KENDRIYA VIDYALAYA SANGATHAN JAMMU REGION
Class- X
Mathematics-STANDARD
Sample Question Paper 2020-21
Max. Marks: 80
Duration:3 hours
General Instructions:
1. This question paper contains two parts A and B.
2. Both Part A and Part B have internal choices.
Part – A:
1. It consists of two sections- I and II
2. Section I has 16 questions. Internal choice is provided in 5 questions.
3. Section II has four case study-based questions. Each case study has 5 case-based sub-parts.
An examinee is to attempt any 4 out of 5 sub-parts.
Part – B:
1. Question No 21 to 26 are Very short answer Type questions of 2 mark each
2. Question No 27 to 33 are Short Answer Type questions of 3 marks each
3. Question No 34 to 36 are Long Answer Type questions of 5 marks each.
4. Internal choice is provided in 2 questions of 2 marks, 2 questions of 3 marks
and 1 question of 5
Question
No.
Part-A
Marks
allocated
Section-I
Section I has 16 questions of 1 mark each. Internal choice is
provided in 5 questions.
1
Given that HCF (306, 657) = 9, find LCM (306, 657).
1
OR
state whether 6/15 will have a terminating decimal expansion or a nonterminating repeating decimal expansion:
2
If 𝛼 𝑎𝑛𝑑 𝛽 are zeroes of x2 - 5 x + k such that 𝛼 − 𝛽 = 1, then find
the value of k.
1|Page
1
3
For which value of k will the following pair of linear equations have no
solution?
1
4.
10 students of Class X took part in a Mathematics quiz. If the number
of girls is 4 more than the number of boys. Represent the situation
algebraically
Which term of the A.P. 3, 8, 13, 18, …….. is 78?
OR
1
5.
1
How many three digit numbers are divisible by 7.
6.
7.
The area of a rectangular plot is 528 m2. The length of the plot (in meters)
is one more than twice its breadth. We need to find the length and breadth
of the plot. Represent the situations in the form of quadratic equations.
Find the roots of quadratic equations by factorization
2x2 + x – 6 = 0
OR
1
1
Find two numbers whose sum is 27 and product is 182.
8.
The length of a tangent from a point A at distance 5 cm from the center of
the circle is 4 cm. Find the radius of the circle.
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1
9.
If two tangents are inclined at 60˚ are drawn to a circle of radius 3cm
then find length of each tangent.
1
OR
10.
Two concentric circles are of radii 5 cm and 3 cm. Find the length of
the chord of the larger circle which touches the smaller circle.
E and F are points on the sides PQ and PR respectively of a ΔPQR. State
whether
EF || QR.
If PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm
1
11.
In the figure, A1,A2, A3,….. have been marked at equal distances. In
what ratio C divides AB?
1
12.
If tan (A+B) =√3 and tan (A-B) =
1
1
, 0° < A + B ≤ 90°, A > B, then
√3
find A and B.
13.
14.
Prove that
The radii of two circles are 19 cm and 9 cm respectively. Find the radius
of the circle which has circumference equal to the sum of the
circumferences of the two circles.
3|Page
1
1
15.
2 cubes each of volume 64 cm3 are joined end to end. Find the surface area
of the resulting cuboids.
1
16.
Five cards−−the ten, jack, queen, king and ace of diamonds, are wellshuffled with their face downwards. One card is then picked up at random.
What is the probability that the card is the queen?
OR
One card is drawn from a well-shuffled deck of 52 cards. Find the
probability of getting a red face card
1
Section-II
Case study based questions are compulsory. Attempt any four sub
parts of each question. Each subpart carries 1 mark
17.
Case Study based-1
The class X students of Vijay Higher Secondary School in city Z have
been allotted a rectangular plot of land for gardening activity
Saplings of Gulmohar are planted on the boundary at a distance of 1m
from each other. There is a triangular grassy lawn in the plot as shown in
fig. The students are to sow seeds of flowering plants in the remaining
area of the plot. Then taking A as the Origin, answer the following
questions
(a)
Refer to above figure
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1
Find the mid-point of the segment joining the points Q and R.
(i) (4, 5)
(ii) (4, 6)
(iii)( 5, 5)
(iv) (4, 4.5)
(b) Refer to above figure
The distance of the point R from the y-axis is
(i)
5
(ii) 6
(iii) 7
(iv) 8
(c)
Refer to above figure
The distance between the points P and Q is
(i)
(d)
(e)
18.
√13
(ii) √15
(iii) √5
1
(iv) √7
Refer to above figure
Find the co-ordinates of the point which divides the line segment joining the
points Q and P in the ratio 1:3 internally.
(i) (7/2, 11/4)
(ii) (5/2, -15/4)
(iii) (-5/2,15/4)
(iv) (5/2, 15/4)
Refer to above figure
The co-ordinates of point P are
(i)
(-4, -6)
(ii) (4, -6)
(iii) (4, 6)
(iv) (-4, 6)
Case Study Based- 2
A famous Greek mathematician Thales gave an important
truth relating to two equiangular triangles which is as
follows: The ratio of any two corresponding sides in two
equiangular triangles is always the same. It is believed that
he had used a result called the Basic Proportionality
Theorem (now known as the Thales Theorem) for the same.
5|Page
1
1
1
(a)
1
If the Thales theorem is applicable to the given figure. The height of the tree
is
(i)
14ft
(ii) 16ft
(iii) 10ft
(iv) 15ft
(b)
1
Using basic proportionality theorem, the value of x is
(i)
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8.2
(ii)8.4
(iii) 8.0
(iv) 8.6
(c)
In the right triangle above a perpendicular is drawn to the hypotenuse.
