List of top Mathematics Questions

In a box, consisting 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is :

Two balls are chosen randomly from an urn containing 8 white balls and 4 black balls by a player. Suppose that he wins ₹30 for each black ball selected and loses ₹15 for each white ball selected. The expected value of winning amount is :

Anita and Bikram are two students. Their chances of solving a problem correctly are \(\frac13\) and \(\frac14\) respectively. If their probability of making a common error is  \(\frac{1}{20}\) and they both obtain same answer then the probability that their answer is correct, is :

If \(P(A)=\frac{3}{10},P(B)=\frac{2}{5}\), and P(A ∪ B) = \(\frac{3}{5}\), then \(P(\frac{B}{A})+P(\frac{A}{B})\) is equal to :

The mean of the number of heads in a simultaneous toss of three coins is :

If \(P(A) = \frac{3}{10}\), \(P(B) = \frac{2}{5}\) and \(P(A \bigcup B) = \frac{3}{5}\), then \(P(B|A)+P(A|B)\) is equal to:

A and B throw a die alternatively till one of them gets a number more than 4 and wins the game. Then the probability of winning the game by B, if A starts first:

A telephone exchange receives on an average 5 calls per minute. The probability of receiving 3 or less calls per minute is :

If A and B are events such that \(P(A'UB')=\frac{1}{3}\) and \(P(AUB) = \frac{4}{9}\) then the value of \(P(A') + P(B')\) is:

The probability of getting a correct answer to a question is \(\frac{x}{12}\). If the probability of not getting the correct answer is \(\frac{2}{3}\), then what is the value of x ?

If P(E)=0.05, what is the probability of 'not E'?

A coin is tossed 5 times. The probability of getting atleast one head is:

If \(A= \begin{bmatrix}1 & 0 \\[0.3em]-1 & 5 \\[0.3em] \end{bmatrix}\) and \(I= \begin{bmatrix}1& 0\\[0.3em]0& 1\\[0.3em] \end{bmatrix}\) then the value of k so that \(A^2 = 6A + kI\) is given by:

The value of det\((A^2-2A)\),If \(A=\begin{pmatrix}      1 & 3  \\[0.3em]    2  &1  \end{pmatrix}\),is

Let \(A = [a_{ij}]\) be a 2×2 matrix such that \(aij=\frac{|-3i + j|}{2}\)  then \(a_{21}\) is :

The number of square matrices of order 2 using numbers 1 and -1 exactly once and the number 0 twice is:

If, A is a square matrix of order \(3 \times 3\) such that \(A^2 = A\) and I is the unit matrix of order \(3 \times 3\), then the value of \((I-A)^3+A^2+I\) is:

If \(A=\begin{bmatrix} 1 & 2 & x \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\), \(B=\begin{bmatrix} 1 & -2 & y \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\) and AB = I₃, where I₃ is the unit matrix of order 3 × 3, then x + y is equal to :

If \(A\)=\( \begin{vmatrix}  3  & 1  \\[0.1em]   -1 & 2  \end{vmatrix}\) then \(A^2-5A=\)

If \(A=\begin{pmatrix}     1 & -2 & 3  \\[0.3em]   4 & 2 &5 \end{pmatrix}\) and \(A=\begin{pmatrix}     1 & 3   \\[0.3em]   4 & 5  \\[0.3em]   2&1 \end{pmatrix}\)and \(BA=(b_{ij})\),then \(b_{21}+b_{32}=\)

The value of 2y-3x, if
\(2\begin {bmatrix}x &5\\ 7&y-3\end{bmatrix}+\begin{bmatrix}3&-4\\ 1&2\end{bmatrix}=\begin{bmatrix}7&6 \\15&14\end{bmatrix}\) is:

If \(\begin{bmatrix}3& 2x + 5y &-2 \\x + 4y  &7 &-5\end{bmatrix}=\begin{bmatrix}3 &10&-2\\ 2&7&-5\end{bmatrix}\) Then the values of x and y are:

If \(\begin{bmatrix} 4x & 5x-7 \\[0.3em] 4x & 2x+y\end{bmatrix}\)=\(\begin{bmatrix} x+6 & y \\[0.3em] 7y-13 & 7\end{bmatrix}\) then the value of 2x + y is:

If A=\(\begin{bmatrix} 2&3 \\ -1&1\end{bmatrix}\)and \(A^2-3A+kI = 0\) then the value of k is:

If \(A= \begin{bmatrix}1&√3&0 \\-√3&1&0 \\ 0&0&2 \end{bmatrix}\) and \(B=\begin{bmatrix}√3&1&0 \\-1&√3&0 \\ 0&0&2 \end{bmatrix}\) then AB is equal to :