Explore topic-wise InterviewSolutions in .

Let $Z$ be the set of integers. If $A=\{x\in Z:{\log }_{10}(x^2-7x+13)=0\}$ and $B=\{x\in Z:(x+2\left)\right(x-3\left)\right(x^2-1)\le 0\}$ then the number of subsets of set $A\times B$ is

The number of different products that can be formed with $8$ prime numbers is

what is the value of θ if tanθ=0.51

The value of $\underset{x\to -5}{lim}\frac{x^2-25}{x^2+2x-15}$ is

What is integral of (ax+b)/(cx+d)

A ray of light is incident along a line which meets another line, $7x–y+1=0$, at the point $(0,1)$. The ray is then reflected from this point along the line, $y+2x=1$. Then the equation of the line of incidence of the ray of light is :

Consider the functions $f\left(x\right)=\{\begin{array}{cc}|x|,& x\le -1\\ x^{1/5}& -1<x\le 1\\ (2-x{)}^3,& x>1\end{array}\text{and}g\left(x\right)=\frac{1}{(x+2{)}^3}-2x-\cos x$. Let $p$ be the number of critical points on the graph of $f\left(x\right)\text{and}q$ be the number of solutions of $g\left(x\right)=0$, then which of the following option(s) is/are correct?

Which of the following is the possible value of $\left(x\right|$ if ${\left(x\right|}^2-6\left(x\right|+8=0$

Using
properties of determinants, prove that:

Three randomly chosen nonnegative integers x, y and z are found to satisfy the equation x + y + z = 10. Then the probability that z is even is ?

A and B are square matrices and A is non-singular matrix, $(A^{-1}BA{)}^n,nϵI^{+}$ is equal to

Choose the correct answer in the following question:
The normal to the curve $x^2=4y$ passing through (1, 2) is

(a) x + y = 3 (b) x - y = 3 (c) x + y = 1 (d) x - y = 1

x² log
x

1. 11

Consider f:
R → R
given by f(x)
= 4x + 3.
Show that f
is invertible. Find the inverse of f.

If $g\left(x\right)=\underset{0}{\overset{x}{\int }}\cos \left(4t\right)dt$, then $g(x+\pi )$ equals

Let $O$ be the origin. Let $\overrightarrow{OP}=x\hat{i}+y\hat{j}-\hat{k}$ and $\overrightarrow{OQ}=-\hat{i}+2\hat{j}+3x\hat{k},x,y\in R,x>0,$ be

such that $\left|\overrightarrow{PQ}\right|=\sqrt{20}$ and the vector $\overrightarrow{OP}$ is perpendicular to $\overrightarrow{OQ}$. If $\overrightarrow{OR}=3\hat{i}+z\hat{j}-7\hat{k},z\in R$ is coplanar with $\overrightarrow{OP}$ and $\overrightarrow{OQ},$ then the value of $x^2+y^2+z^2$ is equal to :

If$\overrightarrow{p}=(2,-10,2),\overrightarrow{q}=(3,1,2)\text{and}\overrightarrow{r}=(2,1,3),\text{then}|\overrightarrow{p}\times (\overrightarrow{q}\times \overrightarrow{r}\left)\right|$ equals to

The solution set of ${\log }_{|\sin x|}(x^2-8x+23)>\frac{3}{{\log }_2|\sin x|}$ contains

$={lim}_{x\to 0}\frac{log(3+x)-log(3-x)}{x}$

Two dice are thrown. The events A, B and C are as follows:

A: getting an even number on the first die.

B: getting an odd number on the first die.

C: getting the sum of the numbers on the dice ≤ 5

State true or false: (give reason for your answer)

(i) A and B are mutually exclusive

(ii) A and B are mutually exclusive and exhaustive

(iii)

(iv) A and C are mutually exclusive

(v) A and
are
mutually exclusive

(vi)
are
mutually exclusive and exhaustive.

In how many ways can a team of $6$ horses be selected out of a stud of $16$, so that there shall always be three out of $ABC{A}^{\prime }{B}^{\prime }{C}^{\prime }$, but never $A{A}^{\prime },B{B}^{\prime }$ or $C{C}^{\prime }$ together.

If $\Delta \left(x\right)=\left|\begin{array}{ccc}1+x+2x^2& x+3& 1\\ x+2x^2& x& 3\\ 3x+6x^2& 3x+11& 9\end{array}\right|$ then ${\int }_0^1\Delta \left(x\right)dx$ is

The equation of the line belonging to the family of lines $(x+y)+\lambda (2x-y+1)=0$ and farthest from point $(1,-3)$ is

The equation 3 cos x +4 sin x=6 has .... solution.

The interior angles of a convex polygon are in A.P. the smallest angle is ${120}^{\circ }$ and the common difference is $5^{\circ }$ the number of its sides are

The value of $k$ for which the equation

$3x^2+2x(k^2+1)+k^2-3k+2=0$

has roots of opposite signs, lies in the interval

If the slope of tangent to the curve $x^{2}y+ax+by=2$ at $(1,1)$ is $2,$ then $(a,b)$ is