is 18km/h in still water

takes 1 hour more to go 24 km upstream than to

return downstream to the same spot. Find the

speed of the stream.

Answer:

38. A solid toy is in the form of a hemisphere

surmounted by a right circular cone of same

radius. The height of the cone is 10 cm and the

radius of the base is 7 cm. Determine the

volume of the toy. Also find the area of the

coloured sheet required to cover the toy.

(Use Л= and 149=12.2)

Answer:

39. A statue 1.6 m tall, stands on the top of a

pedestal.

From a point on the ground, the angle of

elevation of the top of the statue is 600 and

from the same point the angle of elevation of

the top of the pedestal is 450. Find the height of

the pedestal.

(Use 3 =1.73)

Answer:

40) For the following data, draw a ‘less than’ ogive

and hence find the median of the distribution.

Age(in

years):

0-10 10-20 20-30 30-40 40-50 50-60 60-70

Number

of

persons:

5 15 20 25 15 11 9

OR

The distribution given below show the number of

wickets taken by bowlers in one-day cricket

matches. Find the mean and the median of the

number of wickets taken.

Number

of

wickets

20-60 60-100 100-140 140-180 180-220 220-260

Number

of

bowlers:

7 5 16 12 2 3