List of top Mathematics Questions

The monthly incomes of A and B are in the ratio 8 : 7 and their expenditures are in the ratio 19 : 16. If each saves Rs 2500 per month, find the monthly income of each

A circle is inscribed in a right-angled triangle ABC, right-angled at B. If BC = 7 cm and AB = 24 cm, find the radius of the circle

From an external point $P$, two tangents $PA$ and $PB$ are drawn to a circle with centre $O$. At a point $E$ on the circle, a tangent is drawn which intersects $PA$ and $PB$ at $C$ and $D$ respectively. If $PA = 10$ cm, find the perimeter of $\triangle PCD$.

Prove that: \[ \frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta \]

Calculate the mean of the following data :

Class :	4 – 6	7 – 9	10 – 12	13 – 15
Frequency :	5	4	9	10

The sum of two numbers is 18, and the sum of their reciprocals is $\frac{1}{4}$. Find the numbers.

Solve for $x$: \[ \frac{4}{x} - \frac{5}{2x + 3} = 3. \]

$ABCD$ is a trapezium with $AB \parallel DC$. $AC$ and $BD$ intersect at $E$. If $\triangle AED \sim \triangle BEC$, then prove that $AD = BC$.

The interior of a building is in the form of a cylinder of base radius 12 m and height 3×5 m surmounted by a cone of equal base and slant height 14 m. Find the internal curved surface area of the building.

Determine the ratio of the volume of a cube to that of the sphere which will exactly fit inside the cube.

The vertices of a quadrilateral ABCD are A(6, – 2), B(9, 2), C(5, – 1) and D(2, – 5). Prove that ABCD is a rhombus, and not a square.

For what value of \(k\), the product of zeroes of the polynomial \(kx^2 - 4x - 7\) is 2?

In an A.P., if \(a = 8\) and \(a_{10} = -19\), then value of \(d\) is:

The mid-point of the line segment joining the points \((-1, 3)\) and \(\left(8, \frac{3}{2}\right)\) is:

If \(\sin \theta = \frac{1}{3}\), then \(\sec \theta\) is equal to:

HCF \((132, 77)\) is:

If the roots of quadratic equation \(4x^2 - 5x + k = 0\) are real and equal, then value of \(k\) is:

If probability of winning a game is \(p\), then probability of losing the game is:

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

For what value of \(\theta\), \(\sin^2\theta + \sin\theta + \cos^2\theta\) is equal to 2?

A card is drawn from a well-shuffled deck of 52 playing cards. The probability that drawn card is a red queen, is:

If a certain variable \(x\) divides a statistical data arranged in order into two equal parts; then the value of \(x\) is called the:

The radius of a sphere is \(\frac{7}{2}\) cm. The volume of the sphere is:

The mean and median of a statistical data are 21 and 23 respectively. The mode of the data is:

The height and radius of a right circular cone are 24 cm and 7 cm respectively. The slant height of the cone is: