Explore topic-wise InterviewSolutions in Current Affairs.

If the operation $\ast$ is defined by $a\ast b=a^2+b^2$ for all the real numbers ${}^{\prime }{a}^{\prime }$ and ${}^{\prime }{b}^{\prime }$ then $(2\ast 3)\ast 4=$

$\left(\sqrt{-2}\right)\left(\sqrt{-3}\right)$ is equal to

The volume of tetrahedron whose vertices are

A = (3, 2, 1) ,~B = (1, 2, 4),~ C = (4, 0, 3),~ D = (1, 1, 7)~will be $\underset{–}{}$cubic units

2x-7=(x+3)÷3

If the equation of base of an equilateral triangle is 2x - y = 1 and one vertex is (-1, 2), then the length of the side of the triangle is

If point $(k,k^2)$ lies inside the region bounded by parabolas $y^2=64x$ and $-x^2+x-1+y=0$ then $k$ lies in the interval

Let$x=(\sqrt{50}+7{)}^{\frac{1}{3}}-(\sqrt{50}-7{)}^{\frac{1}{3}}$

Find out the appropriate word which fits the 7th blank.

If $x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}$ , then $\frac{dy}{dx}$ is equal to

Find the components of the following compound statements:

(i) The sky is blue and the grass is green.

(ii) The earth is round or the sun is cold.

(iii) All rational numbers are real and all real numbers are complex.

(iv) 25 is a mmultiple of 5 and 8.

The locus of the point of intersection of the lines $axsec\theta +bytan\theta =aandaxtan\theta +bysec\theta =b$, where $\theta$ is the parameter, is

Let $A$ and $B$ be two invertible matrices of order $3\times 3$. If $\text{det}\left(AB{A}^T\right)=8$ and $\text{det}\left(A{B}^{-1}\right)=8$, then $\text{det}\left(B{A}^{-1}{B}^T\right)$ is equal to :

The area of the region in the xy-plane defined by the inequalities $x-2y^2\ge 0,1-x-\left|y\right|\ge 0$ is

Solution of the differential equation $\frac{\sqrt{x}dx+\sqrt{y}dy}{\sqrt{x}dx-\sqrt{y}dy}=\sqrt{\frac{y^3}{x^3}}$ is given by

The co-ordinates of the foot of perpendicular drawn from the origin to the line joining the points (-9, 4, 5) and (10, 0, -1) will be

Let $p,q$ be integers and let $\alpha ,\beta$ be the roots of the equation $x^2–2x+3=0$ where $\alpha \ne \beta .$ For $n=0,1,2,...,$ let $a_n=p{\alpha }^n+q{\beta }^n$ and $a_3=-10,$ then $p^q+q^p=$ ___

The function $f\left(x\right)=|x-2|,xϵR$ is not differentiate at

The arithmetic mean (A.M.) of the observations $\mathrm{1.3.5},\mathrm{3.5.7},\mathrm{5.7.9}...(2n–1).(2n+1).(2n+3)$ is

The number of ways to arrange the letters of the word Cheese are

Let the degree of polynomial ${(\sqrt{x^5-1}+x)}^9-{(\sqrt{x^5-1}-x)}^9$ be ${}^{\prime }{\alpha }^{\prime }$ then $\frac{\alpha -19}{2}$ is___.

3x-7 >x+1

Write the coordinates the vertex of the parabola whose focus is at (-2,1) and directrix is the line x+y-3=0.

Let $\lambda and\alpha$ be real. Find the set of all values of $\lambda$ for which the system of linear equations
$\lambda x+\left(sin\alpha \right)y+\left(cos\alpha \right)z=0,x+\left(cos\alpha \right)y+\left(sin\alpha \right)z=0and-x+\left(sin\alpha \right)y-\left(cos\alpha \right)z=0$
has a non - trivial solution.
For $\lambda =1$, the values of $\alpha$ are ___.
($n$ belongs to integers)

If a+b+c=0, then the solution of the equation $\left|\begin{array}{ccc}a-x& c& b\\ c& b-x& a\\ b& a& c-x\end{array}\right|=0$ is

If at x = 1, y = 2x is tangent to the parabola $y=a{x}^2+bx+c$, then respective values of a, b, c are

Five persons A, B, C, D and E are pulling a cart of mass 100 kg on a smooth surface and cart is moving with acceleration $3m/s^2$ in east direction. When person ‘A’ stops pulling, it moves with acceleration $1m/s^2$ in the west direction. When only person ‘B’ stops pulling, it moves with acceleration $24m/s^2$ in the north direction. The magnitude of acceleration of the cart when only A and B pull the cart keeping their directions same as the old directions, is $\left(\frac{25}{n}\right)m/s^2$, value of n is

The vector having initial and terminal points are (2, 5, 0) and (-3, 7, 4), respectively is

(a) $-\hat{i}+12\hat{j}+4\hat{k}$

(b) $5\hat{i}+2\hat{j}-4\hat{k}$

(c) $-5\hat{i}+2\hat{j}+4\hat{k}$

(d) $\hat{i}+\hat{j}+\hat{k}$

integrating factor of the differential equation $(1-y^2)\frac{dx}{dy}+yx=y(-1<x<1)$ is

Find the equation of the hyperbola with foci (0, $\pm$ 3) and vertices $(0,\pm \frac{\sqrt{11}}{2})$.

The equation that is incorrect is:

If the area of an equilateral triangle inscribed in the circle, $x^2+y^2+10x+12y+c=0$ is $27\sqrt{3}$ sq. units then $c$ is equal to :

Find the sum of all two digit numbers, which when divided by 4, yields 1 as remainder.

The plane which bisects the line segment joining the points $(-3,-3,4)$ and $(3,7,6)$ at right angles, passes through which one of the following points?

If A and B are sets, then prove that A - B, $A\cap B$ and B- A are pair wise disjoint.

Positive integers from $1$ to $45,$ are palced in $5$ groups of $9$ each. Then highest possible average of the medians of these $5$ groups is

Match given gates in Column I with the logical Boolean operation they perform in Column II and mark the correct option from the codes given below.

1. P -2,4,5 ,Q-5, R-3,5 , S-1,2

Study the following information carefully and answer the questions given below.
(i) ${}^{\prime }P÷Q^{\prime }$ means 'P is the sister of Q'.
(ii) ${}^{\prime }P\times Q^{\prime }$ means 'P is the brother of Q'.
(iii) ${}^{\prime }P-Q^{\prime }$ means 'P is the mother of Q'.
(iv) ${}^{\prime }P+Q^{\prime }$ means 'P is the father of Q'.
Which of the following means 'M is the maternal uncle of T'?

Let $f\left(x\right)=f_1\left(x\right)-2f_2\left(x\right)$,

where, $f_1\left(x\right)=\{\begin{array}{cc}min\{x^2,|x|\},& |x|\le 1\\ max\{x^2,|x|\},& |x|>1\end{array}$

and, $f_2\left(x\right)=\{\begin{array}{cc}min\{x^2,|x|\},& |x|>1\\ max\{x^2,|x|\},& |x|\le 1\end{array}$

and, $g\left(x\right)=\{\begin{array}{c}min\left\{f\right(t):-3\le t\le x,-3\le x<0\}\\ max\left\{f\right(t):0\le t\le x,0\le x\le 3\}\end{array}$

For $x\in (-1,0)$, $f\left(x\right)+g\left(x\right)$ is