Download Central Board of Secondary Education (CBSE) Class 10th (10th Board Exam) Maths Standard 2021 Sample Paper
Subject- Mathematics -Standard
Sample Question Paper
Time Allowed: 3 Hours Maximum Marks: 80
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 three sections- I and II.
2. Section I has 16 questions of 1 mark each. Internal choice is provided in 5 questions.
3. Section II has 4 questions on case study. 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
marks.
Question
Part-A
Marks
No.
allocated
Section-I
Section I has 16 questions of 1 mark each. Internal choice is provided
in 5 questions.
1
If xy=180 and HCF(x,y)=3, then find the LCM(x,y).
1
OR
14587
The decimal representation of
wil terminate after how many decimal
21 ? 54
places?
2
If the sum of the zeroes of the quadratic polynomial 3x2-kx+6 is 3, then find
1
the value of k.
Page 1 of 14
3.
For what value of k, the pair of linear equations 3x+y=3 and 6x+ky=8 does
1
not have a solution.
4.
If 3 chairs and 1 table costs Rs. 1500 and 6 chairs and 1 table costs Rs.2400. Form
1
linear equations to represent this situation.
5.
Which term of the A.P. 27, 24, 21,.....is zero?
1
OR
In an Arithmetic Progression, if d= - 4, n=7,an=4, then find a.
6.
For what values of k, the equation 9x2+6kx+4=0 has equal roots?
7.
Find the roots of the equation x2+7x+10=0
1
OR
For what value(s) of `a' quadratic equation 30 2 - 6 + 1 = 0 has no real
roots?
8.
If PQ=28cm, then find the perimeter of PLM
1
9.
If two tangents are inclined at 60? are drawn to a circle of radius 3cm then
1
find length of each tangent.
OR
PQ is a tangent to a circle with centre O at point P. If OPQ is an isosceles
triangle, then find OQP.
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10.
In the ABC, D and E are points on side AB and AC respectively such that
1
DE II BC. If AE=2cm, AD=3cm and BD=4.5cm, then find CE.
11.
In the figure, if B1, B2, B3,...... and A1,A2, A3,..... have been marked at
1
equal distances. In what ratio C divides AB?
12.
+ = 1, = 30? and B is an acute angle, then find the value of B. 1
13.
If x=2sin2 and y=2cos2+1, then find x+y
1
14.
In a circle of diameter 42cm,if an arc subtends an angle of 60? at the centre
1
where =22/7, then what wil be the length of arc.
15.
12 solid spheres of the same radi are made by melting a solid metallic
1
cylinder of base diameter 2cm and height 16cm. Find the diameter of the
each sphere.
16.
Find the probability of getting a doublet in a throw of a pair of dice.
1
OR
Page 3 of 14
Find the probability of getting a black queen when a card is drawn at random
from a well-shuffled pack of 52 cards.
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
SUN ROOM
The diagrams show the plans for a sun room. It wil be built onto the wall of a
house. The four walls of the sunroom are square clear glass panels. The roof
is made using
? Four clear glass panels, trapezium in shape, all the same size
? One tinted glass panel, half a regular octagon in shape
(a)
Refer to Top View
1
Find the mid-point of the segment joining the points J (6, 17) and I (9, 16).
(i) (33/2,15/2)
(i ) (3/2,1/2)
(i i)(15/2,33/2)
(iv) (1/2,3/2)
Page 4 of 14
(b)
Refer to Top View
1
The distance of the point P from the y-axis is
(i) 4
(i ) 15
(i i) 19
(iv) 25
(c)
Refer to Front View
1
The distance between the points A and S is
(i) 4
(i ) 8
(i i)16
(iv)20
(d)
Refer to Front View
1
Find the co-ordinates of the point which divides the line segment joining the
points A and B in the ratio 1:3 internal y.
