CBSE Sample Paper for Class 10 Maths is the best resources to prepare for your board exam. Here, We have made sample papers available for students so they can prepare well for their exam and score more marks. The CBSE Class 10 Maths Sample Paper 2021 has been made available on the official CBSE website. Along with the sample paper, CBSE has also provided the Marking Scheme and Answer key for the paper.Solving the CBSE Class 10 Maths Sample Paper 2021 will give more clarity to the students and help them prepare in an effective way. Here, we have provided the CBSE Class 10 Sample Paper for Maths exam 2021 along with the PDF format. Moreover, we have also compiled the solved and unsolved Maths Sample paper created by us for more practice of the students.
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SECTION – I
- 1 marks each
Q.1 Find the value of ‘b’ if α and 1/α are zeroes of polynomial ax^{2
}+ bx +c = 0
Q.2 A pair of dice is thrown, find the probability of
getting a sum of four.
Q.3 How many polynomials can be formed with -2 & 5
as zeroes?
OR
1,2,3. What will be the probability that the square of this
number is less that or equal to 1.
Q.4 What kind of lines are represented by the
following pair of equations:
6x – 3y + 10 = 0
2x + y +9 = 0
Q.5 Is the equation (√2x + √3)^{2}
+ 3x^{2} – 5x quadratic ? Justify.
Q.6 Find the 30^{th} term of the A.P., 10, 7,
4……..
Q.7 A circle is divided into 12 equal sectors. Fid the
central angle of the each
sector.
Q.8 If the circumference of a circle and the perimeter
of a square are equal, then
find the relation between area of
circle & area of square.
Q.9 The pair of equations x + y – 4 = 0 & 2x + ky
= 3 has no solution, find the value
of k.
Q.10 In the given fig, if ∠AOB = 125⁰,
then find ∠COD.
Q.11 In a triangle ABC the
point D & E are on the sides CA & CB respectively such
that DE ǁ
AB, AD = 2x, DC = x + 3, BE = 2x – 1 & CE = x.
Then the value of x is_____ .
Q.12 Find the value of sin^{2}
60⁰
+ 2 tan 45⁰
- cos^{2} 30⁰.
OR If x = 2 sin^{2} A and
y = 2 cos^{2} A + 1, then find the value of x + y.
Q.13 Find the roots of the
quadratic equation x^{2} – 0.04 = 0
Q.14 The curved surface area
of a cylinder is 264 m^{2} and its volume is 924 cm^{3}.Find the ratio of its height to
its diameter.
Q.15 A solid ball gets
exactly filled in the cubical box of side b. Find the volume of the ball.
Q.16 A line segment AB is to
be divided in the ratio 2:3 then ray AX will be drawn such that ∠BAX is _______ angle.
Section – II
Case Based
Questions – 4 marks each.
Q.17 In a classroom, 4 friends are seated at the points A,B,C & D as shown in the figure. Mohit & Dheeraj walk into the class and after observing for a few minutes, Mohit decides to sit 4 points away from A along y-axis while Dheeraj wants to sit exactly in the middle of ABCD.
a) (8,3) b) (3,8) c) (7,4) (d) (4,7)
(ii) The coordinates of middle points of BC is
a) (6,5) b) (5,6) c) (6,4 d) (4,6)
a) 3√2 unit b) 2√3 unit c) 2√2 unit d) 3√3 unit
(iv) What Is the equation of line CD ?
a) x-y-5=0 b) x+y-5=0 c)x+y+5=0 d) x-y+5=0
a) x-y-5=0 b) x+y-5=0 c)x+y+5=0 d) x-y+5=0
Q.18 An electrician has to repair an electric fault on a pole of height 5m. She needs to reach a point 1.3m below the top of the pole to undertake the repair work. He puts a ladder making an angle of 60⁰ with the ground to reach the point o fault.reach the point o fault.
(i) What is the length of the ladder ?
a) 4.28 m b) 3.7/√3m c) 3.7m d) 7.4m
(ii) The distance of the pole from the foot of the ladder is
a) 3.7 m b) 2.14 m c)
(ii) The distance of the pole from the foot of the ladder is
a) 3.7 m b) 2.14 m c)
(iii) If the ladder is placed at an angle of 30⁰ with the ground, then what should be
the value of length of the ladder ?
a) 7.4 m b) 3.7 m c) 1.3 m d) 5m
(iv) What should be the value of length of the ladder ?
a) 7.4 m b) 3.7 m c) 1.3 m d) 5m
(iv) What should be the angle b/w ladder and the pole ?
a) 60⁰ b) 30⁰ c) 90⁰ d) 45⁰
(v) What is the length of the pole from ground, where repair work is done ?
a) 1.3 m b) 5 m c) 3.7 m d) 3.1 m
a) 1.3 m b) 5 m c) 3.7 m d) 3.1 m
Q.19 There are three sections of class X in Kendriya Vidayala,Delhi Cantt. The total number of students in class 10^{th} are 100. The marks obtained by the students in Preboard exam are presented in a table as given below. The mean obtained is 53.
