Explore topic-wise InterviewSolutions in Current Affairs.

The remainder when $2^{120}$ is divided by $7$.

If f(x+1/x)=x²+1/x², then the value of f(3/2) is:

a) 5/4

b) 4/5

c) 1/4

d) -1/4

Let $L_1:x+y=1$ be a line and two perpendicular lines (which are not parallel or perpendicular to $L_1$) passes through $(2,1)$. If $C$ is incircle of the triangle formed by the three lines, then the locus of incentre of $C,$ is

Find the anti-derivative (or integral) of the following by the method of inspection.
$e^{2x}.$

Evaluate : ${\int }_{-2}^2\frac{x^2}{1+5^x}dx.$

Let $z_1=16+6i,z_2=10+6i$ (where $i=\sqrt{-1})$. If z is any complex number such that amp $\left(\frac{z-z_1}{z-z_2}\right)$ is $\frac{\pi }{4}$, then which of the following is/are always correct?

Probability fo solving specific problem independently by A and B are $\frac{1}{2}and\frac{1}{3}$ respectively. If both try to solve the problem independently, Find the probability that
the problem is solved

Probability fo solving specific problem independently by A and B are $\frac{1}{2}and\frac{1}{3}$ respectively. If both try to solve the problem independently, find the probability that
Exactly one of them solves the problem

One card is drawn at random from a well- shuffled deck of 52 cards. In which of the following cases are the events E and F independent?
E: the card drawn is a spade, F: the card drawn is an ace

The $n^{th}$ term of a sequence is given by $a_n=2n^2+n+1$. Show that it is not an A.P.

The values of 'a' for which( a²-1)x²+2(a-1)x+2 is positive for all real x are

Solve for x

Cos^{​​​​-1}[(x^{​​​​​​2}​​​-1)/(x^​​​2+1)] + Tan^​-1[2x/(x^{​​​​​​2}​​​​​-1)] = 2π/3

^{​​​​​​}

Let $f\left(x\right)=\{\begin{array}{cc}|x^2-3x|+a,0\le x<\frac{3}{2}& \\ -2x+3x\ge \frac{3}{2}& \end{array}$ If f(x) has a local maximum at x =.

Let $f$ be a twice differentiable function defined on $R$ such that $f\left(0\right)=1,$ $f^{\prime }\left(0\right)=2$ and $f^{\prime }\left(x\right)\ne 0$ for all $x\in R.$ If $\left|\begin{array}{cc}f\left(x\right)& f^{\prime }\left(x\right)\\ f^{\prime }\left(x\right)& f^{\prime \prime }\left(x\right)\end{array}\right|=0,$ for all $x\in R,$ then the value of $f\left(1\right)$ lies in the interval

Let the series be $\frac{1^2}{1}+\frac{1^2+2^2}{1+2}+\frac{1^2+2^2+3^2}{1+2+3}+\dots .$ Then

(where $T_n$ and $S_n$ denote the $n^{th}$ term and sum upto $n^{th}$ term respectively.)

A car is moving on a straight road. The velocity of the car varies with time as shown in the figure. Initially (at $t=0$), the car was at $x=0$, where, $x$ is the position of the car at any time ‘$t$’.

The displacement of the car from the starting position will be

Find a, if the coefficients of $x^2$ and $x^3$ in the expansion of $(3+ax{)}^9$ are equal.

Let $\alpha$ and $\beta$ be the roots of $x^2+x+1=0$. If $n$ be positive integer, then ${\alpha }^n+{\beta }^n$ is

The domain of $f\left(x\right)={\left(\frac{2x+1}{x^2-10x-11}\right)}^{2020}$ is

In which city does the person who works in Infotec live?

If ${\log }_{10}a,x,{\log }_{10}\frac{a^3}{b^2}$ are in A.P., then the value of $x$ is

Prove that :

sinA / cotA + cosecA = 2 + sinA / cotA - cosecA

Out of 6 boys and 6 girls, a group of 8 is to be formed. In how many ways can this be done if the group should have 4 boys?

The length of the sides of a triangle are $x,y$ and $\sqrt{x^2+y^2+xy}$ and The measure of the greatest angle is

The coefficient of $X^6$ in the expansion of is $(1+x{)}^{21}+(1+x{)}^{22}+.......+(1+x{)}^{30}$ is

If (9,12) is one end of a double ordinate of the parabola $y^2=16x$ then its equation is

A tangent is drawn to the parabola $y^2=4x$ at a point $P$ on the parabola in the first quadrant and another tangent is drawn to the vertex $A$ of the parabola. Let both the tangent meet at a point $B$,if area of the triangle $ABP=32{\text{unit}}^2$, then equation of the tangent is

For a given P.V. graph choose correct options.

If $\underset{x\to \infty }{lim}{\left(\frac{(x-1)(x+3)}{x^2}\right)}^{4x}=e^P,$ find $P.$

Consider a line $z(i-1)+\overline{z}(i+1)=0$ in the argand plane and a point $z_1=2+3i$ then the reflection of $z_1$ in the given line is

Three persons A, B and C are to speak at a function along with 5 other persons. If the persons speak in random order, the probability that A speaks before B and B speaks before C is:

A unit vector perpendicular to the plane containing the vector $\hat{i}+2\hat{j}+\hat{k}$ and $-2\hat{i}+\hat{j}+3\hat{k}$ is

The perpendicular distance of a line from origin is 2 units and the perpendicular makes an angle α with X-axis such that sin α=13. The equation of line is .

The normal at $P(2,4)$ to $y^2=8x$ meets the parabola at $Q.$ Then the equation of the circle having normal chord $PQ$ as diameter is

Form the differential equation of the family of circles touching the Y-axis at origin.

If f(x) is a differentiable function and ${\int }_0^{x^3}{t}^{2}f\left(t\right)dt=\frac{3}{13}{x}^{13}+5$ then $f\left(\frac{8}{27}\right)$

Two lines $L_1:x=5,\frac{y}{3-\alpha }=\frac{z}{-2}$ and $L_2:x=\alpha ,\frac{y}{-1}=\frac{z}{2-\alpha }$ are coplanar. Then, $\alpha$ can take value(s)

The value of ${\int }_{-\pi }^{\pi }\frac{co{s}^{2}x}{1+a^x}dx,a>0is$

Coefficient of $x^{18}in(1+x+2x^2+3x^3+.......+18x^{18}$is equal to

Let $\ast$ be a binary operation on the set Q of rational number as follows:
$\left(i\right)a\ast b=(a-b{)}^2$
Find which of the binary operation are commutative and which are associative?

Mark the correct alternative in each of the following :

The acute angle between the medians drawn from the acute angles of a right angled isosceles triangle is

If the tangent drawn at point $P(t^2,2t)$ on the parabola $y^2=4x$ is same as the normal drawn at point $Q(\sqrt{5}\cos \theta ,2\sin \theta )$ on the ellipse $4x^2+5y^2=20,$ then

If $\frac{\log x}{b-c}=\frac{\log y}{c-a}=\frac{\log z}{a-b}$, then which of the following is/are true?

A real valued function $f\left(x\right)$ satisfies the function equation $f(x-y)=f\left(x\right)f\left(y\right)-f(a-x)f(a+y)$ where a is a given constant $f\left(0\right)=1$ , $f(2a-x)$ is equal to