Class 10 Mathematics | ICSE Board Board | Mixed Level Practice Test - 40 Questions (2026)

If A = \begin{bmatrix} 2 & -1 \\ 3 & 0 \end{bmatrix} and B = \begin{bmatrix} 1 & 2 \\ -2 & 1 \end{bmatrix}, then find 2A - B.

The coordinates of the point which divides the line segment joining A(1, 3) and B(4, 6) in the ratio 2:1 internally are:

If the mean of the following data is 20, find the value of p: x: 15, 17, 19, 20+p, 23; f: 2, 3, 4, 5, 6

A bag contains 5 red balls and 3 blue balls. A ball is drawn at random. What is the probability that the ball drawn is blue?

The curved surface area of a right circular cylinder is 4.4 m$^2$. If the radius of the base is 0.7 m, find its height.

If the roots of the quadratic equation $2x^2 + kx + 3 = 0$ are equal, then the value of k is:

If tan A = \frac{5}{12}, find the value of (sin A + cos A)sec A.

Solve the following inequation and represent the solution on the number line: 3x - 2 \le 7 + 2x, x \in R

If the 6th term of an A.P. is 19 and the 17th term is 41, then the 40th term is:

A shopkeeper buys a TV set for ₹ 9,000 and sells it for ₹ 10,800. Find the gain percent.

If the matrix A = $\begin{bmatrix} 2 & 1 \ 3 & 2 \end{bmatrix}$, find the value of |A|.

A die is thrown once. What is the probability of getting a number greater than 4?

Find the value of 'p' for which the quadratic equation $px^2 - 6x + 9 = 0$ has equal roots.

If the curved surface area of a cone is 1232 cm$^2$ and the radius of its base is 56 cm, then find the slant height of the cone.

The coordinates of the midpoint of the line segment joining the points (2, -3) and (4, 7) are:

Solve the following inequation: $3x - 2 \geq 7$ and $2x - 3 < 5$

Find the value of $\sin 30^{\circ} + \cos 60^{\circ}$.

A shopkeeper buys an article for ₹2500 and sells it for ₹3000. Find his profit percentage.

If $7$ is the mean of $5, 3, 9, 12, 6, x, 8$, find the value of $x$.

If the matrix A = $\begin{bmatrix} 1 & x \\ 0 & 1 \end{bmatrix}$ and $A^2 = I$, where I is the identity matrix, then the value of x is:

The coordinates of the point which divides the line segment joining the points (6, 3) and (-4, 5) in the ratio 3:2 internally are:

If the 6th term of an A.P. is 10 and the 16th term is 30, then the 4th term is:

The angle of elevation of a ladder leaning against a wall is $60^{\circ}$ and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

If the roots of the quadratic equation $x^2 - 4x + k = 0$ are equal, then the value of k is:

The curved surface area of a right circular cylinder of height 14 cm is 88 cm$^2$. The diameter of the base is:

Given sin$\theta$ = $\frac{3}{5}$, find the value of tan$\theta$.

What is the value of $\int_{0}^{1} x^2 dx$?

If the volume of a cube is 64 cm$^3$, then the surface area of the cube is:

If the points A(4,3) and B(x,5) lie on a circle with centre O(2,3), find the value of x.

A bag contains 5 red balls and 3 blue balls. If two balls are drawn at random without replacement, what is the probability that both are red?

If $A = \begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}$, find the value of $|A|$.

The curved surface area of a right circular cylinder of height 14 cm is 88 cm². Find the diameter of the base of the cylinder.

The sum of the first n terms of an A.P. is given by $S_n = 3n^2 + 5n$. Find the common difference.

If tan θ = 4/3, find the value of (3 sin θ + 2 cos θ) / (3 sin θ - 2 cos θ).

What is the reflection of the point (3, -5) in the x-axis?

If the HCF of two numbers is 9 and their LCM is 270, and one of the numbers is 45, find the other number.

Solve the quadratic equation: $x^2 - 5x + 6 = 0$

A man invests ₹2000 at 10% per annum compound interest for 2 years. Find the interest for the 2nd year.

A shopkeeper marks an article at \(₹ 80\). What price should he quote so that after allowing a discount of 20% he still makes a profit of 20% on the cost price of \(₹ 50\)?

If \(A = \begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}\), then find \(|A|\).