(i) (8.5,2.0)
(i ) (2.0,9.5)
(i i) (3.0,7.5)
(iv) (2.0,8.5)
(e)
Refer to Front View
1
If a point (x,y) is equidistant from the Q(9,8) and S(17,8),then
(i) x+y=13
(i ) x-13=0
(i i) y-13=0
(iv)x-y=13
18.
Case Study Based- 2
SCALE FACTOR AND SIMILARITY
SCALE FACTOR
A scale drawing of an object is the same shape as the object but a different
size.
The scale of a drawing is a comparison of the length used on a drawing to
the length it represents. The scale is written as a ratio.
SIMILAR FIGURES
The ratio of two corresponding sides in similar figures is called the scale
factor.
Scale factor =
If one shape can become another using Resizing then the
shapes are Similar
T
h
Page 5 of 14
T
h
Rotation or Turn
Reflection or Flip
Translation or Slide
Hence, two shapes are Similar when one can become the other after
a resize, flip, slide or turn.
(a)
A model of a boat is made on the scale of 1:4. The model is 120cm long. The 1
full size of the boat has a width of 60cm. What is the width of the scale
model?
(i) 20 cm
(i ) 25 cm
(i i) 15 cm
(iv)240 cm
Page 6 of 14
(b)
What wil effect the similarity of any two polygons?
1
(i) They are flipped horizontally
(i )They are dilated by a scale factor
(i i)They are translated down
(iv)They are not the mirror image of one another
(c)
If two similar triangles have a scale factor of a: b. Which statement regarding 1
the two triangles is true?
(i)The ratio of their perimeters is 3a : b
(i )Their altitudes have a ratio a:b
(i i)Their medians have a ratio : b
2
(iv)Their angle bisectors have a ratio a2 : b2
(d)
The shadow of a stick 5m long is 2m. At the same time the shadow of a tree
1
12.5m high is
(i)3m
(i )3.5m
(i i)4.5m
(iv)5m
(e)
Below you see a student's mathematical model of a farmhouse roof with
1
measurements. The attic floor, ABCD in the model, is a square. The beams
that support the roof are the edges of a rectangular prism, EFGHKLMN. E is
the middle of AT, F is the middle of BT, G is the middle of CT, and H is the
middle of DT. Al the edges of the pyramid in the model have length of 12 m.
Page 7 of 14
What is the length of EF, where EF is one of the horizontal edges of the
block?
(i)24m
(i )3m
(i i)6m
(iv)10m
19.
Case Study Based- 3
Applications of Parabolas-Highway Overpasses/Underpasses
A highway underpass is parabolic in shape.
Parabola
A parabola is the graph that
results from p(x)=ax2+bx+c
Parabolas are symmetric
about a vertical line known
as the Axis of Symmetry.
The Axis of Symmetry runs
through the maximum or
minimum point of the
parabola which is called the
Page 8 of 14
Vertex
(a)
If the highway overpass is represented by x2?2x ?8. Then its zeroes are
(i) (2,-4)
(i ) (4,-2)
(i i) (-2,-2)
(iv) (-4,-4)
(b)
The highway overpass is represented graphically.
Zeroes of a polynomial can be expressed graphically. Number of zeroes of
polynomial is equal to number of points where the graph of polynomial
(i) Intersects x-axis
(i ) Intersects y-axis
(i i) Intersects y-axis or x-axis
(iv)None of the above
Page 9 of 14
(c)
Graph of a quadratic polynomial is a
(i) straight line
(i ) circle
(i i)parabola
(iv)ellipse
(d)
The representation of Highway Underpass whose one zero is 6 and sum of
the zeroes is 0, is
(i)x2 ? 6x + 2
(i ) x2 ? 36
(i i)x2 ? 6
(iv)x2 ? 3
(e)
The number of zeroes that polynomial f(x) = (x ? 2)2 + 4 can have is:
(i)1
(i ) 2
(i i) 0
(iv) 3
20.
Case Study Based- 4
100m RACE
A stopwatch was used to
find the time that it took a
group of students to run 100
m.
