Explore topic-wise InterviewSolutions in Current Affairs.

The sum of the roots of the equation $\sqrt{5x^2-6x+8}-\sqrt{5x^2-6x-7}=1$ is

If $f\left(x\right)=\cos x-2px$ is an invertible function, then which of the following is/are CORRECT?

The positive root of the quadratic equation,

$x^2+x-2=0$ is

A natural number x is chosen at random from the first $100$ natural numbers. The probability for the inequality $x+\frac{100}{x}>50$ to hold good is:

If the system of equations $ax+hy+g=0,hx+by+f=0$ and $gx+fy+c=k$

is consistent and

$k=\frac{1}{\lambda }\left|\begin{array}{ccc}a& h& g\\ h& b& f\\ g& f& c\end{array}\right|$, then $\lambda$ is equal to

Let $PQR$ be a triangle of area $\Delta$ with $a=2,b=\frac{7}{2},c=\frac{5}{2},$ where $a,b,$ and $c$ are the lengths of the sides of the triangle opposite to the angles at $P,Q$ and $R,$ respectively. Then the value of $\frac{2\sin P-\sin 2P}{2\sin P+\sin 2P}$ is :

Consider f:
R₊ →
[4, ∞)
given by f(x)
= x²
+ 4. Show that f
is invertible with the inverse f⁻¹
of given f by,
where R₊
is the set of all non-negative real numbers.

In the following equilibria :-
(1) $A+2B\rightleftharpoons C;K_{eq}=K_1$
(2) $C+D\rightleftharpoons 3A;K_{eq}=K_2$
(3) $6B+D\rightleftharpoons 2C;K_{eq}=K_3$
Hence:

For three sets $A,B\&C,$

$A\cap (B\cup C)=$

Let $A$ be the sum of the first $20$ terms and $B$ be the sum of the first $40$ terms of the series

$1^2+2\cdot 2^2+3^2+2\cdot 4^2+5^2+2\cdot 6^2+\dots .$

If $B-2A=100\lambda$, then $\lambda$ is equal to

What will be the next number in the following sequence?



5, 7, 11, 13, 17, 19, __

1. -0.8216

Determine
whether or not each of the definition of given below gives a binary
operation. In the event that * is not a binary operation, give
justification for this.

(i) On
Z⁺,
define * by a *
b =
a −
b

(ii) On
Z⁺,
define *
by a *
b =
ab

(iii) On
R,
define *
by a *
b =
ab²

(iv) On
Z⁺,
define *
by a *
b =
|a −
b|

(v) On
Z⁺,
define *
by a *
b =
a

If both the roots of $x^2+2(a+2)x+9a-1=0$ are negative, then ${}^{\prime }{a}^{\prime }$ lies in

A man has a certain number of chickens and goats. Their head count is 30. If the total number of their legs is 84, what is the ratio between the number of chickens and goats?

Find the equation of the hyperbola whose foci are at (0,$\pm 6)$ and the length of whose conjugate axis is $2\sqrt{11}$.

If the curves $y^2=6x,9x^2+b{y}^2=16$ intersect each other at right angles, then the value of $b$ is :

The number of ways in which $5$ balls can be selected from a bag containing $5$ identical and $5$ different balls is

If $f(x+y)=f\left(x\right)+f\left(y\right)\forall x,y\in R$ and $f\left(4\right)$ is the sum to infinite terms of the series $2,1,\frac{1}{2},\frac{1}{4},\dots .$, then the image of $y=\ln (x+3)$ with respect to $y=f\left(x\right)$ is:

The value of determinant $\left|\begin{array}{ccc}1+a^2-b^2& 2ab& -2b\\ 2ab& 1-a^2+b^2& 2a\\ 2b& -2a& 1-a^2-b^2\end{array}\right|$ is equal to

If $I={\int }_0^{\pi /2}{\cos }^{n}x{\sin }^{n}x\mathrm{dx}=k{\int }_0^{\pi /2}{\sin }^{n}x\mathrm{dx}$, then k equals

The probability density function of a ramdom variable X is given by



$f_x\left(x\right)=\{\begin{array}{cc}\lambda (x-2)(x^2+4);& 2\le x<4\\ 0& otherwise\end{array}$



The value of the constant $\lambda$ is

If sum of three numbers is $4$, sum of their squares is $14$, sum of their cubes is $34$ and their products is $-6$, then sum of products of two numbers at a time is

A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of february calendars should it prepare to serve for all the possibilities it future years ?

If $\overrightarrow{a}$ and $\overrightarrow{c}$ are unit vectors and $\overrightarrow{a}=2(\overrightarrow{b}\times \overrightarrow{c})+(\overrightarrow{c}\times \overrightarrow{a})$, then

Consider the letters of the word $MATHEMATICS$.

The possible number of words in which no two vowels are together is

If $\sin \theta +\sin \varphi =a$ and $\cos \theta +\cos \varphi =b$, $(a\ne b,a\ne 0,b\ne 0)$ then