Explore topic-wise InterviewSolutions in Current Affairs.

Let $x_1,x_2,x_3$ be three positive numbers such that $x_1+x_2+x_3=z$.

Which of the following is/are correct?

If the product of the roots of the quadratic equation $m{x}^2-2x+(2m-1)=0$ is $3$, then the value of $m$ is

Let $f\left(x\right)=\{\begin{array}{cc}{x}^2+kx,& x<0\\ \sin x,& x\ge 0\end{array}.$ If $f\left(x\right)$ is differentiable at $x=0,$ then

Let E and F be two independent events. The probability that both E and F happen is 1/12 and the probability that neither E nor F happens is 1/2 .Then,

Let $P=\left[\begin{array}{ccc}1& 0& 0\\ 3& 1& 0\\ 9& 3& 1\end{array}\right]$ and $Q=\left[q_{ij}\right]$ be two $3\times 3$ matrices such that $Q-P^5=I_3.$ Then $\frac{q_{21}+q_{31}}{q_{32}}$ is equal to

The length of normal at any point of the curve $y=\frac{1}{2}a(e^{\frac{x}{a}}+e^{-\frac{x}{a}})$ is :

Find the equation of pair of tangents to the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ from (5, 4).

if $Z_1$ and $Z_2$ are 2 non - complex number such that |$Z_1$ + $Z_2$| = |$Z_1$| + |$Z_2$|,Then arg ($Z_1$) - arg($Z_2$) is equal to

Hint: Square on both sides.

For $0\le t<\infty ,$ the maximum value of the function $f\left(t\right)=e^{-t}-2e^{-2t}$ occurs at

If $\theta =178°$, then the value of $\sin \theta \sqrt{1+{\cot }^2\theta }+\cos \theta \sqrt{1+{\tan }^2\theta }$ is

The sum of all natural numbers which are divisible by 3 and less than 100 is

Give an example of two functions $f:N\to N$ and $g:N\to N$ such that gof is onto but f is not onto.

The range of $f\left(x\right)=x-{\sin }^{2}x,x\in R$ is

The minimum value of $\frac{{\sec }^4{\theta }_1}{{\tan }^2{\theta }_2}+\frac{{\sec }^4{\theta }_2}{{\tan }^2{\theta }_1}$, wherever defined, is

​​​​​​​(correct answer + 1, wrong answer - 0.25)

Write the first five terms of the sequences whose n^th term is

The equations of the tangents to the circle $x^2+y^2=36$ which are inclined at an angle of ${45}^o$ to the x-axis are

There are $15$ boys and $10$ girls in a class. If three students are selected at random, then what is the probability that $1$ girl and $2$ boys are selected?

If the set A has p elements, B has q elements, then the number of elements in $A\times B$ is

Find the shortest
distance between the lines

The locus of the point of intersection of tangents drawn at the extremities of a normal chord to the parabola $y^2=4ax$ is the curve

Locus of the centre of the circle which always passes through the fixed point $(a,0)$ and $(-a,0)$, where $a\ne 0$, is

The Cartesian equation of the curve whose parametric equations are $x=t^2+2t+3$ and y = t + 1 is

Sixteen players $P_1.P_2.\dots \dots \dots P_{16}$ play in a tournament. They are divided into eight pairs at random.From each pair a winner is decided on the basis of a game played between the two players of the pair.Assuming that all the players are of equal strength, the probability that exactly one of the two players $P_1$ and $P_2$ is among the eight winners is

If the distance between the foci and the distance between the two directricies of a hyperbola are in the ratio $5:4$ , then the eccentricity of the hyperbola is :

Give examples of two functions f:
N → Z and g: Z → Z such
that g o f is injective but g is not injective.

(Hint:
Consider f(x) = x and g(x) =)

If $x^m.y^n=(x+y{)}^{m+n}$, then $\frac{dy}{dx}$ is

$Ify=\left|\begin{array}{ccc}f\left(x\right)& g\left(x\right)& h\left(x\right)\\ l& m& n\\ a& b& c\end{array}\right|,provethat\frac{dy}{dx}=\left|\begin{array}{ccc}{f}^{\prime }\left(x\right)& g^{\prime }\left(x\right)& h^{\prime }\left(x\right)\\ l& m& m\\ a& b& c\end{array}\right|$

The locus of the centre of a circle touching the lines $2x+3y–2=0\text{and}2x–3y+2=0$ may be

Determine
whether each of the following relations are reflexive, symmetric and
transitive:

(i)Relation
R in the set A
= {1, 2, 3…13, 14} defined as

R
= {(x,
y):
3x
− y
= 0}

(ii) Relation R in the set N
of natural numbers defined as

R
= {(x,
y):
y
= x
+ 5 and x
< 4}

(iii) Relation R in the set A
= {1, 2, 3, 4, 5, 6} as

R
= {(x,
y):
y
is divisible by x}

(iv) Relation R in the set Z
of all integers defined as

R
= {(x,
y):
x
− y
is as integer}

(v) Relation R in the set A
of human beings in a town at a particular time given by

(a) R
= {(x,
y):
x and
y
work at the same place}

(b) R
= {(x,
y):
x
and y
live in the same locality}

(c) R
= {(x,
y):
x is
exactly 7 cm taller than y}

(d) R
= {(x,
y):
x
is wife of y}

(e) R
= {(x,
y):
x
is father of y}

If $P(a,b)$ are the coordinates of a point on the line $x+y=3$ such that $P$ lies below $x-$axis and a distance of $3\sqrt{2}$ units from the point $Q(1,2)$, then number of integral values of $k$ for which both $a$ and $b$ lie between the roots of quadratic equation $\frac{x^2-10}{k}=kx$ is

If ${}^{18}{C}_x{=}^{18}{C}_{x+2},$ find x.

Let P be the image of the point (3, 1, 7) with respect to the plane x - y + z = 3. Then, the equation of the plane passing through P and containing the straight line $\frac{x}{1}=\frac{y}{2}=\frac{z}{1}$ is

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning prize is $\frac{1}{100}$. What is the probability that he will win a prize.

Atleast once ?

exactly once ?

atleast twice ?