List of top Mathematics Questions

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

Let function $ f(x)={{(x-1)}^{2}}{{(x+1)}^{3}}. $ Then, which of the following is false?

In an isosceles right angled triangle $ABC$, a value of $ \tan \left( \frac{A}{2} \right)+\tan \left( \frac{B}{2} \right)+\tan \left( \frac{C}{2} \right) $ is

The function is $ f(x)=\frac{1}{2-\cos \,3x},\,x\,\in \left[ 0,\frac{\pi }{3} \right], $ is

The last digit in the integer $ {{3}^{101}}+1 $ is

$ \underset{x\to 0}{\mathop{\lim }}\,\,\frac{\sin {{x}^{2}}}{1-\cos x} $ is

The derivative of $sin\, x$ with respect to $ cos\text{ }x $ is