CBSE Previous Year Question Papers Class 10 Maths
CBSE Board Paper Solution-2020
Class : X
Subject : Mathematics (Standard) –
Set : 1
Code No : 30/5/1
Time allowed : 3 Hours
Maximum Marks : 80 Marks
Read the following instructions very carefully and strictly
(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.
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
3 -4x + 3
2 + 3x – 4
2 – 4x – 3
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
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)
The centre of a circle whose end points of a
diameter are (─ 6, 3) and 6, 4) is
(A) (8, ─ 1)
(B) (4, 7)
(C) 0, 2
(D) 4, 2
4) The value(s) of k for which the quadratic
equation 2×2 + kx + 2 = 0 has equal roots, is
(C) ─ 4
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
6) The pair of linear equations
+ =7 and 9x + 10y = 14 is
(C) consistent with one solution
(D) consistent with many solutions
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
8) The radius of a sphere (in cm) whose volume is
12Л cm3, is
(B) 3 3
9) The distance between the points (m,–n) and
(–m, n) is
2 + n2
(B) m + n
(C) 2 m
2 + n2
(D) 2m2+ 2n2
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
Fill in the blanks in question number 11 to 15
11) The probability of an event that is sure to
happen is __.
1 tan A2
12) Simplest form of 1 cot A2
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 ____.
14)In the formula x a fi i
(D) 2 2 cm
15) All concentric circles are ______ to each other.
Answer the following question numbers 16 to 20.
16) Find the sum of the first 100 natural numbers.
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.
18) The LCM of two numbers is 182 and their HCF is
13. If one of the numbers is 26, Find the other.
19) Form a quadratic polynomial, the sum and
product of whose zeroes are (-3) and 2
Can (x2 – 1) be a remainder while dividing x4 –
3×2 + 5x – 9 by (x2 +3)? Justify your answer
2 tan 450 cos 600
Question number 21 to 26 carry 2 marks each. 21)
In the given Figure-5, DE ||AC and DF||AE.
Prove that BF BE
22) Show that 5+2 7 is an irrational number, where
7 is given to be an irrational number.
Check whether 12n can end with the digit 0 for any
natural number n.
23) If A, B and C are interior angles of a ABC,
then show that
cos B+C2 =sin A2.
24) In Figure 6, a quadrilateral ABCD is drawn to
circumscribe a circle.
AB + CD = BC +AD.
In Figure-7, find the perimeter of ABC, if AP =
25) Find the mode of the following distribution:
Marks 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60
4 6 7 12 5 6
26) 2 cubes, each of volume 125 cm3, are joined
end to end. Find the surface area of the
27) A fraction becomes when 1 is subtracted
from the numerator and it becomes when 8 is
added to its denominator. Find the fraction.
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
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.
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.
Show that the points (7, 100, (-2, 5) and (3, -4)
are vertices of an isosceles right triangle.
30) Prove that:
sec A + tan A
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.
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
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:
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?
34. In figure – 9, a square OPQR is inscribed in a
quadrant OAQB of a circle. If the radius of circle
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.
What minimum must be added to
2x -3x + 6x +7 so that resulting polynomi3 2
al will be divisible by x – 4x +8 ?2
36) Prove that the ratio of the areas of two similar
triangles is equal to the square of the ratio of
their corresponding sides.
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.
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.
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)
39. A statue 1.6 m tall, stands on the top of a
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
(Use 3 =1.73)
40) For the following data, draw a ‘less than’ ogive
and hence find the median of the distribution.
0-10 10-20 20-30 30-40 40-50 50-60 60-70
5 15 20 25 15 11 9
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.
20-60 60-100 100-140 140-180 180-220 220-260
7 5 16 12 2 3