Class 10 CBSE Maths Basic Specimen 2024

Maximum Marks: 80

Time Allowed: Three hours

This Question Paper has 5 Sections A, B, C, D, and E.

Section A has 20 Multiple Choice Questions (MCQs) carrying 1 mark each.

Section B has 5 Short Answer-I (SA-I) type questions carrying 2 marks each.

Section C has 6 Short Answer-II (SA-II) type questions carrying 3 marks each.

Section D has 4 Long Answer (LA) type questions carrying 5 marks each.

Section E has 3 sourced based/Case Based/passage based/integrated units of assessment (4 marks each) with sub-parts of the values of 1, 1 and 2 marks each respectively.

All Questions are compulsory. However, an internal choice in 2 Qs of 2 marks, 2 Qs of 3 marks and 2 Questions of 5 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E.

Draw neat figures wherever required. Take π =22/7 wherever required if not stated

Class 10 CBSE Maths Basic Specimen 2024

Section-A

Question 1

If two positive integers a and b are written as a = x3y 2 and b = xy3 ; where x, y are prime numbers, then HCF (a,b) is: a) xy b) xy2 c) x3y3 d) x2y2

Question 2

The LCM of smallest two digit composite number and smallest composite number is: a) 12 b) 4 c) 20 d) 44

Question 3

If x = 3 is one of the roots of the quadratic equation x2 – 2kx – 6 = 0, then the value of k is a) −(1/2) b) 1/2 c) 3 d) 2

Question 4

The pair of equations y = 0 and y = -7 has: a) one solution b) two solutions c) infinitely many solutions d) no solution

Question 5

Value(s) of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is : a) 0 only b) 4 c) 8 only d) 0,8

Question 6

The distance of the point(3, 5) from x-axis is k units, then k equals: a) 3 b) 4 c) 5 d) 8

Question 7

If in ∆ ABC and ∆ PQR then a) ∆PQR ~∆CAB b) ∆PQR ~∆ABC c) ∆CBA ~∆PQR d) ∆BCA ~∆PQR

Question 8

Which of the following is NOT a similarity criterion of traingles? a) AA b) SAS c) AAA d) RHS

Question 9

In figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to (a) 60° (b) 70° (c) 80° (d) 90°

Question 10

If cos A = 4/5 then tan A is : (a) 3/5 (b) 3/4 (c) 4/3 (d) 1/8

Question 11

If the height of the tower is equal to the length of its shadow, then the angle of elevation of the sun is _____ a) 30° b) 45° c) 60° d) 90°

Question 12

(1 – cos2 A) is equal to a) sin2A b) tan2A c) 1 – sin2A d) sec2A

Question 13

The radius of a circle is same as the side of a square. Their perimeters are in the ratio a) 1 : 1 b) 2 : 𝜋 c) 𝜋 : 2 d) √𝜋 : 2

Question 14

The area of the circle is 154 cm2 . The radius of the circle is a) 7cm b) 14cm c) 3.5cm d) 17.5cm

Question 15

When a dice is thrown once, the probability of getting an even number less than 4 is a) 1/4 b) 0 c) 1/2 d) 1/6

Question 16

For the following distribution: The lower limit of modal class is: a) 15 b) 20 c) 10 d) 5

Question 17

A rectangular sheet of paper 40cm x 22cm, is rolled to form a hollow cylinder of height 40cm. The radius of the cylinder(in cm) is : a) 3.5 b) 7 c) 80/7 d) 5

Question 18

Consider the following frequency distribution: The median class is: a) 6-12 b) 12-18 c) 18-24 d) 24-30

Question 19

Question 20

SECTION-B

Question 21

Find whether the following pair of linear equations is consistent or inconsistent: 3x + 2y = 8 6x – 4y = 9

Question 22

.In the given figure, if ABCD is a trapezium in which AB║CD ║ EF, then prove that OR In figure, if AD = 6cm, DB = 9cm, AE = 8cm and EC = 12cm and ∠ADE = 48˚. Find ∠ABC.

Question 23

The length of a tangent from a point A at distance 5cm from the centre of the circle is 4cm. Find the radius of the circle.

Question 24

Evaluate: sin2 60˚ + 2 tan 45˚ - cos230˚

Question 25

Find the diameter of a circle whose area is equal to the sum of the areas of two circles of radii 40cm and 9cm. OR A chord of a circle of radius 10cm subtends a right angle at the centre. Find the area of minor segment. (Use 𝜋 = 3.14)

SECTION-C

Question 26

Prove that √3 is an irrational number.

