List of top Mathematics Questions

Find two consecutive negative integers, sum of whose squares is 481.

Solve any one of the following internal choices (a) or (b):
32(a) The median of the following data is 137. Find the values of x and y, given that total of frequencies is 68.

Find the length of the plank that can be used to measure the lengths 4 m 20 cm and 5 m 4 cm exactly, in the least time.

The diagonals of a quadrilateral ABCD intersect each other at the point O such that $\frac{AO}{OC} = \frac{BO}{OD}$. Show that quadrilateral ABCD is a trapezium.

A toy is in the form of a cone mounted on a hemisphere of radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.

Assertion (A) : $\tan 2\theta$ is not defined at $\theta = 45^\circ$.
Reason (R) : $\sin 90^\circ \neq \cos 90^\circ$.

Solve any one of the following internal choices (a) or (b):
22(a) In an A.P., the first term is 32 and the last term is -10. If the common difference is -2, then find the number of terms and their sum.

Diagonals AC and BD of square ABCD intersect at P. Coordinates of points B and D are (9, -2) and (1, 6) respectively.
23(a)(i) Find the co-ordinates of point P.

The value of $\left(\frac{1}{2} \tan^2 45^\circ - \cos^2 60^\circ\right)$ is :

Given that $\sin 2\alpha = \frac{\sqrt{3}}{2}$, the value of $\sin 3\alpha$ is :

The median and mode of a distribution are $25.2$ and $26.1$ respectively. The mean of the distribution is :

Assertion (A) : Radius is the smallest distance of a tangent from the centre of the circle.
Reason (R) : Radius is perpendicular to the tangent.

In the given figure, $\Delta ABC$ is an equilateral triangle. $AD$ is a median of the triangle joining the points $A\left(0, \frac{5\sqrt{3}}{2}\right)$, $D(0, 0)$. Points B and C are (in same order) :

In the given figure, PT is a tangent to the circle with centre O and radius r. If $\angle POT = 45^\circ$, then the length of OP is :

If the roots of the quadratic equation $\sqrt{3}x^2 - kx + 2\sqrt{3} = 0$ are real and equal, then the value(s) of k is/are :

It is given that $\Delta ABC \sim \Delta QRP$ such that $AB = 9$ cm, $BC = 5$ cm and $PR = 2$ cm. Length of side QR is :

The $n^{\text{th}}$ term of the A.P. $\frac{-1}{3}, \frac{2}{3}, \frac{5}{3}, \frac{8}{3}, \dots$ is :

The sum and product of zeroes of a quadratic polynomial $p(x)$ are $-\frac{1}{3}$ and $2$ respectively. The polynomial $p(x)$ is :

A cone of maximum size is carved out from a solid cube of edge length $l$. The volume of the cone is :

If the length of the shadow of a tower is $\sqrt{3}$ times that of its height, then altitude of the Sun is :

Two dice are rolled together. The probability that the sum of the numbers obtained is divisible by 6, is :

$(3 \times 11 \times 13 + 3)$ is :

The number of multiples of 4 lying between 12 and 250 is :

Equation of another line parallel to the line represented by $2x - 6y = 7$ is :

In $\Delta DEF$, AB $\parallel$ EF. The value of x is :