Class 10 Question Paper 2022-23 Maths (Half Yearly)

HALF YEARLY EXAMINATION

Question Paper
2022-23

NCERT BASED SYLLABUS
FOR CBSE AND STATE BOARD
FOLLOWING NCERT

QUESTION PAPER
PT-
PT-2/HALF
2/HALF YEARLY EXAMINATION, 2022
2022-
22-23
MATHEMATICS
Time – 3 hrs. Class – X M.M. : 80
Date – 12.09.2022 (Monday)
Name of the student _________________________________________________ Section _____

General Instructions -
• The question paper consists of 26 questions divided into
4 sections A, B, C & D.
• All questions are compulsory.
• Section A comprises of 11 questions of 2 marks each.
Internal choice has been provided in two questions. It
contains two case study-based questions of 5 marks each.
• Section B comprises of 7 questions of 3 marks each.
Internal choice has been provided in two questions.
• Section C comprises of 3 questions of 4 marks each.
Internal choice has been provided in two questions.
• Section D comprises of 3 questions of 5 marks each.
Internal choice has been provided in two questions.

Section - A (2 marks each)
Q1 The HCF of 45 and 105 is 15. Then their L.C. M. is:
a) 305 b) 315 c) 153 d) 113
OR
The L.C. M. of 2 × 3 and 2 × 3 is:
a) 36 b) 216 c) 156 d) 108
Q2 The value of k for which the pair of linear equations 4 − 1 = − 6 and
2 +  − 7 = 0 represents intersecting lines is :
a) k ≠ 3/2 b) k ≠ 2 c) k ≠ 4 d) k ≠ 3
Q3 In the figure, AB is parallel to CD. If  = 3 − 19,  =  − 4,  =  − 3 and OD = 4,
determine x.

a) 5 b) 6 c) 7 d) 8

PT-2 / HALF YEARLY EXAM | MATHEMATICS | CLASS 10 | 2022-23 | PRINTED Q 26 PRINTED PAGES 6 | PAGE# 1

Q4 If A and B are the points −6, 7 and −1, −5 respectively, then the distance 2AB is
equal to :
a) 13 b) 26 c) 169 d) 238
Q5 
If sin
= , then the value of 2 cot 
+ 2 is:

a) 18 b) 26 c) 20 d) 38
Q6 A number is selected at random from the numbers 5 to 35. Then the probability of
selecting a prime number is:
a) 3/10 b) 5/29 c) 11/30 d) 9/31
Q7 Two tankers contain 850 litres and 680 litres of petrol respectively. The
maximum capacity of a container which can measure the petrol of either tanker in
exact number of times is :
a) 17 b) 160 c) 200 d) 170
Q8 If 37 + 43 = 123 and 43 + 37 = 117 are pair of linear equations then the value
of x – y is :
a) -2 b) 2 c) 1 d) - 1
OR
The parallel line of 2x + 5y = –3 is:
a) – 4x + 10y = – 6 b) 2x – 5y = – 3
c) 2x + 5y – 3 = 0 d) 4x + 10y + 6 = 0
Q9 In a ∆ $%&, ‘ $ = 50° and ‘& = 60°. If ∆ $%& ~ ∆ ()*, then ‘ ) is -
a) 70 b) 50° c) 30 d) 60
Q10 From the following statements, which one is correct ?
i) The value of tanA is always less than 1.
ii) sinA = cosA when A is half of right angle.
iii) The value of cosA decreases as A increases.
iv) cosA = 4/3 for some angle A
a) only i) and ii) correct b) only ii) and iii) correct
c) only iii) and iv) correct d) only i) and iv) correct
Q11 From the following statements, which one is correct ?
i) all circles are similar.

ii) all isosceles triangles are similar.
iii) all equilateral triangles are similar.
iv) all squares are similar.
a) only i) and ii) correct b) only ii) and iii) correct
c) only i) , ii) iii) correct d) only i), iii) and iv) correct
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Q12 Case Study 1 (1 mark each)
Shadow’s Similarity:: During an afternoon of 15th August, Indian flag fluttering in
air casted its shadow of length 400 m at 4:00 pm., whereas a girl of height 1.2 m
casted a shadow of 4.8 m at the same time.

