List of top Mathematics Questions

For an acute angle $\theta$, if $\cos \theta = \frac{1}{8}$, then $\frac{8\sec\theta + 1}{8\sec\theta - 1}$ equals

The line segment joining the points $P(-4, -2)$ and $Q(10, 4)$ is divided by y-axis in the ratio

In the given figure, $PQ$ is tangent to the circle with centre $O$. $S$ is a point on the circle such that $\angle SQT = 55^\circ$. The $m\angle QPS$ is

In an A.P., if $a_{14} - a_8 = 24$, then the common difference of the A.P. is

Devansh proved that $\Delta ABC \sim \Delta PQR$ using SAS similarity criteria. If he found $\angle C = \angle R$, then which of the following was proved true?

A circle of diameter $20\text{ cm}$ is equally divided into five sectors. Find the area and perimeter of one of the sectors.

PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.

Venkat can row a boat in still water at the speed of $12\text{ km/h}$. He ferries tourists $15\text{ km}$ upstream and $18\text{ km}$ downstream in $3$ hours. Find the speed of the stream.

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

Solve the system of linear equations: $x = 4$ and $3x - 2y = 6$ graphically.

The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

Assertion (A) : H.C.F. ($36\text{ m}^2, 18\text{ m}$) = $18\text{ m}$, where m is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

Prove that $2 - 5\sqrt{3}$ is an irrational number given that $\sqrt{3}$ is irrational.

In the given figure, $PQ \parallel YZ$ such that $XP : PY = 2 : 3$. If $PQ = 5\text{ cm}$, then $YZ$ equals

Simplest form of $\frac{\sec A}{\sqrt{\sec^2 A - 1}}$ is

Meena calculates that the probability of her winning the first prize in a lottery is $0.08$. If total $800$ tickets were sold, the number of tickets bought by her, is

A wire is attached from a point $A$ on the ground to the top of a pole $BC$, making an angle of elevation as $60^\circ$. If $AB = 5\sqrt{3}\text{ m}$, then length of the wire is

For an acute angle $\theta$, if $\sin\theta = \frac{1}{9}$, then value of $\frac{9\csc\theta + 1}{9\csc\theta - 1}$ is

An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

A camping tent in hemispherical shape of radius $1.4\text{ m}$, has a door opening of area $0.50\text{ m}^2$. Outer surface area of the tent is

If $a_n$ represents $n^{\text{th}}$ term of the A.P. $-\frac{15}{4}, -\frac{10}{4}, -\frac{5}{4}, \dots$ then value of $a_{16} - a_{12}$ is

Which of the following can not be the probability of an event ?