SAMPLE QUESTION PAPER

I.C.S.E. – MATHS (2024 – 25)

[ SECTION - A ]

Q1. Multiple Choice Questions: [1 × 15]

i) If x + 3 divides x2 + kx + 12, then k is-

a) 8 b) 7 c) 6 d) 4
ii) The probability of getting a number, divisible by 3 in throwing a die is-
1 1 1 2
a) 6 𝑏) 3 𝑐) 2 d)3
iii) Which one of the following is an inter-state GST mode?
a) CGST b) SGST c) IGST d) UTGST
iv) The slope of the line 3x + y – 12 = 0 is-
−1 −1
a) 3 𝑏) − 3 𝑐) 2 𝑑) 2
1 2 1 2
v) A = & B= 𝑎𝑟𝑒 𝑡𝑤𝑜 𝑒𝑞𝑢𝑎𝑙 𝑚𝑎𝑡𝑟𝑖𝑐𝑒𝑠, 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑥 𝑖𝑠
4𝑥 3 8 3
a) 3 b) 4 c) 2 d) -2
vi) The solution of inequation: 3-2x ≥ 𝑥 − 12 , x∈ 𝑁 𝑖𝑠-
a) {5, 6, 7} b) {1, 2, 3, 4, 5} c) {1, 2, 3, 4} d) {6, 7, 8}
vii) Which of the term of the AP : 3, 7, 11, 15, …. Will be 132 less than its 78th term?
a) 54 b) 45th c) 32nd d) none
th

viii) The reflection of the point p (1, -2) in the line y = -1 is-
a) (-3, -2) b) (1, -4) c) (1, 4) d) (1, 0)
ix) The equation of the line joining points (3,4) and (5, 8) is-
1) Y = 2x -1 (2) y = 2x + 2 (3) y = 2x + 1
a) Only 1 b) Only 2 c) Only 3 d) neither 1 nor 2
x) The locus of the mid point of the radii of the circle is-
a) Concentric circle b) concentric circle with half the radius c) diameter of the circle d) chord of a circle.
xi) The mean of the following numbers 23, 45, 87, 40 and 50 is-
a) 39 b) 49 c) 34 d) 56
xii) A round roller has diameter 1m and length 2m. Area of the road covered by it in 100 rev ( in sq m) is-
a) 200 ᴨ b) 400 ᴨ c) 100 ᴨ d) none
xiii) The nature of the roots of the equation 4x 2 - 12x + 9 = 0 is-
a) Real roots b) Real & equal roots c) Not real Roots d) Real unequal roots
xiv) If 6 : x : : 2 : 13, Find x-
a) 93 b) 94 c) 39 d) 40
xv) A vertical stick 12 cm long casts shadow 8cm long on the ground & at the same time a tower casts shadow
40 cm long. The height of the tower is-
a) 60 b) 30 c) 90 d ) none
√(𝑎+1) + √(𝑎−1)
Q2. i) If : = x, Using properties of proportion show that x2 – 2ax +1 =0 [4]
√𝑎+1 − √(𝑎−1)

1
ii) Sonia had a recurring deposit account in a bank and deposited Rs 600 per month for 2 2 𝑦𝑒𝑎𝑟𝑠. If the rate
of interest was 10% p.a. Find the maturity value of this account. [4]
√( 1+cos 𝐴)
iii) Prove that = 𝐶𝑜𝑠𝑒𝑐 𝐴 + cot 𝐴. [4]
√(1−cos 𝐴)
Q3. i) The difference between the outer & inner curved surfaces of a cylinder 14 cm long is 88 cm 2. Find the
outer and the inner radii of the cylinder, given that the volume of the metal is 176 cm3.
[4]
𝑎 𝑐 𝑒 (𝑎 3+ 𝑏3 )2 𝑒6
ii) If 𝑏 = = , prove that (𝑏3 + 𝑑3 )2 = 𝑓6 [4]
𝑑 𝑓

iii) Use graph paper for this question

a) The point P (2, -4) is reflected about the line x = 0 to get the image Q. Find the coordinate of Q.
b) Point Q is reflected about the line y = 0 to get the image R. Find the coordinate of R.
c) Name the fig PQR.
d) Find the area of PQR. [5]

