effective answers in it very helpfull

ICSE EXAMINATION PAPER - 2024
MATHEMATICS
Class-10th
(Solved)
Maximum Marks: 80
Time allowed: Two and half hours
Answer to this Paper must be written on the paper provided separately.
You will not be allowed to write during first 15 minutes.
This time is to be spent in reading the question paper.
The time given at the head of this Paper is the time allowed for writing the answers.
Attempt all question from Section A and any four questions from Section B.
All working, including rough work, must be clearly shown, and must be done on
the same sheet as the rest of the answer.
Omission of essential working will result in loss of marks.
The intended marks for questions or parts questions are given in brackets [ ]
Mathematical tables and graph papers are to be provided by the school.

SECTION-A (40 MARKS) (vii) The given table shows the distance covered and the
(Attempt all questions from this Section.) time taken by a train moving at a uniform speed
along a straight track.
Question 1  [15]
Distance (in m) 60 90 y
Choose the correct answers to the questions from
the given options. Time (in s) 2 x 5
(Do not copy the questions, write the correct answers The values of x and y are:
only.) (a) x = 4, y = 150 (b) x = 3, y = 100
(i) For an Intra-state sale, the CGST paid by a dealer to (c) x = 4, y = 100 (d) x = 3, y = 150
the Central government is ` 120. If the marked price (viii) The 7th term of the given Arithmetic Progression
of the article is ` 2000, the rate of GST is: (A.P.):
(a) 6% (b) 10% 1 1  1 
(c) 12% (d) 16.67% ,   1 ,   2 ....is :
a  a   a 
(ii) What must be subtracted from the polynomial x3 +
x2 – 2x +1, so that the result is exactly divisible by 1  1 
(x – 3)? (a)   6  (b)   7 
a  a 
(a) – 31 (b) – 30
1  1 7 
(c) 30 (d) 31 (c)   8  (d)   7 
(iii) The roots of the quadratic equation px2 – qx + r = 0 a  a 
are real and equal if: (ix) The sum invested to purchase 15 shares of a company
(a) p2 = 4qr (b) q2 = 4pr of nominal value ` 75 available at a discount of 20%
(c) – q = 4pr2
(d) p2 > 4qr is:
2 2  4 x  (a) ` 60 (b) ` 90
(iv) If matrix A =   and A2 =  , (c) ` 1350 (d) ` 900
0 2  0 4  then the
(x) The circumcentre of a triangle is the point which is:
value of x is: (a) at equal distance from the three sides of the
(a) 2 (b) 4 triangle.
(c) 8 (d) 10 (b) at equal distance from the three vertices of the
triangle.
(v) The median of the following observations arranged
in ascending order is 64. Find the value of x: (c) the point of intersection of the three medians.
27, 31, 46, 52, x, x + 4, 71, 79, 85, 90 (d) the point of intersection of the three altitudes of
(a) 60 (b) 61 the triangle.
(c) 62 (d) 66 (xi) Statement 1: sin2 q + cos2 q = 1
(vi) Points A (x, y), B (3, –2) and C (4, –5) are collinear. The Statement 2: cosec2 q + cot2 q = 1
value of y in terms of x is: Which of the following is valid?
(a) 3x – 11 (b) 11 – 3x (a) only 1 (b) only 2
(c) both 1 and 2 (d) neither 1 nor 2
(c) 3x – 7 (d) 7 – 3x

, 2 Oswaal ICSE, MATHEMATICS, Class-X

(xii) In the given diagram, PS and PT are the tangents to (iii) 15, 30, 60, 120... are in G.P. (Geometric Progression).
the circle. SQ || PT (a) Find the nth term of this G.P. in terms of n.
and ∠SPT = 80°. The (b) How many terms of the above G.P. will give the
value of ∠QST is: sum 945?  [4]
(a) 140° Question 3
(b) 90° (i) Factorize: sin3q + cos3q
(c) 80° Hence, prove the following identity:  [4]
(d) 50° sin 3 cos3
 sincos 1
(xiii) Assertion (A): A die is thrown once and the prob- sin cos
2 (ii) In the given diagram, O is the centre of the circle.
ability of getting an even number is .
3 PR and PT are R
Reason (R): The sample space for even numbers on two tangents
a die is {2, 4, 6}. drawn from Q
(a) A is true, R is false. the external N
(b) A is false, R is true. point P and
(c) Both A and R are true. touching the 42°
O
(d) Both A and R and false. circle at Q and
(xiv) A rectangular sheet of paper of size 11 cm × 7 cm S respectively. M
is first rotated about the side 11 cm and then about MN is a 25°
P T
the side 7 cm to form a cylinder, as shown in the dia- diameter of the S

gram. The ratio of their curved surface areas is: circle. Given ∠PQM = 42° and ∠PSM = 25°.  [4]
Find:
(a) ∠OQM (b) ∠QNS
7 cm




(c) ∠QOS (d) ∠QMS
7 cm




(iii) Use graph sheet for this question. Take 2 cm = 1 unit
along the a  [5]
11 cm 11 cm (a) Plot A(0, 3), B(2, 1) and C(4, –1).
(a) 1:1 (b) 7:11 (b) Reflect point B and C in y-axis and name their
11p 7 p images as B’ and C’ respectively. Plot and write
(c) 11:7 (d) : coordinates of the points B’ and C’.
7 11
(c) Reflect point A in the line BB’ and name its
(xv) In the given diagram, DABC ~ DPQR. If AD and PS images as A’.
are bisectors of ∠BAC and ∠QPR respectively then: (d) Plot and write coordinates of point A’.
A
P (e) Join the points ABA’B’ and give the geometrical
name of the closed figure so formed.
SECTION-B (40 MARKS)
(Attempt any four questions from this Section.)
Question 4
B
D
C Q
S
R (i) Suresh has a recurring deposit account in a bank.
He deposits ` 2000 per month and the bank pays
(a) DABC ~ DPQS (b) DABD~ DPQS
interest at the rate of 8% per annum. If he gets ` 1040
(c) DABD~ DPSR (d) DABC ~ DPSR
as interest at the time of maturity, find in years total
Question 2
time for which the account was held.  [3]
x 0  4 0  4 0 
(i) A   ,B    and C    (ii) The following table gives the duration of movies in
1 1  y 1  x 1  [4]
minutes.  [3]

Find the values of x and y, if AB = C. Duration
No. of movies
(ii) A solid metallic cylinder is cut into two identical (in minutes)
halves along its height (as shown in the diagram). 100 - 110 5
The diameter of the cylinder is 7 cm and the height 110 - 120 10
is 10 cm. Find:  [4] 120 - 130 17
(a) the total surface area (both the halves). 130 - 140 8
(b) the total cost of painting the two halves at the 140 - 150 6
 22 
rate of 30 per cm2 Use p   150 - 160 4
 7 
Using step - deviation method, find the mean
duration of the movies.
( a  b )3 64
(iii) If  [4]
( a  b )3 27 
ab
(a) Find
ab
(b) Hence using properties of proportion, find a : b.