List of practice Questions

If $A$ and $B$ are two mutually exclusive events then $P (A \cap B)$ =

If A and B are two sets, then A $\cap$ (A $\cup$ B)' equals :

If $A$ and $B$ are subsets of universal set $U$ such that $n(U) = 800$, $n(A) = 300$, $n(B) = 400$ and $n(A \cap B) = 100$. The number of elements in the set $A^c \cap B^c$ is

If A and B are symmetric matrices of the same order, then

If $A$ and $B$ are two events, then the set $(A \cap B)$ denotes the event

If $A$ and $B$ are mutually exclusive events, then

If $A$ and $B$ are not disjoint sets, then $n(A \cup B)$ is equal to

If A and B are square matrices of size n ? n such that $A^2 - B^2 = (A- B)(A+ B)$ , then which of the following will be always true?

If $A(6, 3, 2), B(5, 1, 4), C(3, -4, 7), D(0, 2, 5)$ be four points, the projection of segment $CD$ on the line $ AB$ is

If $A = [a_{ij}]_{m \times n}$ be a scalar matrix, then trace of $A$ is equal to

If $A$ and $B$ are independent events then $P \left( \frac{B}{A} \right)$ =

If $A = \begin{bmatrix}6&8&5\\ 4&2&3\\ 9&7&1\end{bmatrix} $ is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is

If $A= (3,81)$ and $f : A \rightarrow B$ is a surjection defined by $f[x] = \log_3 x$ then $B = $

if $A = \begin{bmatrix}4&1&0\\ 1&-2&2\end{bmatrix} , B = \begin{bmatrix}2&0&-1\\ 3&1&x\end{bmatrix} , C = \begin{bmatrix}1\\ 2\\ 1\end{bmatrix}$ and $D =\begin{bmatrix}15+x\\ 1\end{bmatrix}$ such that $(2A -3B)C=D$, then $x$ =

if $A = \begin{bmatrix}3&-4\\ 1&-1\end{bmatrix}$ is the sum of a symmetric matrix $B$ and a skew-symmetric matrix $C$, then $C$ is

If $a^2 + b^2 + c^2 = 1 $ then the range of ab+bc+ca is

If $a^2, b^2, c^2$ are in A.P. consider two statements $\left(i\right)\, \frac{1}{b+c}, \frac{1}{c+a}, \frac{1}{a+b}$ are in A.P. $\left(ii\right)\, \frac{a}{b+c}, \frac{b}{c+a}, \frac{c}{a+b}$ are in A.P., then

if $A=\begin{bmatrix}2x&0\\ x&x\end{bmatrix}$ and $A^{-1}= \begin{bmatrix}1&0\\ -1&2\end{bmatrix},then x equals$

If $a_1, a_2,...... a_{n+1}$ are in A.P. then $\frac{1}{a_{1}a_{2}}+\frac{1}{a_{2}a_{3}}+.......+\frac{1}{a_{n}a_{n+1}}$ is

If $a_1 ,b_1 ,c_1$ and $a_2 , b_2 ,c_2$ are the d.rs of two lines then $( a_1 a_2 + b_1 b_2 + c_1 c_2)^2 + \sum (b_1 c_2 - b_2 c_1)^2 =$

If A = {1, 2, 5} and B = {3, 4, 5, 9}, then $A \Delta B$ is equal to

If $a_1,a_2,a_3,............$ is an A.P. such that $a_1+a_5+a_{10}+a_{15}+a_{20}+a_{24}=225,$ then $a_1+a_2+a_3+.....+a_{23}+a_{24}$ is equal to

if A = $\begin{bmatrix}1&3\\ 3&4\end{bmatrix}$ and $A^2 - kA - 5I = 0$, then $k$ =

If $A = \{1, 2, 3, 4, 5\}$, then the number of proper subsets of A is

if $A = \begin{bmatrix}1&-1\\ 2&-1\end{bmatrix} , B =\begin{bmatrix}x&1\\ y&-1\end{bmatrix}$ and $\left(A + B\right)^{2} =A^{2} + B^{2},$ then $x + y$ =