Question 27

Find the zeroes of the quadratic polynomial 4s2 – 4s + 1 and verify the relationship between the zeroes and the coefficients.

Question 28

Question 29

A circle touches all the four sides of quadrilateral ABCD. Prove that AB + CD = AD + BC.

Question 30

Prove that OR Prove that sec A (1 – sin A) (sec A + tan A) = 1.

Question 31

A bag contains 6 red, 4 black and some white balls. (i) Find the number of white balls in the bag if the probability of drawing a white ball is 1/3 . (ii) How many red balls should be removed from the bag for the probability of drawing a white ball to be 1/2 ?

SECTION-D

Question 32

Question 33

Question 34

Question 35

The following table gives the distribution of the life time of 400 neon lamps: OR Find the average life time of a lamp.

SECTION-E

Question 36

Question 37

Question 38

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If two positive integers a and b are written as a = x³y ² and b = xy³ ; where x, y are prime numbers, then HCF (a,b) is:
a) xy b) xy² c) x³y³ d) x²y²

The LCM of smallest two digit composite number and smallest composite number is:
a) 12
b) 4
c) 20
d) 44

If x = 3 is one of the roots of the quadratic equation x² – 2kx – 6 = 0, then the value of k is
a) −(1/2)
b) 1/2
c) 3
d) 2

The pair of equations y = 0 and y = -7 has:
a) one solution
b) two solutions
c) infinitely many solutions
d) no solution

Value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is :
a) 0 only
b) 4
c) 8 only
d) 0,8

The distance of the point(3, 5) from x-axis is k units, then k equals:
a) 3
b) 4
c) 5
d) 8

If in ∆ ABC and ∆ PQR then
a) ∆PQR ~∆CAB
b) ∆PQR ~∆ABC
c) ∆CBA ~∆PQR
d) ∆BCA ~∆PQR

Which of the following is NOT a similarity criterion of traingles?
a) AA
b) SAS
c) AAA
d) RHS

In figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to
(a) 60°
(b) 70°
(c) 80°
(d) 90°

If cos A = 4/5 then tan A is :
(a) 3/5
(b) 3/4
(c) 4/3
(d) 1/8

If the height of the tower is equal to the length of its shadow, then the angle of elevation of the sun is _____
a) 30°
b) 45°
c) 60°
d) 90°

(1 – cos² A) is equal to
a) sin²A
b) tan²A
c) 1 – sin²A
d) sec²A

The radius of a circle is same as the side of a square. Their perimeters are in the ratio
a) 1 : 1
b) 2 : 𝜋
c) 𝜋 : 2
d) √𝜋 : 2

The area of the circle is 154 cm² . The radius of the circle is
a) 7cm
b) 14cm
c) 3.5cm
d) 17.5cm

When a dice is thrown once, the probability of getting an even number less than 4 is
a) 1/4
b) 0
c) 1/2
d) 1/6

For the following distribution:

The lower limit of modal class is:
a) 15
b) 20
c) 10
d) 5

A rectangular sheet of paper 40cm x 22cm, is rolled to form a hollow cylinder of height 40cm. The radius of the cylinder(in cm) is :
a) 3.5
b) 7
c) 80/7
d) 5

Consider the following frequency distribution:
The median class is:

a) 6-12
b) 12-18
c) 18-24
d) 24-30

Find whether the following pair of linear equations is consistent or inconsistent:
3x + 2y = 8
6x – 4y = 9

.In the given figure, if ABCD is a trapezium in which AB║CD ║ EF, then prove that

OR
In figure, if AD = 6cm, DB = 9cm, AE = 8cm and EC = 12cm and ∠ADE = 48˚. Find ∠ABC.

Evaluate: sin² 60˚ + 2 tan 45˚ - cos²30˚

Find the diameter of a circle whose area is equal to the sum of the areas of two circles of radii 40cm and 9cm.
OR
A chord of a circle of radius 10cm subtends a right angle at the centre. Find the area of minor segment. (Use 𝜋 = 3.14)

Find the zeroes of the quadratic polynomial 4s² – 4s + 1 and verify the relationship between the zeroes and the coefficients.

Prove that

OR
Prove that sec A (1 – sin A) (sec A + tan A) = 1.

A bag contains 6 red, 4 black and some white balls.
(i) Find the number of white balls in the bag if the probability of drawing a white ball is 1/3 .
(ii) How many red balls should be removed from the bag for the probability of drawing a white ball to be 1/2 ?

The following table gives the distribution of the life time of 400 neon lamps:
OR

Find the average life time of a lamp.