List of top Mathematics Questions

Show that the square of an odd integer is of the form \( 8k + 1 \).

The ratio of incomes of two persons is \(9:7\) and the ratio of their expenditures is \(4:3\). If each of them saves Rs. \(5000\) per month, find their monthly incomes.

Find the area of a circle whose radius is 7 cm.

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

Define mode of a frequency distribution.

State and prove Basic Proportionality Theorem.

Write down the formula to find the area of a triangle whose vertices are \((x_1,y_1)\), \((x_2,y_2)\) and \((x_3,y_3)\).

Write down the quadratic equation whose roots are 2 and -3.

What is the first term of the quotient when \(2x^3 + x^2 - 3x + 5\) is divided by \(1 - 3x + x^2\)?

Prove that the area of a sector of sectorial angle \( \theta \) and radius \( r \) is \( \dfrac{\pi r^2 \theta}{360} \).

Write the full form of SCORES.

How many tangents can be drawn to a circle through a point lying outside the circle?

Write the statement of Euclid's Division Lemma.

In a right triangle \( ABC \), right angled at \( B \), prove that \( \sin A = \cos (90^\circ - A) \) and \( \cos A = \sin (90^\circ - A) \).

Solve the quadratic equation \(ax^2 + bx + c = 0\), \((a \neq 0)\) by the method of completing square.

If $p(x)$ is a polynomial of degree $\geq 1$ and $a$ is any real number, then the remainder when $p(x)$ is divided by $x-a$ is

The remainder when \(4x^3 + 4x^2 + x - 4\) is divided by \(2x - 1\) is

The volume of the hemisphere of radius \(r\) is

Solve graphically:
\[ 2x + 3y = 5 \] \[ 5x - 4y + 22 = 0 \]

A point P is at a distance of 13 cm from the centre of a circle. If the radius of the circle is 5 cm, the length of the tangent from P to the circle is

The sum of the first n terms of the AP whose first term is 1 and common difference is 2 is :

If $x + 1$ is a factor of $p(x) = 4x^2 + 3x + k$, then the value of $k$ is

If one root of the equation $2x^2 - 3x + k = 0$ be reciprocal of the other, then the value of $k$ is

Two concentric circles are of radii \(6\) cm and \(10\) cm. The length of a chord of the larger circle which touches the smaller circle is

Length of an arc of a sector of a circle with radius \(r\) and sectorial angle \(\theta\) (measured in degrees) is