Explore topic-wise InterviewSolutions in Current Affairs.

The value of $\left|\begin{array}{ccc}41& 1& 5\\ 79& 7& 9\\ 29& 5& 3\end{array}\right|$ is:

Match the conditions/expressions in Column I with statement in Column II.

Let $f_1:R\to R,f_2:[0,\infty ]\to R,f_3:R\to R$ and $f_4:R\to [0,\infty )$ be defined by $f_1\left(x\right)=\{\begin{array}{c}|x|,ifx<0\\ e^x,ifx\ge 0\end{array}{f}_2\left(x\right)=x^2;f_3\left(x\right)=\{\begin{array}{c}sinx,ifx<0\\ x,ifx\ge 0\end{array}$ and $f_4\left(x\right)=\{\begin{array}{c}{f}_2\left[f_1\right(x\left)\right],ifx<0\\ f_2\left[f_1\right(x\left)\right]-1,ifx\ge 0\end{array}$
$\begin{array}{cc}\text{Column I}& \text{Column II}\\ a.f_{4}is& p.\text{onto but not one-one}\\ b.f_{3}is& q.\text{neither continuous nor one-one}\\ c.f_{2}of{f}_{1}is& r.\text{differentiable but not one-one}\\ d.f_{2}is& s.\text{continuous and one-one}\end{array}$

For $x\in R,\text{let}\left[x\right]$ denote the greatest integer $\le x,$ then the sum of the series $[-\frac{1}{3}]+[-\frac{1}{3}-\frac{1}{100}]+[-\frac{1}{3}-\frac{2}{100}]+....+[-\frac{1}{3}-\frac{99}{100}]$ is :

Find the Cartesian equation of the following plane:

$r.\left[\right(s-2t)\hat{i}+(3-t)\hat{j}+(2s+t\left)\hat{k}\right]=15$

The solution of differential equation $(1+y^2)dx=({\tan }^{-1}y-x)dy$ is

(where $C$ is integration constant)

Prove the following by using the principle of mathematical induction for all n ∈ N:

Statements: H G, D E, H ! E

Conclusions:

a) D ! H

b) G © D

The integer $n$ for which $\underset{x\to 0}{lim}\frac{(\cos x-1)(\cos x-e^x)}{x^n}$ is a finite non-zero number is

Which of the following point(s) lies on the line $\frac{x-3}{-2}=\frac{y-2}{3}=\frac{z+1}{4}$

$\left|\begin{array}{ccc}a-b-c& 2a& 2a\\ 2b& b-c-a& 2b\\ 2c& 2c& c-a-b\end{array}\right|=(a+b+c{)}^3$

$\left|\begin{array}{ccc}x+y+2z& x& y\\ z& y+z+2x& y\\ z& x& z+x+2y\end{array}\right|=2(x+y+z{)}^3$

In a cricket tournament 16 school teams participated. A sum of Rs.16000 is to be awarded among themselves as prize money. If the team in the last place is awarded RS 550 in prize money and the award increases by the same amount for successive finishing places, how much amount will the team in the first place receive?

Let $\Delta \left(x\right)=\left|\begin{array}{ccc}x+a& x+b& x+a-c\\ x+b& x+c& x-1\\ x+c& x+d& x-b+d\end{array}\right|$ and $\underset{0}{\overset{2}{\int }}\Delta \left(x\right)dx=-16,$ where $a,b,c,d$ are in A.P. Then the common difference of the A.P. can be

If $f$ is a function such that $f\left(0\right)=2,$ $f\left(1\right)=3$ and $f(x+2)=2f\left(x\right)-f(x+1)$ for every real $x,$ then the value of $f\left(5\right)$ is

A curve is given as $y=x^3+3x^2+7$. The rate of change of abscissa at a certain point is equal to $\frac{1}{9}$ of the rate of change of ordinate. Which of the following denotes that point , if it is known to lie in $1^{st}$ Quadrant.

All the pairs $(x,y)$ that satisfy the inequality $2^{\sqrt{{\sin }^{2}x-2\sin x+5}}\cdot \frac{1}{4^{{\sin }^{2}y}}\le 1$ also satisfy the equation :

If the sum of n
terms of an A.P. is (pn + qn²), where p
and q are constants, find the common difference.

The angle between plane

The area(in $\text{sq.units}$) of the region between the curve $y=a\sin x(a>0),x$-axis when $0\le x\le \pi ,$ is

If a normal to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ meets the axes at $M\&N$ and the lines $MP\&NP$ are drawn perpendicular to the axes meeting at $P$, then locus of $P$ is

If $(2x^2-3x+1)(2x^2+5x+1)=9x^2$, then the absolute value of the sum of all real roots of the equation is:

1. 22

Solve the following system of inequalities graphically: x + y ≤ 6, x + y ≥ 4

If $\omega$ is a non-real cube root of unity, then the value of $1\cdot (2-\omega )(2-{\omega }^2)+2\cdot (3-\omega )(3-{\omega }^2)+\cdots$ sum upto $19$ terms is