Maths

Let A and B be two 3 * 3 non-zero real matrices such that AB is a zero matrix. Then

If z = 2 + 3 i, then z5 + ${\left(\overline{z}\right)}^5$ is equal to:

Let R be a relation from the set $\left\{1,2,3,.....,60\right\}$ to itself such that R = $\left\{\left(a,b\right):b=pq\right\}$ where p, q $\ge$ 3 are prime numbers. Then, the number of elements in R is:

Let $\left\{x\right\}$ and $\left[x\right]$ denote the fractional part of $x$ and the greatest integer $\le x$ respectively of $a$ real number $x$ . if ${\int }_0^n \left\{x\right\}dx,{\int }_0^n \left[x\right]dx$ and $10\left(n^2-n\right),(n\in N,n>1)$ are three consecutive terms of a G.P. then $\mathrm{n}$ is equal to(Integration)

If the variance of the following frequency distribution :

$\begin{array}{lllll}\text{Class}& :& 10-20& 20-30& 30-40\\ \text{Frequency}& :& 2& x& 2\end{array}$ is 50 , then $x$ is equal to:

Let $PQ$ be a diameter of the circle $x^2+y^2=9$ . If $\alpha$ and $\beta$ are the lengths of the perpendiculars from $P$ and $Q$ on the straight line, $x+y=2$ respectively, then the maximum value of $\alpha \beta$ is.

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is

If $\vec{a}=2\hat{i}+\hat{j}+2\hat{k}$ , then the value of $|\hat{i}*(\vec{a}*\hat{i}){|}^2+|\hat{j}*(\vec{a}*\hat{j}){|}^2+|\hat{k}*(\vec{a}*\hat{k}){|}^2$ is equal to

Let $a_1,a_2,\dots a_n$ be a given A.P. whose common difference is an integer and $S_n=a_1+a_2$ $+\dots +a_n$ . If $a_1=1,a_1=300$ and $15\le n\le 50$ , then the ordered pair $\left(S_{n-4},a_{n-4}\right)$ is equal to:

If the perpendicular bisector of the line segment joining the points $P\left(\mathrm{1,4}\right)$ and $Q(k,3)$ has $y$ -intercept equal to -4 , then a value of $k$ is: