Explore topic-wise InterviewSolutions in Current Affairs.

Let (2, 3) be the focus of a parabola and x + y = 0 and x – y = 0 be its two tangents, then equation of its directrix will be

The value of $\frac{3}{2^3}+\frac{4}{2^4\cdot 3}+\frac{5}{2^6\cdot 3}+\frac{6}{2^7\cdot 5}+\cdots \infty$ is equal to

The value of determinant $\Delta =\left|\begin{array}{ccc}1+a& b& c\\ a& 1+b& c\\ a& b& 1+c\end{array}\right|$ is equal to

The foot of the perpendicular from P(1, 0, 2) to the line $\frac{x+1}{3}=\frac{y-2}{-2}=\frac{z+1}{-1}$ is

The value of $\underset{x\to \infty }{lim}\sqrt{x}(\sqrt{x+c}-\sqrt{x})is:$

If the expression $f\left(x\right)=x^2+6x+k$ is non negative $\forall x\in R$, then the interval in which $k$ lies is

The number of solutions of ${16}^{{\sin }^{2}x}+{16}^{{\cos }^{2}x}=10$ in the interval $x\in [0,\pi ]$ is

For the differential equation in given question find the general solution.​​​​

$\frac{dy}{dx}=\sqrt{4-y^2}$

The number of intersection points of the function $f\left(x\right)=cotx$ and $y=3$ in $x\in (0,3\pi )$ is:

List
all the elements of the following sets:

(i) A
= {x:
x
is an odd natural number}

(ii) B
= {x:
x
is an integer,}

(iii) C
= {x:
x
is an integer,}

(iv) D
= {x:
x
is a letter in the word “LOYAL”}

(v) E
= {x:
x
is a month of a year not having 31 days}

(vi) F
= {x:
x
is a consonant in the English alphabet which proceeds k}.

Let two circles touch each other externally and $P$ is the point of intersection of there direct common tangents. If the direct common tangents from $P$ touches the circles at $A$ and $B$ on same side and $PA=AB=4$, then the radius of smaller circle (in units) is

Mean of $n$ items is $\overline{x}$. If these $n$ items are successively increased by $2,2^2,2^3,..,2^n$, then the new mean is

A straight line through the point $(3,-2)$ is inclined at an angle ${60}^{\circ }$ to the line $\sqrt{3}x+y=1$. If it intersects the
$x$-axis, then the equation will be

If $a$ and $b$ are unit vectors and $\theta$ is the angle between them, then $|a+b|<1$, if

In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees that each section of each class will plant, will be same as the class, in which they are studying, e.g., a section of class $\text{I}$ will plant $1$ tree, a section of class $\text{II}$ will plant $2$ trees and so on till class $\text{XII}$, If there are three sections of each class, then the number of trees planted is

Let f:[0, infinity) to R be a function defined by f(x)= 9x² +6x-5. Proove that f is not invertible.Modify ,only the codomain of f to make f invertible and then find it's inverse .Also , find f^{​​​​​​-1}(43)

The general solution of the equation ${\sin }^2\theta ={\sin }^2\alpha$ is/are

The line x + y = 1 meets x - axis at A and y - axis at B. P is the mid - point of AB $P_1$ is the foot of the perpendicular from P to OA; $M_1$ is that from $P_1$ to OP; $P_2$ is that from $M_1$ to OA; $M_2$ is that from $P_2$ to OP; $P_3$ is that from $M_2$ to OA and so on. If $P_n$ denotes the nth foot of the perpendicular on OA from $M_{n-1}$, then $O{P}_n$ =

Coefficient of variation of two distribution are $60\%$ and $70\%$ and their standard deviations are 21 and 16 respectively. What are their arithmetic means ?

The function f (x) = a^x, 0 < a < 1 is

If $A$ is the set of letters of the word $"damascus",$ then the letter is an element of the set $A.$

Five cards are drawn successively with replacement from well- shuffled deck of 52 cards. What is the probability that

None is a spade?

If $f\left(x\right)={\int }_1^x\frac{dt}{2+t^4}$, then

Which of the following is equivalent to the Boolean expression p $\wedge \sim q$?

${\int }_0^{\pi /2}\frac{dx}{4{\cos }^{2}x+9{\sin }^{2}x}=$

In the circle given below, let $OA=1$ unit, $OB=13$ unit and $PQ\perp OB.$ Then, the area of the triangle $PQB$ (in square units) is :