[ SECTION – B ]

5 4 −4 7
Q4. i) If [ ] − 3𝑋 = [ ]
8 −3 5 −9
Find the matrix X [3]
ii) If the rate of GST is 5%, Mr Arun Lal has to pay Rs 7200 for a
coat. What amount he has to [3]
pay if the rate of GST is increased by 7%?

iii) In the given fig AB is a diameter of a circle with centre O &

CP is the tangent to the circle at point C. If AP = 20 cm & CP =
10 cm. Find the radius of the circle. [4]

Q5. i) Find the equation of the line through (0, -3) & perpendicular to the line joining (-3, 2) & (4, 1).
[3]
ii) One card is drawn at random from a well shuffled pack of 52 cards. Find the probability that the card
drawn is :
a) A face card b) Neither king nor queen c) A red queen. [3]
iii) The sum of first 7 terms of A.P is 49 & that of first 17 terms is 289. Find the sum of first 30 terms. [4]

Q6. i) Find the value of K for which Kx(x - 2) + 6 = 0 has real and equal roots. [3]
ii) If a, b, c, d are in proportion, Prove that (5a + 7b)(2c – 3d) = (5c + 7d)(2a – 3b) [3]
iii) If (x+2) & (x -3) are factors of x3 + ax + b, Find a & b. With these values factorise the expression. [4]

Q7.i) A man invests Rs 9600 shares on Rs 100 shares at Rs 80. If the company pays him 18% dividend find
a) The number of shares he buys
b) His total dividend
c) His percentage of return on the share. [3]
ii) Solve the inequation & represent the solution on the number line.
3𝑥 −2
4x – 19 ≤ 5
−2 ≤ 5
+ 𝑥, 𝑥 ∈ 𝑅 [3]
5
iii) The line segment A (-1, ) & B (a, 5) is divided in the ratio 1 : 3 at P, the point where the segment AB
3
intersects the Y axis.
Calculate a) The value of a (b) the coordinates of P. [4]
Q8. i) Compute mean for the following table: (By step- deviation method) [3]

MARKS NUMBER OF STUDENTS

Less that 10 12
Less that 20 19
Less that 30 35
Less that 40 47
Less that 50 58
Less that 60 65
Less that 70 84
Less that 80 100

ii) < EDB = < ACB. If BE = 6cm EC = 4cm BD = 5cm & area ∆ 𝐵𝐸𝐷 = 9cm2.
Calculate a) length of AB b) Area of ∆ 𝐴𝐵𝐶.
[3]

iii) Construct a ∆ 𝐴𝐵𝐶 with BC = 6.5 cm, AB = 5.5 cm & AC = 5 cm. Construct the incircle of the triangle.
Measure and record the radius of the incircle. [4]

−1 1
Q9. i) the 2nd and the 5th terms of a GP are 𝑎𝑛𝑑 respectively. Find the sum of the series upto 8 terms.
2 16
[3]
ii) Prove that (sin A + cos A)(tan A + cot A) = sec A + cosec A [3]
iii) From a circular cylinder of diameter 10cm & height 12cm, a conical cavity of the same base radius & of
the same height is hollowed out. Find the Volume & the whole surface area of the remaining solid. (Take ᴨ =
3.14) [4]

Q10. i) The following table shows the age distribution of cases of certain disease admitted during a year in
particular hospital. [5]

AGE (in years) NUMBER OF CASES

4.5 – 14.5 6
14.5 – 24.5 11
24.5 – 34.5 21
34.5 – 44.5 23
44.5 – 54.5 14
54.5 – 64.5 5

Draw a histogram, frequency polygon & hence find the mode from the graph.

ii) A pole of height 5m is fixed on the top the tower. The angle of elevation of the top of the pole as observed
from a point A on the ground is 60° 𝑎𝑛𝑑 the angle of depression of the point A from the top of the tower is
45°. Find the height of the tower. (√3 = 1.732) [5]

_______________________________