Time
0-20
20-40
40-60
60-80
80-100
(in sec)
No. of
8
10
13
6
3
students
Page 10 of 14
(a)
Estimate the mean time taken by a student to finish the race.
(i)54
(i )63
(i i)43
(iv)50
(b)
What wi l be the upper limit of the modal class ?
(i)20
(i )40
(i i)60
(iv)80
(c)
The construction of cummulative frequency table is useful in determining the
(i)Mean
(i )Median
(i i)Mode
(iv)Al of the above
(d)
The sum of lower limits of median class and modal class is
(i)60
(i )100
(i i)80
(iv)140
(e)
How many students finished the race within 1 minute?
(i)18
(i )37
(i i)31
(iv)8
Part ?B
All questions are compulsory. In case of internal choices, attempt any
one.
21.
3 bells ring at an interval of 4,7 and 14 minutes. Al three bel rang at 6 am,
2
when the three balls wil the ring together next?
22.
Find the point on x-axis which is equidistant from the points (2,-2) and (-4,2) 2
OR
Page 11 of 14
P (-2, 5) and Q (3, 2) are two points. Find the co-ordinates of the point R on
PQ such that PR=2QR
23.
Find a quadratic polynomial whose zeroes are 5-32 and 5+32.
2
24.
Draw a line segment AB of length 9cm. With A and B as centres, draw
2
circles of radius 5cm and 3cm respectively. Construct tangents to each circle
from the centre of the other circle.
25.
If tanA=3/4, find the value of 1/sinA+1/cosA
2
OR
If 3 sin-cos=0 and 0?< <90?, find the value of
26.
In the figure, quadrilateral ABCD is circumscribing a circle with centre O
2
and ADAB. If radius of incircle is 10cm, then the value of x is
27..
Prove that 2-3 is irrational, given that 3 is irrational.
3
28.
If one root of the quadratic equation 3x2+px+4=0 is 2/3, then find the value
3
of p and the other root of the equation.
OR
The roots and of the quadratic equation x2-5x+3(k-1)=0 are such that -
=1. Find the value k.
Page 12 of 14
29.
In the figure, ABCD is a square of side 14 cm. Semi-circles are drawn with
3
each side of square as diameter. Find the area of the shaded region.
30.
The perimeters of two similar triangles are 25cm and 15cm respectively. If
3
one side of the first triangle is 9cm, find the length of the corresponding side
of the second triangle.
OR
In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3
BC. Prove that 9 AD2 = 7 AB2
31.
The median of the following data is 16. Find the missing frequencies a and b, 3
if the total of the frequencies is 70.
Class
0-5
5-10 10-15 15-20 20-25 25-30 30-35 35-40
Frequency 12
a
12
15
b
6
6
4
32.
3
If the angles of elevation of the top of the candle from two coins distant `a'
cm and `b' cm (a>b) from its base and in the same straight line from it are
30? and 60?, then find the height of the candle.
Page 13 of 14
Section V
33.
The mode of the following data is 67. Find the missing frequency x.
3
Class
40-50
50-60
60-70 70-80
80-90
Frequency
5
x
15 12
7
34.
The two palm trees are of equal heights and are standing opposite each
5
other on either side of the river, which is 80 m wide. From a point O
between them on the river the angles of elevation of the top of the trees
are 60? and 30?, respectively. Find the height of the trees and the
distances of the point O from the trees.
OR
The angles of depression of the top and bottom of a building 50 meters
high as observed from the top of a tower are 30? and 60? respectively.
Find the height of the tower, and also the horizontal distance between the
building and the tower.
35.
Water is flowing through a cylindrical pipe of internal diameter 2cm, into a
5
cylindrical tank of base radius 40 cm at the rate of 0.7m/sec. By how
much wil the water rise in the tank in half an hour?
36.
A motorboat covers a distance of 16km upstream and 24km downstream
5
in 6 hours. In the same time it covers a distance of 12 km upstream and
36km downstream. Find the speed of the boat in stil water and that of the
stream.
Page 14 of 14
This post was last modified on 07 March 2021