List of top Mathematics Questions

If $\quad \tan \theta \cdot \tan \left(120^{\circ}-\theta\right) \tan \left(120^{\circ}+\theta\right)=\frac{1}{\sqrt{3}}$, then $\theta$ is equal to

If $f: R \rightarrow R, g: R \rightarrow R$ are defined by $f(x)=5\, x-3, g(x)=x^{2}+3$, then $g o f^{-1}(3)$ is equal to

The system $2\,x+3 y+z=5,3\,x+y+5\,z=7$ and $x+4\,y-2\,z=3$ has

The value of the sum $1 \cdot 2 \cdot 3+2 \cdot 3 \cdot 4+3 \cdot 4 \cdot 5+\ldots$ upto $n$ terms is equal to

The common roots of the equations $z^{3}+2 z^{2}+2 z+1=0, z^{2014}+z^{2015}+1=0$ are

If $\omega$ is a complex cube root of unity, then $\omega^{\left(\frac{1}{3}+\frac{2}{9}+\frac{4}{27}+\ldots \infty\right)}+\omega^{\left(\frac{1}{2}+\frac{3}{8}+\frac{9}{32}+\ldots \infty\right) \text { is equal to }}$

If $A=\left\{x \in R / \frac{\pi}{4} \leq x \leq \frac{\pi}{3}\right\}$ and $f(x)=\sin x-x$, then $f(A)$ is equal to

If $a, b, c$ are distinct and the roots of $(b-c) x^{2}+(c-a) x+(a-b)=0 $ are equal, then $a, b$ and $c$ are in

$\displaystyle \sum_{k=1}^{6}\left[\sin \frac{2 k \pi}{7}-i \cos \frac{2 k \pi}{7}\right]$ is equal to

The value of $\int \limits \frac {dx}{x^2(x^4+1)^{3/4}}$ is

The value of the determinant $\begin{vmatrix}b^{2}-a b & b-c & b c-a c \\ a b-a^{2} & a-b & b^{2}-a b \\ b c-a c & c-a & a b-a^{2}\end{vmatrix}$ is

If $A$ is a square matrix of order 3 , then | adj $\left(\operatorname{adj} A^{2}\right) \mid$ is equal to

If $f\left(x\right) = 2 \tan^{-1} x + \sin^{-1} \left(\frac{2x}{1+x^{2}}\right), x > 1$, then $f(t)$ is equal to :

If $\theta \in\left(\frac{\pi}{2}, \frac{3 \pi}{2}\right)$, then the value of $\sqrt{4 \cos ^{4} \theta+\sin ^{2} 2 \theta}+4 \cot \theta \cos ^{2}\left(\frac{\pi}{4}-\frac{\theta}{2}\right)$

It $\displaystyle \lim_{x \to 0}$$\frac{axe^{x}-b\, \log\left(1+x\right)}{x^{2}}=3$ then the values of $a, b$ are respectively

Evaluate $\left|\begin{array}{ll}\cos 15 & \sin 15 \\ \sin 75 & \cos 75\end{array}\right|$

Consider the curve given by $ {{({{x}^{2}}+{{y}^{2}})}^{2}}=4({{x}^{2}}-{{y}^{2}}) $ . Which of the following is not true?

Which of the following is a tangent to the curve given by $ {{x}^{3}}+{{y}^{3}}=2xy? $

If $ ^{32}{{P}_{6}}=k\,{{(}^{32}}{{C}_{6}}), $ then $k$ is equal to

The sum of lengths of major and minor axes- of an ellipse whose eccentricity is $ \frac{4}{5} $ and length of latuserectum is $ 14.4 $ , is

The points $ (1,3,4),\,(-1,6,10),\,(-7,4,7) $ and $ (-5,1,1) $

An ellipse passes through the foci of the hyperbola, $9x^2? 4y^2 = 36$ an and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is $\frac{1}{2},$ then which of the following points does not lie on the ellipse ?

Locus of the image of the point $(2, 3)$ in the line $\left(2x - 3y + 4\right) + k\left(x - 2y + 3\right) = 0, k \in R,$ is a

If $ |\vec {a} |=7 $ and $ |\vec {b} |=11, $ then the angle between the vectors $\vec {a} +\vec {b} $ and $\vec {a} -\vec {b} $ is equal to

At present, a firm manufactures 1099 items. It is estimated that the rate of change of production P with respect to additional number of workers x is given by $ \frac{dP}{dx}=100-12\sqrt{x}. $ . If the firm empower 25 more workers, then the new level of production of items is