Explore topic-wise InterviewSolutions in Current Affairs.

A set of integers is given as (3,6,8,14,17). What is the probability that a triangle can be constructed.?

Suppose
that two cards are drawn at random from a deck of cards. Let X be the
number of aces obtained. Then the value of E(X) is

(A) (B) (C) (D)

If the function 'f' and 'g' are continuous at c then. Choose the incorrect alternative.

If ${\cos }^{-1}\left(a\right)+{\cos }^{-1}\left(b\right)+{\cos }^{-1}\left(c\right)=3\pi$ and $f$ be a function such that $f\left(1\right)=2$ and $f(x+y)=f\left(x\right)\cdot f\left(y\right)$ for all $x,y\in R,$ then the value of $a^{2f\left(1\right)}+b^{2f\left(2\right)}+c^{2f\left(3\right)}+\frac{a+b+c}{a^{2f\left(1\right)}+b^{2f\left(2\right)}+c^{2f\left(3\right)}}$ is

If for $x\in (0,\frac{\pi }{2}),{\log }_{10}\sin x+{\log }_{10}\cos x=-1$ and ${\log }_{10}(\sin x+\cos x)=\frac{1}{2}({\log }_{10}n-1),n>0$

then the value of $n$ is equal to:

If $3^x=4^{x-1}$, then $x=$

If $\sec (x-y),\sec x,\sec (x+y)$ are in arithmetic progression and $\sec y\ne 1,$ then the angle $y$ can be

If $I(m,n)=\underset{0}{\overset{1}{\int }}{t}^m(1+t{)}^{n}dt$ $(m,n\in N),$ then $I(m,n)$ is:

If $|4x-5|+|6x-12|=|2x-7|$, then $x$ belongs to

The diagram shows a circle with radius 3 and centre at O.
The circumference and the area of this circle are rational or irrational? [2 MARKS]

Prove that 2sin x/ sin 3x = 1 - tan x * cot 3x

If $x^2+4+3\sin (ax+b)-2x=0$ has atleast one real solution, where $a,b\in [0,2\pi ]$, then the value of $a+b$ can be

If $\theta$ is the angle between the lines whose DR's are $(1,-2,1),(4,3,2),$ then $\sec \frac{\theta }{2}+\text{cosec}\frac{\theta }{2}=$

The value of ${\sin }^{-1}\left(\frac{12}{13}\right)-{\sin }^{-1}\left(\frac{3}{5}\right)$ is equal to :

If $A=\{8,16,24,32\}$ and $B=\{5,25,125\}$ and $R$ is relation defined from A to B such that $aRb$ means $a<b$ for all $a\in A,b\in B$ and $(a,b)\in R,$ then $R=$ ___.

If $2|x+1{|}^2-3|x+1|+1=0$, then $x=$

Insert 4 A.M.s between 4 and 19.

Solve
system of linear equations, using matrix method.

If ${\sin }^{-1}x+{\sin }^{-1}y+{\sin }^{-1}z=\frac{-3\pi }{2}$ and $\lambda =\frac{x^2+y^4}{x^4+y^8+z^{16}},$ then $\sum _{k=1}^{\infty }{\lambda }^k=$

Each student in a class of $40$, studies at least one of the subjects English, Mathematics and Physics. $16$ study English, $22$ study Physics and $26$ study Mathematics, $5$ study English and Physics, $14$ Mathematics and Physics and $2$ study all the three subjects. The number of students who study English and Mathematics but not Physics is

Match the pairs which give same answers.

Two events
A and B will be independent, if

(A) A and
B are mutually exclusive

(B)

(C) P(A) =
P(B)

(D) P(A) +
P(B) = 1

Let $f\left(x\right)=\sqrt{4-\sqrt{2-x}}$ and $g\left(x\right)=(x-a)(x-a+3).$ If $g\left(f\right(x\left)\right)<0\forall x\in D_f,$ then the complete set of values of $a$ is
$[D_f$ denotes the domain of the function $f]$

Find the value of $\frac{co{s}^{3}A-cos3A}{cosA}$ + $\frac{si{n}^{3}A-sin3A}{sinA}$

If $y=mx-b\sqrt{1+m^2}$ is a common tangent to $x^2+y^2=b^2$ and $(x-a{)}^2+y^2=b^2$, where $a>2b>0$, then the positive value of $m$ is