CBSE Previous Year Question Papers Class 10 Maths
CBSE Board Paper Solution-2020
Class : X
Subject : Mathematics (Basic)
Set : 1
Code No : 430/5/1
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
questions. All questions are compulsory.
(ii) Section A: Question Number 1 to 20 comprises
of 20 questions of one mark each.
(iii) Section B: Question Number 21 to 26
comprises of 6 questions of two marks each.
(iv) Section C: Question Number 27 to 34
comprises of 8 questions of three marks each.
(v) Section D: Question Number 35 to 40
comprises of 6 questions of four marks each.
(vi) There is no overall choice in the question Paper.
However, an internal choice has been provided
in 2 questions of one mark, 2 questions of two
marks, 3 questions of three marks and 3
questions 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 calculators is not permitted.
Section A
Question numbers 1 to 20 carry 1 mark each.
Choose the correct option in question numbers 1
to 10.
1. If a pair of linear equations is consistent,
then the lines represented by them are
(A) parallel
(B) intersecting or coincident
(C) always coincident
(D) always intersecting
Answer:
2. The distance between the points (3, –2) and
(–3, 2) is
(A) 52 units
(B) 4 10 units
(C) 2 10 units
(D) 40 units
3. 8 cot2 A – 8 cosec2 A equal to
(A) 8
(B)
(C) -8
(D) –
4. The total surface area of a frustum-shaped
glass tumbler is (r1> r2)
(A) r l + r l
1 2
(B) l
r1 + r2 + r2
2
(C)h r
2 + r
2 + r r
1 2 1 2
2
(D) h + r – r
2 1 2
5. 120 can be expressed as a product of its
prime factors as
(A) 5 8 3
(B) 15 23
(C) 10 22 3
(D) 5 23 3
6. The discriminant of the quadratic equation
4×2–6x + 3 = 0 is
(A) 12
(B) 84
(C) 2 3
(D) –12 Answer:
7. If (3, – 6) is the mid-point of the line
segment joining (0, 0) and (x, y), then the
point (x, y) is (A) (–3, 6)
(B) (6, – 6)
(C) (6, –12)
3
(D) 2 ,-3
8) In the circle given in Figure-1, the number of
tangents parallel to tangent PQ is
(A) 0
(B) many
(C) 2
(D) 1
9) For the following frequency distribution:
Class: 0─5 5─10 10─15 15─20 20─25
8 10 19 25 8
The upper limit of median class is
(A) 15
(B) 10
(C) 20
(D) 25
10) The probability of an impossible event is
(A) 1
(B)
(C) not defined
(D) 0
Fill in the blanks in question numbers 11 to 15.
11) A line intersecting a circle in two points is
called a______.
12) If 2 is a zero of the polynomial ax2 ─ 2x, then
the value of ‘a’ is _________.
13) All squares are________. (congruent/similar)
14) If the radii of two spheres are in the ratio 2:3,
then the ratio of their respective volumes
is_______.
15) If ar (ΔPQR) is zero, then the points P, Q and R
are_______.
Answer the following question numbers 16 to 20:
16) In Figure-2, the angle of elevation of the top of
a tower AC from a point B on the ground is 60°.
If the height of the tower is 20 m, find the
distance of the point from the foot of the tower.
17) Evaluate:
tan 40° tan 50°
OR
If cos A = sin 42°, then find the value of A.
18) A coin is tossed twice. Find the probability of
getting head both the times.
19) Find the height of a cone of radius 5 cm and
slant height 13 cm.
20) Find the value of x so that ─6, x, 8 are in A.P.
OR
Find the 11th term of the A.P. ─27, ─22, ─17, ─12,
….
Section – B
Question numbers 21 to 26 carry 2 marks each.
21) Find the roots of the quadratic equation.
3x -4 3x+4=02
22) Check whether 6n can end with the digit ‘0’
(zero) for any natural number n.
OR
Find the LCM of 150 and 200.
1
If tan A + B = 3 and tan (A-B)= , 0 < A + B
23) 3
90°, A > B, then find the values of A and B.
24. In Figure-3, ABC and XYZ are shown. If AB =
3 cm, BC = 6 cm, AC = 2 3 cm, A = 800
, B
600, XY = 4 3 cm, YZ = 12 cm and XZ = 6 cm,
then find the value of Y.
