List of top Mathematics Questions

If the area and perimeter of a circle are numerically the same, then the radius of that circle will be:

In \( \triangle PQR \), \( \angle Q = 90^\circ \), if \( \tan P = \frac{1}{\sqrt{3}} \), then find the value of \( \sin P \cos R + \cos P \sin R \).

Find the length of a line segment joining the points \( A(2, -2) \) and \( B(3, 7) \).

Find the roots of the quadratic equation \( 4x^2 + 3x + 5 = 0 \).

The distance of the point \( (-3, 5) \) from the y-axis will be:

If ratio of volumes of two spheres is \( 27 : 64 \), then ratio of their surface areas will be:

If \( 3 \cot \theta = 4 \), then the value of \( \cos \theta \) will be:

Value of \( \frac{\sin 15^\circ}{\cos 75^\circ} \) will be:

The mean of the following table will be:

If mode and mean of some observations are 45 and 27 respectively, then median will be:

The roots of the equation \( x^2 - 2x + 1 = 0 \) will be:

The sum of powers of prime factors of the number 144 will be:

The biggest number which divides 125 and 70, and gives remainder 8 and 5 respectively will be:

If \( AB = 6\sqrt{3} \) cm, \( AC = 12 \) cm and \( BC = 6 \) cm in triangle \( ABC \), then the value of \( \angle B \) will be:

If \( C \left( \frac{\alpha}{8}, 4 \right) \) is the mid-point of the line joining the points \( A(-4, 2) \) and \( B(5, 6) \), then the value of \( \alpha \) will be:

If \( \sin \theta = \cos \theta \), \( 0^\circ \leq \theta \leq 90^\circ \), then the value of \( \theta \) is:

If the length of diagonals of a rhombus are 12 cm and 16 cm, then the length of the side of the rhombus will be:

If one root of the equation \( x^2 + kx - 6 = 0 \) is -2, then the value of \( k \) will be:

A hollow sphere whose inner and outer diameters are 4 cm and 8 cm respectively is melted to form a cone whose base is 8 cm in diameter. Find the slant height and curved surface area of the cone.

A well of 3 meter in diameter is dug to a depth of 14 meter. An embankment is made by spreading the soil out of it, making a circular ring of 4 meters wide, evenly around the well. Find the height of the embankment.

From the top of a tower 60 meters high, the angles of depression of top and bottom of a building (house) are 45° and 60° respectively. Find the height of the building and its distance from the tower.

Solution of equations \( 3x + 2y = 6 \) and \( y = 0 \) will be:

Two poles of equal height are placed opposite to each other on either side of a road 80 meters wide. From a point on the road between these two poles, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of the poles and the distance from the point from the poles.

Sum of areas of two squares is 117 m\(^2\). If the difference between their perimeters is 12 m, then find the sides of both the squares.

Solve the following pair of equations by converting these into linear pair of equations: \[ \frac{1}{2x} - \frac{1}{3y} = 2, \quad \frac{1}{3x} + \frac{1}{2y} = \frac{13}{16}. \]