List of top Mathematics Questions

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.

Prove that : $(1 + \cot \theta - \csc \theta)(1 + \tan \theta + \sec \theta) = 2$

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

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.

Prove that $4 - 2\sqrt{5}$ is an irrational number given that $\sqrt{5}$ is irrational.

Use graphical method to solve the system of linear equations : $y = -3$ and $x + 2y = 4$.

The area of a sector of a circle of radius $10\text{ cm}$ is $\frac{55}{3}\text{ cm}^2$. The value of central angle 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.

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

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.

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

The value of k for which the equation $kx^2 - 6x - 4 = 0$ has real and equal roots, 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 $\pi = 3.14$)

If sum and product of zeroes of a polynomial are ($-3$) and ($-2$) respectively, then a polynomial 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

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

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

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

A card is drawn at random from a well shuffled deck of 52 playing cards. The probability that it is either a ten or a king is

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

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

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

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