Figure-3
25. 14 defective bulbs are accidentally mixed with
98 good ones. It is not possible to just look at
the bulb and tell whether it is defective or not.
One bulb is taken out at random from this lot.
Determine the probability that the bulb taken
out is a good one.
26. Find the mean for the following distribution:
Classes 5 – 15 15 – 25 25 – 35 35 – 45
Frequency 2 4 3 1
OR
The following distribution shows the transport
expenditure of 100 employees:
Expenditure
(in `) :
200-400 400-600 600-800 800-1000 1000-1200
Number of
employees :
21 25 19 23 12
Find the mode of the distribution.
SECTION C
Question number 27 to 34 carry 3 marks each.
27. A quadrilateral ABCD is drawn to circumscribe a
circle. Prove that
AB + CD = AD + BC.
28. The difference between two numbers is 26 and
the larger number exceeds thrice of the smaller
number by 4. Find the numbers. OR Solve for x
and y:
2 3 5 4
+ =13 and – =–2
x y x y
29. Prove that 3 is an irrational number.
30. Krishna has an apple orchard which has a 10
m ×10 m sized kitchen garden attached to it. She
divides it into a 10 ×10 grid and puts soil and
manure into it. She grows a lemon plant at A, a
coriander plant at B, an onion plant at C and a
tomato plant at D. Her husband Ram praised her
kitchen garden and points out that on joining A,
B, C and D they may form a parallelogram. Look
at the below figure carefully and answer the
following questions:
(i) Write the coordinates of the points A, B,
C and D, using the 10 ×10 grid as
coordinate axes.
(ii) Find whether ABCD is a parallelogram or
not.
31. If the sum of the first 14 terms of an A.P. is
1050 and its first term is 10, then find the 21st
term of the A.P.
32. Construct a triangle with its sides 4 cm, 5 cm
and 6 cm. Then construct a triangle similar to it
whose sides are of the corresponding sides of
the first triangle.
OR
Draw a circle of radius 2.5 cm. Take a point P at a
distance of 8 cm from its centre. Construct a pair of
tangents from the point P to the circle.
33. Prove that:
1
cosec A–sin A sec A–cos A =
tan A + cot A
34. In Figure – 4, AB and CD are two diameters of a
circle (with centre O) perpendicular to each
other and OD is the diameter of the smaller
circle. If OA = 7 cm, then find the area of the
shaded region.
OR
In Figure – 5 ABCD is a square with side 7 cm. A
circle is drawn circumscribing the square. Find
the area of the shaded region.
Section D
Question numbers 35 to 40 carry 4 marks each.
35. Find other zeroes of the polynomial
p x =3x –4x –10x +8x+8,4 3 2
if two of its zeroes are 2and – 2.
OR
Divide the polynomial g x =x -3x +x+23 2 by the
polynomial x –2x+12 and verify the division
algorithm.
36. From the top of a 75 m high lighthouse
from the seal level, the angles of depression of
two ships are 30°and 45° if the ships are on the
opposite sides of the lighthouse, then find the
distance between the two ships.
37. If a line is drawn parallel to one side of a
triangle to intersect the other two sides in
distinct points, prove that the other two sides
are divided in the same ratio.
OR
In Figure-6, in an equilateral triangle ABC, AD
BC, BE AC and CF AB. Prove that
4(AD2+BE2+CF2) = 9 AB2.
38. A container open at the top and made up of a
metal sheet, is in the form of a frustum of a
cone of height 14 cm with radii of its lower and
upper circular ends as 8 cm and 20 cm.
respectively. Find the capacity of the container.
39. Two water taps together can fill a tank in
hours. The tap of larger diameter takes 10
hours less than the smaller one to fill the tank
separately. Find the time in which each tap can
separately fill the tank.
OR
A rectangular park is to be designed whose breadth
is 3 m less than its length. Its area is to be 4
square metres more than the area of a park that
has already been made in the shape of an isosceles
triangle with its base as the breadth of the
rectangular park and of altitude 12 m. Find the
length and breadth of the park.
40. Draw a ‘less than’ ogive for the following
frequency distribution:
Classes: 0-10 10–20 20–30 30–40 40–50 50–60 60–70 70–80
Frequency: 7 14 13 12 20 11 15 8
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