List of top Mathematics Questions

The value of the integral $\int\limits_{0}^{\pi/ 4} \frac{1+\sin^{2} }{ \cos^{3} x} dx $ is
If $\lambda_1 , \lambda_2$ and $\lambda_3$ are the eigen values (i.e. characteristic values) of the matrix $\begin{vmatrix}1&2&15\\ 3&4&11\\ 5&6&7\end{vmatrix}$ then $ \left(1 -\lambda_{1}\right)\left(1+\lambda _{2}\right)\left(1+\lambda _{3}\right)$ equals
If $p, q , r$ are the roots of the equation $\begin{vmatrix}x&1&2\\ 1&x&2\\ 1&2&x\end{vmatrix} = 0$ , then $\frac{p^{4} +q^{4}+r^{4}}{p^{2}+q^{2} +r^{2}}$ is equal to
If $A$ is a square matrix.such that $A^3 = 0$, then $(I + A)^{-1}$ is
If $n$ is a positive integer which is relatively prime to $6,$ and if $n$ has $8$ divisors, then $12n$ has
If $\sin(\pi \cos \theta) = \cos(\pi \sin \theta),$ then $\sin 2 \theta$ equals
The number of integral values of k for which the equation $7 \cos x + 5 \sin x = 2k + 1$ has solution is
The matrix [5103−2−46−1−2b]is a singular matrix, if b equals
If $\omega$ is a complex cube-root of unity then, $\begin{vmatrix} {1}&{\omega} &{\omega^2}\\ {\omega}&{\omega^2}& {1} \\ {\omega^2}&{1}&{\omega}\\ \end{vmatrix} $ is equal to
A unit vector perpendicular to the plane containing the vectors $\hat {i}-\hat {j}+\hat{k} $ and $ -\hat{i}+\hat {j}+\hat{k}$ is
The contrapositive of the inverse of $p \to \sim q$ is
The shortest distance from the point $(3, 0)$ to the parabola $y = x^2$ is.
If $x dy = y(dx+y dy),y(1)=1$ and $y(x) > 0$. Then, $y(-3)$ is equal to
If $\sin A , \sin B , \cos A$ are in GP, then roots of $x ^{2}+2 x \cot B +1=0$ are always
The system of equations $\alpha \, x + y + z = \alpha - 1$ $x + \alpha y + z = \alpha - 1$ $x + y + \alpha z = \alpha - 1$ has infinite solutions, if $\alpha$ is
Let $S$ be a set containing n elements and we select two subsets $A$ and $D$ of S at random, then the probability that $A \cup B = S$ and $A \cap B = \phi$ is:
Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house, is:
The sum of the series $1+\frac{1}{4\cdot2!}+\frac{1}{16\cdot 4!}+\frac{1}{64\cdot 6!} + \ldots \infty$ is :
The normal to the curve $x=a\left(cos\,\theta+\theta\,sin\,\theta \right). y=a\left(sin\,\theta -\theta\,cos\,\theta \right)$ at any point $'\theta'$ is such that :
$\int\left\{\frac{\left(log \,x -1\right)}{1+\left(log \,x\right)^{2}}\right\}^{2}dx$ is equal to :
If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number:
Area of the greatest rectangle that can be inscribed in the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ is :
Let $P$ be the point $(1, 0)$ and $Q$ a point on the locus $y^2 = 8x$. The locus of mid point of $PQ$ is:
If $C$ is the mid point of $AB$ and $P$ is any point outside $AB$, then :
The value of $a$ for which the sum of the squares of the roots of the equation $x^2 - (a - 2) x - a - 1 = 0$ assume the least value is