ICSE 10th Maths question paper - 2024

For an Intra-state sale, the CGST paid by a dealer to the Central government is ₹120. If the marked price of the article is ₹2000, the rate of GST is:

What must be subtracted from the polynomial x³ + x² - 2x + 1, so that the result is exactly divisible by (x-3)?

The roots of the quadratic equation px² - qx + r = 0 are real and equal if:

If matrix A = [[2, 2], [0, 2]] and A² = [[4, x], [0, 4]], then the value of x is:

The median of the following observations arranged in ascending order is 64. Find the value of x: 27, 31, 46, 52, x, x + 4, 71, 79, 85, 90

Points A(x, y), B(3, -2) and C(4, -5) are collinear. The value of y in terms of x is:

The given table shows the distance covered and the time taken by a train moving at a uniform speed along a straight track. The values of x and y are:

Distance (in m): 60, 90, y
Time (in s): 2, x, 5

The 7th term of the given Arithmetic Progression (A.P.): 1/a, (1/a + 1), (1/a + 2)... is

The sum invested to purchase 15 shares of a company of nominal value ₹75 available at a discount of 20% is:

The circumcentre of a triangle is the point which is:

Statement 1: sin²θ + cos²θ = 1
Statement 2: cosec²θ + cot²θ = 1
Which of the following is valid?

In the given diagram, PS and PT are the tangents to the circle. SQ || PT and ∠SPT = 80°. The value of ∠QST is:

Assertion (A): A die is thrown once and the probability of getting an even number is 2/3
Reason (R): The sample space for even numbers on a die is {2, 4, 6}.
Which of the following is valid?

A rectangular sheet of paper of size 11 cm × 7 cm is first rotated about the side 11 cm and then about the side 7 cm to form a cylinder. The ratio of their curved surface areas is:

In the given diagram, ΔABC ~ ΔPQR. IF AD and PS are bisectors of ∠BAC and ∠QPR respectively then:

What is the common ratio of the geometric progression 2, 8, 32, 128...?

If a coin is tossed and a six-sided die is rolled, what is the probability of getting a head on the coin and an even number on the die?

If a quadratic equation has roots -2 and 5, which of the following is the equation?

The solution set for the inequation 3x + 5 < 14, x ∈ N is:

If [[3, 2], [1, 4]] * [[1, 0], [0, 1]] = [[x, y], [z, w]], the value of x, y, z, and w are:

A man's salary is increased by 20% and then decreased by 20%. The percentage change in his salary is:

The selling price of a product including 18% GST is ₹1180. The original price of the product is:

The sum of the first 10 terms of an Arithmetic Progression is 120. If the first term is 3, what is the common difference?

If a, 2, 8 are in geometric progression, the value of a is:

The polynomial 2x³ - 5x² + ax + b has factors (x-1) and (x+2). The value of a and b respectively are:

The coordinates of the centroid of a triangle with vertices (2, 3), (4, 5) and (6, 7) is:

A box contains 5 red marbles and 7 blue marbles. If a marble is drawn at random, what is the probability that it is a blue marble?

The mean of the data 5, 8, x, 12, 15 is 10. The value of x is:

If sinθ = 3/5, what is the value of cosθ?

What is the slope of the line passing through points (2, 5) and (4, 9)?

The volume of a cone with radius 3 cm and height 4 cm is:

What is the solution set for the linear inequation 2x+1 > 7, x ∈ I?

The number of lines of symmetry in an equilateral triangle is:

The sum of the roots of the quadratic equation 2x² - 8x + 5 = 0 is:

If A = [[1, 2], [3, 4]] and B = [[-1, 0], [2, 1]], then A+B is:

The volume of a sphere with a radius of 3 cm is:

A recurring deposit account is opened for 2 years with a monthly installment of ₹500. If the rate of interest is 12% per annum, the interest earned is:

The distance between the points (2, 3) and (-1, 7) is:

The value of 2sin30° + 3cos60° is:

What is the mode of the data set: 2, 3, 5, 2, 7, 3, 2, 8?

If (x+1) is a factor of the polynomial x³ + 4x² + ax - 2, then the value of 'a' is:

If a, b, c, d are in proportion, which of the following is true?

A man buys 10 shares of a company with a nominal value of ₹50 each at a premium of ₹10. The total investment is:

In a right-angled triangle, if the sides are in the ratio 3:4:5, the measure of the angles are:

The distance of the point (3, 4) from the origin is:

The volume of a cuboid with length 5 cm, width 4 cm, and height 3 cm is:

The circumference of a semi-circle with diameter 14 cm is:

The sum of the first 'n' odd natural numbers is:

If a point (p, 2) lies on the line 3x + 4y = 11, the value of p is:

The value of 2sinAcosA is equal to: