List of top Mathematics Questions

For a complex number $z$, let $Re(z)$ denote the real part of $z$. Let $S$ be the set of all complex numbers $z$ satisfying $z^{4}-|z|^{4}=4 i z^{2}$, where $i=\sqrt{-1}$. Then the minimum possible value of $\left|z_{1}-z_{2}\right|^{2}$, where $z_{1}, z_{2} \in S$ with \(Re\left( z _{1}\right)\)\(>\)0 and \(Re\left( z _{2}\right)\) \(<\) 0, is ______

The locus of a point which divides the line segment joining the point (0, -1) and a point on the parabola, $x^2 = 4y$, internally in the ratio 1 : 2, is :

The mean and variance of $20$ observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was $11$. Then the correct variance is :

An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k = 3, 4, 5, otherwise X takes the value ? 1. Then the expected value of X, is :

The value of $cos\left(\sin^{-1}\frac{\pi}{3}+\cos^{-1}\frac{\pi}{3}\right)$ is

Let the function $f: R \rightarrow R$ and $g: R \rightarrow R$ be defined by
$f(x)=e^{x-1}-e^{-|x-1|}$ and $g(x)=\frac{1}{2}\left(e^{x-1}+e^{1-x}\right)$.
Then the area of the region in the first quadrant bounded by the curves $y=f(x), y=g(x)$ and $x=0$ is

In a triangle \(P Q R\), let \(\vec{a}=\overrightarrow{Q R}, \vec{b}=\overrightarrow{R P}\) and \(\vec{c}=\overrightarrow{P Q}\) If
 \(|\vec{a}|=3,|\vec{b}|=4\) and \(\frac{\vec{a} \cdot(\vec{c}-\vec{b})}{\vec{c} \cdot(\vec{a}-\vec{b})}=\frac{|\vec{a}|}{|\vec{a}|+|\vec{b}|}\) then the value of \(|\vec{a} \times \vec{b}|^{2}\) is

Let $x, y$ and $z$ be positive real numbers Suppose $x, y$ and $z$ are the lengths of the sides of a triangle opposite to its angles $X, Y$ and $Z$, respectively If $\tan \frac{x}{2}+\tan \frac{z}{2}=\frac{2 y}{x+y+z}$ then which of the following statements is/are TRUE?

The order of the differential equation obtained by eliminating arbitrary constants in the family of curves $c_1y = (c_2 +c_3 )e^{x+c_4}$ is

Let \(f:[0,2] \rightarrow R\) be the function defined by
\(f(x)=(3-\sin (2 \pi x)) \sin \left(\pi x-\frac{\pi}{4}\right)-\sin \left(3 \pi x+\frac{\pi}{4}\right)\) If \(\alpha, \beta \in[0,2]\) are such that \(\{x \in[0,2]: f(x) \geq 0\}=[\alpha, \beta]\), then the value of \(\beta-\alpha\) is ______

Corner points of the feasible region determined by the system of linear constraints are $(0, 3), (1, 1)$ and $(3, 0)$. Let $z = px = qy$, where $p, q > 0$. Condition on $p$ and $q$ so that the minimum of $z$ occurs at $(3, 0)$ and $(1, 1)$ is

If a line makes an angle of $\pi/3$ with each of $x$ and and $y$-axis, then the acute angle made by $z$-axis is

The distance of the point (1, 2, -4) from the line $\frac{x-3}{2} = \frac {y-3}{3} = \frac {z+5}{6}$ is

If the curves $2x = y^2$ and $2xy = K$ intersect perpendicularly, then the value of $K^2$ is

The standard deviation of the data $6, 7, 8, 9, 10$ is

The maximum value of $\frac{log_ex}{x}$, if x > 0 is

if $(xe)^y = e^x$, then $\frac{dy}{dx}$ is =

If $y = 2x^{n+1} + \frac {3}{x^n}$ ,then $x^2 \frac{d^2y}{dx^2}$ is

The value of $\int^{\frac{1}{2}}_{-\frac{1}{2}}cos^{-1}xdx$ is

The feasible region of an LPP is shown in the figure. If $Z = 11x + 7y$, then the maximum value of $Z$ occurs at

The general solution of the differential equation $x^2dy - 2xydx = x^4\cos\,x\, dx$ is

Events $E_1$ and $E_2$ from a partition of the sample space S. A is any event such that $P(E_1) = P(E_2) = \frac{1}{2}, P(E_2/A) = \frac{1}{2}$ and $P(A/E_2)=\frac{2}{3}$, then $P(E_1/A) $ is

If $A = \{a,b,c\}$, then the number of binary operations on $A$ is

Which of the following inequalities is/are TRUE?