Using similarity of the triangles, the value of x + y + z is
(i)
(d)
(ii) 22.5
(iii) 15
(iv) 24.2
The figure shows an isosceles triangle ABC with AB = BC. The line DE
cuts AC extended at F. If AD = 5, CE = 3, and EF = 8, DE would be equal to
(i)
(e)
22.2
15/3
(ii) 16/3
(iii) 18/3
In the given two similar triangles the length L is given by
E
(i)
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10
(ii) 30
(iii) 20
1
(iv) 40
1
(iv) 19/3
1
19.
Case Study Based- 3
The zero of the p(x) are precisely the x coordinate of the points, where the
graph of y= p(x) intersect the x axis.
(a)
Zeroes of below polynomial are
(i)
(b)
-2, 1
1
(ii) -2, 0, 1
(iii) -4, 0
(iv) 0, 1
If the arc above the bridge is represented by the polynomial x2-4x-5. Then its
zeroes are
(i)
1, 5
(ii) -1, -5
(iii) 1, -5
c) The number of zeroes that the polynomial p(x) = x3-4x can have
(i)
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1
(ii) 0
(iii) 2
(iv) 3
1
(iv)-1, 5
1
(d)
The graph of the linear polynomial is
(i)
(e)
(ii) Parabola (iii) Circle (iv) Ellipse
The representation of underpass bridge whose one zero is 3 and sum of
zeroes is 10 is given by
(i)
20.
Straight line
1
x2-30
(ii) x2-10x+21
(iii) x2-3
1
(iv) x2-10
Case Study Based- 4
Daily wages of the 50 workers of the factory is shown as below:
Daily wages in 100-120
Rupees
Number of
12
Workers
(a)
120-140
140-160
160-180
180-200
14
8
6
10
The mean daily wages of the workers of the factory is
(i)
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Rs145.20
(ii) Rs145.00
(iii) Rs145.40
1
(iv) Rs145.60
(b)
How many workers earn less than Rs 180
(i)
(c)
22.
(iv) 34
100
(ii) 120
1
(iii) 140
(iv) 180
120
(ii) 140
(iii) 180
1
(iv) 200
The mode of the above data is
(i)
21.
(iii) 50
What is the upper limit of the median class
(i)
(e)
(ii) 40
The lower limit of the modal class is
(i)
(d)
6
1
135
(ii) 115
1
(iii) 145
(iv) 125
Part –B
All questions are compulsory. In case of internal choices, attempt any
one.
There is a circular path around a sports field. Sonia takes 18 minutes to drive
one round of the field, while Ravi takes 12 minutes for the same. Suppose
they both start at the same point and at the same time, and go in the same
direction. After how many minutes will they meet again at the starting point?
Find the coordinates of a point A, where AB is the diameter of circle whose
Centre is (2, − 3) and B is (1, 4)
OR
Find the ratio in which the line segment joining the points
(− 3, 10) and (6, − 8) is divided by (− 1, 6).
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2
2
23.
Find a quadratic polynomial whose zeroes are 7- 4√3 and 7+ 4√3.
2
24.
Draw a circle of radius 3 cm. Take two points P and Q on one of its extended
diameter each at a distance of 7 cm from its center. Draw tangents to the
circle from these two points P and Q.
Given 15 cot A = 8. Find sin A and sec A
OR
2
25.
2
26.
If √3 sinƟ - cosƟ=0 and 0˚<Ɵ <90˚, find the value of Ɵ
A quadrilateral ABCD is drawn to circumscribe a circle. Prove that
AB + CD = AD + BC
2
27.
Prove that 3 + 2√5 is irrational, given that √5 is irrational.
3
28.
If one zero of the quadratic equation 5x2 + 13x + k =0 is the reciprocal of the
other, then find the value of k
OR
If α and β are zeros of the quadratic equation x2 - 5x + k = 0 such that
𝛼 − 𝛽 = 1,then find the value of k
Calculate the area of the designed region in the given figure common
between the two quadrants of circles of radius 8 cm each.
Use π = 22/7
3
29.
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3
30.
In an equilateral triangle, prove that three times the square of one side is
equal to four times the square of one of its altitudes.
OR
D and E are points on the sides CA and CB respectively of a triangle ABC
right angled at C. Prove that AE2 + BD2 = AB2 + DE2
3
31.
The median of the following data is 28.5. Find the missing frequencies X and
Y, if the total of the frequencies is 60.
3
Class
Frequen
cy
32.
33.
0-10
5
10-20
X
20-30
20
30-40
15
40-50
Y
50-60
5
Total
60
A straight highway leads to the foot of a tower. A man standing at the top of
the tower observes a car as an angle of depression of 30°, which is
approaching the foot of the tower with a uniform speed. Six seconds later, the
angle of depression of the car is found to be 60°. Find the time taken by the
car to reach the foot of the tower from this point.
The following data gives the information on the observed lifetimes (in hours)
of 225 electrical components
Lifetime
s (in
Hours)
Frequen
cy
0-20
20-40
40-60
60-80
80-100
100-120
10
35
52
61
38
29
Determine the modal lifetimes of the components.
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3
3
34.
Two poles of equal heights are standing opposite each other on either side of
the road, which is 80 m wide. From a point between them on the road, the
angles of elevation of the top of the poles are 60° and 30º, respectively. Find
the height of poles and the distance of the point from the poles.
OR
The angle of elevation of the top of a building from the foot of the tower is
30° and the angle of elevation of the top of the tower from the foot of the
building is 60°. If the tower is 50 m high, find the height of the building.
5
35.
A wooden article was made by scooping out a hemisphere from each end of a
solid cylinder, as shown in given figure. If the height of the cylinder is 10
cm, and its base is of radius 3.5 cm, find the total surface area of the
article. Use π = 22/7
5
36.
Two water taps together can fill a tank in 75/8 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.
5
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