Based on the above information answer the following questions:
1. Which of the following is irrelevant in context of finding the height of the flag?
a) Pythagoras theorem b) Similarity
c) Ratio and Proportion d) Sun’s elevation
2. Which criteria is applied for the similarity of FGS and HGQ ?
a) RHS b) AAA c) SAS d) SSS
3. Height of flag is:
a) 50 m b) 100 m c) 150 m d) 200 m
4. The length of FH is :
a) 98.8 cm b) 988 cm c) 9880 cm d) 9800 cm
5. Which of the following is not a criteria for the congruency of triangles?
a) AAA b) SSA c) SSS d) RHS
Q.13 Case Study 2 (1 mark each)
Basketball and Soccer are played with a spherical ball. Even though the athlete
dribbles the ball in both the sports, a basketball player uses his hands and a soccer

player uses his feet. Usually, soccer is played outdoors on a large field and
basketball iss played indoor on a court made out of wood. The projectile (path
traced) of soccer ball and basketball are in the form of parabola representing
quadratic polynomial.

Based on the above information, answer the following questions:
1. The shape of the path traced as shown in the figure is:
a) Spiral b) Ellipse c) Linear d) Parabola
2. The graph of parabola opens upwards, if:
a) a = 0 b) a 0 c) a + 0 d) a , 0
3. Observe the graph and answer the question.

0

How many zeroes are there for the polynomial w.r.t. horizontal axis?
a) 0 b) 1 c) 2 d) 3
4. The three zeroes shown in the above graph are:
a) 2, 3, –1 b) –2, 3, 1 c) –3, –1, 2 d) –2, –3, –1
5. What can be the expression of a quadratic polynomial in which the sum and
the
he product of the zeroes are 1 and 3 respectively?
a)   + x + 3 b)   – x + 3 c)   – 3x – 1 d)   + 3x –1

Section - B (3 Marks each)
Q14 Find the zeroes of the quadratic polynomial 6  + 12 − 17  and verify the
relationship between the zeroes and the coefficients of the polynomial.
x y
Q15 Solve for x and y : + y = 4 ; x − = 8
2 3

OR
Places A and B are 240 km apart on a highway. One car starts from A and another
from B at the same time. If the cars travel in the same direction at different
speeds, they meet in 5 hours. If they travel towards each other, they meet in 2
hours. What are the speeds of the two cars?
Q16 The point R divides the line segment AB, where A(
A(–4, 0) and B(0, 6) such that
3
AR = AB. Find the coordinates of R.
4
sin θ − 2 sin 3 θ
Q17 Show that : = tan θ
2 cos 3 θ − cosθ
Q18 In the given figure, () ∥  and (* ∥  . Prove that )* ∥  .

Q19 axis which is equidistant from the points 5, −2
Find the point on y-axis −  and −3, 2.
Q20 Prove that : (sinA + cosecA)2 + (cosA + secA)2 = tan2A + cot2A + 7
OR
2 0 2 0 2 0 2 0
Evaluate : 2 tan 60 + 3cos 30 − 4 sin 45 + sec 60
Section - C (4 Marks)
Q21 Prove that 2 - 3√5 is an irrational number.
Q22 State and prove Basic proportionality theorem.
OR
Side AB and BE of a right triangle, right angled at B
are of the length 16 cm and 8 cm respectively. What
will be the length of the sides of the largest square
FDGB that can be inscribed in the triangle ABE.

Q23 A card is drawn at random from a well-shuffled deck of playing cards. Find the
probability that the card drawn is (i) a card of spade or an ace (ii) a black king (iii)
neither a jack nor a king (iv) either a king or a queen.
OR
A die is thrown once. Find the probability of getting -
a) a prime number b) a composite number
c) a factor of 6 d) a multiple of 2

Section - D (5 marks)
Q24 If we add 1 to the numerator and subtract 1 from the denominator, a fraction

reduces to 1. It becomes if we only add 1 to the denominator. What is the

fraction?
OR
The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5
units and breadth is increased by 3 units. If we increase the length by 3 units and
the breadth by 2 units, the area increases by 67 square units. Find the dimensions
of the rectangle.
/
Q25 Given tan A= , find the other trigonometric ratios of angle A.

OR
Prove the following identity, where the angle involved is an acute angle for which
the expression is defined as:
1
01230  − sin  sec  − cos  =
tan  + cot 

Q26 A group consists of 12 persons of which 3 are extremely patient, other 6 are
extremely honest and rest are extremely kind. A person is equally likely to be
selected, find the probability of selecting a person who is:

a) Extremely patient
b) Extremely kind or honest
c) Extremely patient and kind.

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HALF YEARLY EXAM
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