List of top Mathematics Questions

If $P$, $Q$ are two points on the curve $y = 2x^2$ in the rectangular Cartesian coordinate system such that $\vec{OP} \cdot \vec{i} = -1$, $\vec{OQ} \cdot \vec{i} = 2$, then $\vec{OQ} - 4\vec{OP} =$
If the equation of the plane passing through the point $A(-2, 1, 3)$ and perpendicular to the vector $3\vec{i} + \vec{j} + 5\vec{k}$ is $ax + by + cz + d = 0$, then $\dfrac{a + b}{c + d} =$
If the mean of the data $p,6,6,7,8,11,15,16$ is 3 times $p$, then the mean deviation of the data from its mean is
In a triangle $ABC$, $\dfrac{a}{b} = 2 + \sqrt{3}$ and $\angle C = 60^\circ$. Then the measure of $\angle A$ is
If $a = 2$, $b = 3$, $c = 4$ in a triangle $ABC$, then $\cos C =$
D, E, F are respectively the points on the sides $BC$, $CA$ and $AB$ of a $\triangle ABC$ dividing them in the ratio $2:3$, $1:2$, $3:1$ internally. The lines $BE$ and $CF$ intersect on the line $AD$ at $P$. If $\overrightarrow{AP} = x_1 \cdot \overrightarrow{AB} + y_1 \cdot \overrightarrow{AC}$, then $x_1 + y_1 =$
$OABC$ is a tetrahedron. If $D, E$ are the midpoints of $OA$ and $BC$ respectively, then $\overrightarrow{DE} =$
If $4 + 6(e^{2x} + 1)\tanh x = 11\cosh x + 11\sinh x$, then $x =$
In a triangle $ABC$, $2(bc \cos A + ac \cos B + ab \cos C) =$
In a triangle $ABC$, $(b + c)\cos A + (c + a)\cos B + (a + b)\cos C =$
If $A + B + C = \pi$, $\cos B = \cos A \cos C$, then $\tan A \tan C =$
The value of $\tan\left(\dfrac{7\pi}{8}\right)$ is
If $\dfrac{13x + 43}{2x^2 + 17x + 30} = \dfrac{A}{2x + 5} + \dfrac{B}{x + 6}$, then $A^2 + B^2 = $
$1 + \sec^2 x \cdot \sin^2 x = $
In a triangle $ABC$, $\left(\tan \dfrac{A}{2} \tan \dfrac{B}{2} \tan \dfrac{C}{2} \right)^2 \le$
The least value of $n$ so that ${}^{n-1}C_3 + {}^{n-1}C_4>{}^nC_3$ is
In how many ways can the letters of the word “MULTIPLE” be arranged keeping the position of the vowels fixed?
A natural number $n$ such that $n!$ ends in exactly 1000 zeros is
If the difference between the roots of $x^2 + ax + b = 0$ and that of $x^2 + bx + a = 0$ is same and $a \ne b$, then
The sum of the real roots of the equation $|x - 2|^2 + |x - 2| - 2 = 0$ is
For what values of $a \in \mathbb{Z}$, the quadratic expression $(x + a)(x + 1991) + 1$ can be factorised as $(x + b)(x + c)$, where $b, c \in \mathbb{Z}$?
If $e^{i\theta = \cos\theta + i\sin\theta$ then}
$\sum_{n=0}^{\infty} \dfrac{\cos(n\theta)}{2^n} \div \sum_{n=0}^{\infty} \dfrac{\cos(n\theta)}{5^n} =$
If $f(f(0)) = 0$, where $f(x) = x^2 + ax + b$, $b \neq 0$, then $a + b =$
If a set $A$ has $m$ elements and the set $B$ has $n$ elements, then the number of injections from $A$ to $B$ is
Multiplicative inverse of the complex number $(\sin\theta, \cos\theta)$ is