List of top Mathematics Questions

For $\alpha>0$, the value of the integral $\displaystyle \int_{-\infty}^{+\infty} x e^{-\alpha x^2} \, dx$ is

The equation $\sin \frac{\theta}{2}\, (\sin \frac{\theta}{2} + \cos \frac{\theta}{2}) = \beta$ has a solution, where $\beta$ is a natural number. Then $\beta$ is ______.

A function $f : D \to \mathbb{R}$ is defined as $f(x) = \dfrac{x^2 + 1}{x^2 + x + 1}$ where $D \subseteq \mathbb{R}$ is the domain. The domain(s) on which the function $f(x)$ is one-to-one is/are

If $x + \dfrac{1}{x} = 1$, then the value of $x^6 + \dfrac{1}{x^6}$ is

The distance between the parallel lines $2x + 5y = 7$ and $2x + 5y = 15$ is ______ (rounded off to 2 decimals).

A stationary enemy ship is docked in the sea at a distance of 10 km from the coastline. A gun located at the sea level on the coastline can fire projectiles at a velocity of 120 m/s. What is the angle (in degrees) above the horizontal at which the gun must fire to hit the ship? [g = 9.8 m/s$^2$]

If \(\vec{a}.\vec{b}=0\) and \(\vec{a}+\vec{b}\) makes an angle 60° with \(\vec{a}\) then

The number of ways a committee of 3 women and 5 men can be formed from a panel of 8 men and 5 women is

If p and q are positive integers such that \(^{p+q}P_2=42\ and\ ^{p-q}P_2=20\), then the values of p and q respectively

If $a^x = b^y = c^z$ and $b^2 = ac$, then the value of $y$ is equal to:

In a group of cows and hens, the number of legs is 14 more than twice the number of heads. The number of cows is:

If A and B are the coefficients of $x^n$ in the expansion of $(1 + x)^2n$ and $(1 + x)^2n - 1$, then:

If the system of linear equations: \[ x + 2ay + az = 0 \] \[ x + 3by + bz = 0 \] \[ x + 4cy + cz = 0 \] has a non-zero solution, then $a, b, c$ are:

If the middle term of the $A.P$ is $300$ then the sum of its first $51$ terms is

If the area of the Ellipse is $\frac{x^{2}}{25}+\frac{y^{2}}{\lambda^{2}}=1$ is $20 \pi$ square units, then $\lambda$ is

The number of solutions of $\frac{d y}{d x}=\frac{y+1}{x-1}$ when $y(1)=2$ is

A vector $\vec{a}$ makes equal acute angles on the coordinate axis. Then the projection of vector $\vec{ b }=5 \hat{ i }+7 \hat{ j }-\hat{ k }$ on $\vec{ a }$ is

Solution of Differential Equation $xdy - ydx = 0$ represents

If $\vec{a} \cdot \vec{b}=0$ and $\vec{a}+\vec{b}$ makes an angle $60^{\circ}$ with $\vec{a} $ then

If the area of the parallelogram with $\vec{a}$ and $\vec{b}$ as two adjacent sides is $15$ s units then the area of the parallelogram having $3 \vec{a}+2 \vec{b}$ and $\vec{a}+3 \vec{b}$ as two adjacent sides in s units is

The equation of the line joining the points $(-3,4,11)$ and $(1,-2,7)$ is

The angle between the lines whose direction cosines are $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)$ and $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)$ is

If a plane meets the coordinate axes at $A, B$ and $C$ in such a way that the centroid of triangle $ABC$ is at the point $(1,2,3)$ then the equation of the plane is