ICSE 10th Maths question paper 2nd Semester - 2022

The probability of getting a number divisible by 3 in throwing a dice is:

The volume of a conical tent is 462 m³ and the area of the base is 154 m², the height of the cone is:

The median class for the given distribution is: Class Interval: 0-10, 10-20, 20-30, 30-40. Frequency: 2, 4, 3, 5.

If two lines are perpendicular to one another then the relation between their slopes m₁ and m₂ is:

A lighthouse is 80 m high. The angle of elevation of its top from a point 80 m away from its foot along the same horizontal line is:

The modal class of a given distribution always corresponds to the:

The coordinates of the point P(-3,5) on reflecting on the x-axis are:

ABCD is a cyclic quadrilateral. If ∠BAD = (2x+5)° and ∠BCD = (x+10)° then x is equal to:

The points A(1,4), B(4,1) and C(x,4) are the vertices of a triangle. If the centroid of the triangle is G (4,3), then x is equal to:

The radius of a roller 100 cm long is 14 cm. The curved surface area of the roller is:

Using remainder theorem, find the value of k if on dividing 2x³+3x²-kx+5 by x - 2, leaves a remainder 7.

Given A = [2 0; -1 7], I = [1 0; 0 1] and A² = 9A + mI. Find m.

The mean of the numbers 45, 52, 60, x, 69, 70, 26, 81, and 94 is 68. Find the value of 'x'.

The slope of a line joining P(6,k) and Q(1-3k,3) is 1/2. Find the value of k.

If b is the mean proportion between a and c, show that (a⁴+a²b²+b⁴)/(b⁴+b²c²+c⁴) = a²/c²

Solve the equation 4x²-5x-3=0 and give your answer correct to two decimal places.

AB and CD are two parallel chords of a circle with radius 13 cm. If AB=24 cm and CD=10 cm, find the distance between the two chords.

Evaluate without using trigonometric tables: sin²28°+sin²62°+tan²38°-cot²52°+1/4 sec²30°

If A = [3 1; -3 2] and B = [3 4; -2 1] and A²-5B²=5C. Find matrix C, where C is a 2x2 matrix.

Jaya borrowed Rs. 50,000 for 2 years. The rates of interest for two successive years are 12% and 15% respectively. She repays 33,000 at the end of the first year. Find the amount she must pay at the end of the second year to clear her debt.

Find the value of 'x' and 'y' if: 2[x 7; 9 y-5] + [6 -7; 4 5] = [10 7; 22 15]

Sonia had a recurring deposit account in a bank and deposited 600 per month for 2½ years. If the rate of interest was 10% p.a., find the maturity value of this account.

Cards bearing numbers 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20 are kept in a bag. A card is drawn at random. Find the probability of getting a prime number.

The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. Find the volume of the cylinder. (use π=22/7)

Solve the following inequation and write down the solution set: 11x-4 < 15x+4 ≤ 13x+14, x ∈ W

A man invests 4500 in shares of a company which is paying 7.5% dividend. If Rs. 100 shares are available at a discount of 10%, find the number of shares he purchases.

In a class of 40 students, marks obtained by the students in a class test (out of 10) are given below. Calculate the median. Marks: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Number of students: 1, 2, 3, 3, 6, 10, 5, 4, 3, 3.

Solve the following Quadratic Equation: x²-7x+3=0. Give your answer correct to two decimal places.

Given A = [x 3; y 3]. If A² = 3I, where I is the identity matrix of order 2, find x and y.

Use factor theorem to factorise 6x³+17x²+4x-12 completely.

A man observes the angle of elevation of the top of a tower to be 45°. He walks towards it and on covering 20 m the angle of elevation changes to 60°. Find the height of the tower correct to 2 significant figures.

The difference of two natural numbers is 7 and their product is 450. Find the numbers.

A model of a high rise building is made to a scale of 1:50. If the height of the model is 0.8 m, find the height of the actual building.

From a solid wooden cylinder of height 28 cm and diameter 6 cm, two conical cavities are hollowed out. The diameters of the cones are also 6 cm and their height is 10.5 cm. Find the volume of the remaining solid.

The 4th term of an A.P. is 22 and 15th term is 66. Find the first term and the common difference.

The angles of depression of two ships A and B as observed from the top of a lighthouse 60 m high are 60° and 45° respectively. If the two ships are on opposite sides of the lighthouse, find the distance between the two ships. Give your answer correct to the nearest whole number.

Using the Remainder Theorem find the remainders obtained when x³+(kx+8)x+k is divided by x+1 and x-2. Hence find k if the sum of the two remainders is 1.

The sum of the ages of a father and his son is 45 years. The product of their ages in years is 550. Find their ages.

A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be 'x' km/h, form an equation and solve it to evaluate 'x'.

Prove that: cosA/(1+sinA) + tanA = secA

If the 6th term of an A.P. is equal to four times its first term and the sum of first six terms is 75, find the first term and the common difference.

From a point P on the ground, the angle of elevation of the top of a tower is 30°. On moving 20 m towards the tower, the angle of elevation becomes 60°. Find the height of the tower.

The mean of the numbers 2, 4, x, 6, 8, 10, 12 is 7. Find the value of x.

The volume of a right circular cone is 1232 cm³. If its height is 24 cm, find its radius.

Find the value of k for which the quadratic equation kx² - 5x + 3 = 0 has real roots.

A die is thrown. Find the probability of getting a number less than 3.

The perimeter of a rectangular field is 48 m and its area is 128 m². Find the length and breadth of the field.

Find the value of 'a' and 'b' if (a+b, 2a-3b) = (5, 0).

A sum of money doubles itself at a certain rate of simple interest in 10 years. In how many years will it triple itself?

Find the sum of the series: 1 + 3 + 5 + ... + 49