Marks Obtained |
0-20 |
20-40 |
40-60 |
60-80 |
80-100 |
No. Of Students |
15 |
18 |
21 |
29 |
p |
(Sorry For Mistake, Plz Download The PDF File For Complete Sample Paper)
(i) How many students got
marks between 80-100 ?
a) 21 b) 38 c)
17 d) 26
(ii) What is the lower limit of modal class ?
a) 20 b) 40 c)
60 d) 80
(iii) What is value of modal marks ?
a) 58 b) 62 c)
65 d) 68
(iv) What is value of ∑fixi
?
a) 2900 b) 5300 c)
1500 d) 100
(v) What is the upper limit of the
median class ?
a) 20 b) 40 c)
60 d) 80
Q.20 For 71th Republic Day Parade on 26/01/2021 in Delhi, Captain RS Meel is planning for parade of following two groups: (i) First group of Army contingent of 624 members behind an army band of 32 members. (2) Second group of CRPF troops with 468 soldiers behind the 228 members of bikers.These two groups are to march in the same no. of columns. This sequence of soldiers is followed by different states of Jhanki which are showing the culture of the respective states.
(i) What is the maximum no. of columns in which the army troop can march?
a) 8 b)
16 c) 4 d) 32
(ii) What is the maximum no. of columns in which the CRPF troop can march ?
a) 4 b)
8 c) 12 d) 16
(iii) What is the maximum no. of columns in which total army troop and CRPF troop together can march past?
a) 2 b)
4 c) 6 d) 8
(iv) What should be subtracted with the numbers of CRPF soldiers and the number of bikers so that their
maximum number of column is equal to the maximum number of column of army
troop?
a) 4 soldiers & 4 bikers
b) 4
soldiers & 2 bikers
c) 2 soldiers & 4 bikers
d) 2
soldiers & 2 bikers
(v) What should be added with the numbers of CRPF soldiers and number of bikers so that their maximum number
of column is equal to the maximum number of column of army troop?
a) 4 soldiers & 4 bikers
b) 12
soldiers & 12 bikers
c) 6 soldiers & 6 bikers
d) 12
soldiers & 6 bikers
Part - B
Very ShortAnswer Type Questions, 2 Marks Each.
Q.21 Find the
value of d if HCF of 759 and 44 is 2d-13.
Q.22
Determine the nature of roots of quadratic equation x^{2} – 5x – 7 = 0.
Q.23 If
(4,p) & (1,0) are end points of the diameter of a circle of length 10cm,
find the coordinates of center of
the circle.
Q.24 A
quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.
Q.25 In the
fig., MN & MP are tangents to a circle with centre O. Find the length of the chord PN if MN = 4.5cm.
Q.26 If x
= a sec ϴ and y = b tan ϴ then show that b^{2}x^{2} -a^{2}y^{2} = a^{2}b^{2}.
Short Answer Type Questions, 3 Marks Each.
Q.27 The
length of the minute hand of a clock is 14cm. Find the area swept by the minute in 5 minutes.
Q.28 The
mean of the following data is 25.2. Find the missing value K.
Class |
0-10 |
10-20 |
20-30 |
30-40 |
40-50 |
Frequency |
8 |
12 |
10 |
11 |
K |
Q.29 State
and prove pythagoras theorem.
Q.30 The
sum of the three digits of a positive integer is 15 & these digits are in A.P.. The number obtained by
reversing the digits is 396 less than the original number. Find the
number.
Q.31 Draw a
pair of tangents to a circle of radius 4 cm which are inclined to each other at an angle of 45⁰.
Q.32 Three consecutive positive integers are such
that the sum of square of second integer and the product
of first and third integer is 49. Find
the integers.
Q.33 Find the median weight of the 30 students as per the distribution given below:
Weight |
40-45 |
45-50 |
50-55 |
55-60 |
60-65 |
65-70 |
70-75 |
No. of students |
2 |
3 |
8 |
6 |
6 |
3 |
2 |
Long Answer Type Questions, 5 marks each.
Q.34 A
vessel is in the form of a hollow hemisphere mounted by a hollow cylinder.The diameter of the hemisphere
is 14 cm and the total height of the vessel is13 cm. Find the inner surface
area of the vessel.
Q.35 8
women and 12 men can together finish a work
in 10 days, while 6 women and 8 men can finish it in 14
days. Find the time taken by 1 woman alone to finish the work and also that
taken by 1 man alone.
Q.36 From
the top of a vertical tower, the angles of depression of two cars, in the same straight line with the base
of the tower, at an instant are found to be30⁰ and 45⁰. If the cars are 83 m apart and on the same side of the tower, find the height of the tower.
OR
Two poles AB & PQ of same
height 35m are standing opposite each other on either side of the road. The
angles of elevation of the top of the poles, from point C between them on the
rooad, are 60⁰ and 30⁰ respectively. Find the distance between the poles.
Importance of Solving CBSE Class 10 Maths Sample Papers
- By solving the CBSE Class 10 Maths sample papers, students will get an idea of exam pattern, the types of questions asked and weightage of each section.
- Solving class 10 CBSE sample paper will be good practise for students.
- These Maths Sample Papers cover all the important topics and also the questions which are repeated every year.
- CBSE Class 10 Maths sample paper will help the students to analyze their performance. This will also help with time management.
- This will boost up the students’ confidence level.
- After this much of practice, students will have a good idea about what to expect in exams.