List of top Mathematics Questions

If the coefficient of $x^7$ in $\left[ ax^2 + (\frac{1}{bx} ) \right]^{11}$ equals the coefficient of $x^{-7}$ in $\left[ax - \left(\frac{1}{bx^{2}}\right)\right]^{11}$ , then a and b satisfy the relation
The identity element in the group $M = \left\{ \begin{bmatrix} x & x \\ x & x\\ \end{bmatrix} | x \ \in \ R, x \neq 0 \right\}$ with respect to matrix multiplication is
The converse of the contrapositive of $p \to \sim q$ is
The solutions of the equation $\begin{vmatrix} {x}&{2} &{-1}\\ {2}&{5}& {x} \\ {-1}&{z}&{x}\\ \end{vmatrix} =0$ are
If $A=\begin{bmatrix} {3}&{5}\\ {2}&{0}\\ \end{bmatrix} $ and $B$ = $\begin{bmatrix} {1}&{17}\\ {0}&{-10}\\ \end{bmatrix} $then $|AB|$ is equal to
The inverse of the matrix $\begin{bmatrix} {5}&{-2}\\ {3}&{1}\\ \end{bmatrix}$ is is
The contrapositive of "If two triangles are identical, then these are similar" is
Define $f (x) = min{x^2 + 1, x + 1]$ for.$x e\in R$. Then $ \int\limits_{-1}^1f (x)dx $ is
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 $n$ is a positive integer which is relatively prime to $6,$ and if $n$ has $8$ divisors, then $12n$ has
If $A$ is a square matrix.such that $A^3 = 0$, then $(I + A)^{-1}$ is
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
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 :