List of top Mathematics Questions

The first term of an AP is $p$ and the common difference is $q$, then its 10th term is :

Shown below are three triangles. The measures of two adjacent sides and included angle are given for each triangle :

Which of these triangles are similar?

If $\cos y = 0$, then what is the value of $\frac{1}{2} \cos \frac{y}{2}$ ?

For an event $E$, $P(E) + P(\bar{E}) = x$, then the value of $x^2 - 3$ is :

The HCF of 96 and 432 is :

Prove that $\sqrt{3}$ is an irrational number.

A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is $20\text{ cm}$ and the diameter of the cylinder is $7\text{ cm}$. Find the total volume of the solid. (Use $\pi = \frac{22}{7}$)

The coordinates of the centre of a circle are $(x - 7, 2x)$. Find the value(s) of $'x'$, if the circle passes through the point $(-9, 11)$ and has radius $5\sqrt{2}$ units.

The mean of the following frequency distribution is 35. Find the values of $x$ and $y$, if the sum of frequencies is 25:

Two concentric circles are of radii $5\text{ cm}$ and $4\text{ cm}$. Find the length of the chord of the larger circle which touches the smaller circle.

Find the ratio in which the $x$-axis divides the line segment joining the points $(-6, 5)$ and $(-4, -1)$. Also, find the point of intersection.

Determine graphically, the coordinates of vertices of a triangle whose equations are $2x - 3y + 6 = 0$; $2x + 3y - 18 = 0$ and $x = 0$. Also, find the area of this triangle.

A die is thrown once. Probability of getting a number other than 3 is :

If the mean and mode of a data are 12 and 21 respectively, then its median is :

If $\alpha, \beta$ are the zeroes of the polynomial $p(x) = x^2 - 3x - 1$, then find the value of $\frac{1}{\alpha} + \frac{1}{\beta}$.

The total surface area of a solid hemisphere of diameter $'2d'$ is :

Assertion (A) : The polynomial $p(y) = y^2 + 4y + 3$ has two zeroes.
Reason (R) : A quadratic polynomial can have at most two zeroes.

Assertion (A) : The probability that a leap year has 53 Mondays is $\frac{2}{7}$.
Reason (R) : The probability that a non-leap year has 53 Mondays is $\frac{5}{7}$.

The length of the arc of the sector of a circle with radius $21\text{ cm}$ and of central angle $60^\circ$, is :

The hour hand of a clock is $7\text{ cm}$ long. The angle swept by it between 7:00 a.m. and 8:10 a.m. is :

In the given figure, PA is a tangent from an external point P to a circle with centre O. If $\angle POB = 125^\circ$, then $\angle APO$ is equal to :

A car is moving away from the base of a $30\text{ m}$ high tower. The angle of elevation of the top of the tower from the car at an instant, when the car is $10\sqrt{3}\text{ m}$ away from the base of the tower, is :

If $\cos A = \frac{1}{2}$, then the value of $\sin^2 A + 2\cos^2 A$ is :

If TP and TQ are two tangents to a circle with centre O from an external point T so that $\angle POQ = 120^\circ$, then $\angle PTQ$ is equal to :

If $\Delta ABC$ and $\Delta DEF$ are similar such that $2 AB = DE$ and $BC = 8\text{ cm}$, then $EF$ is equal to :