List of top Mathematics Questions

In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.

Use graphical method to solve the system of linear equations : $x = -3$ and $5x - 2y = -5$.

Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

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.

Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

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.

The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is

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.

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

While calculating mean of a grouped frequency distribution, step deviation method was used $\left(\frac{x - a}{h} = u\right)$. It was found that $\bar{x} = 64$, $h = 5$ and $a = 62.5$. The value of $\bar{u}$ is

The value of m for which the quadratic equation $3x^2 - 7x + m = 0$ has real and equal roots, 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

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?

In the given figure, $AB \parallel EF$. If $AB = 24\text{ cm}$, $EF = 36\text{ cm}$ and $DA = 7\text{ cm}$, then $AE$ equals

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

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

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

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

$PQ$ is tangent to a circle with centre $O$. If $OQ = a$, $OP = a + 2$ and $PQ = 2b$, then relation between $a$ and $b$ is

A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius $10\text{ cm}$. Curved surface area of the cavity carved out is (use $\pi = 3.14$)

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

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

By selling an article for Rs. 48, a trader loses as much percent as half of the cost price of the article. Calculate the cost price and loss amount of the article.

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.