Explore topic-wise InterviewSolutions in Current Affairs.

If $f\left(x\right)={\log }_{[x-1]}\left(\frac{|x|}{x}\right),$ where $[\cdot ]$ is greatest integer function, then domain $D_f$ and range $R_f$ of $f\left(x\right)$ are

You are given
$\cos x=1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}......$;
$\sin x=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}......$;
$\tan x=x+\frac{x^3}{3}+\frac{2x^5}{15}......$
Then the value of
$\underset{x\to 0}{lim}\frac{x\cos x+\sin x}{x^2+\tan x}$ is

If A = 1 and B = 0, what is the value of A.A+B?

The sum of the slopes of the tangents to the parabola $y^2=8x$ from the point $(-2,3),$ is

If 1 $\le$ $\left|x\right|$ $\le$ 3,then x belongs to the interval

Let R={(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)}

be a relation on the set A={3, 6, 9, 12}. The relation is

If Rolle’s theorem holds for the function $f\left(x\right)=x^3–a{x}^2+bx–4,x\in [1,2]$ with $f^{\prime }\left(\frac{4}{3}\right)=0,$ then ordered pair (a, b) is equal to :

If $A$ and $B$ are two events of a sample space $S$ such that $P\left(A\right)=0.2,P\left(B\right)=0.6$ and $P\left(A|B\right)=0.5$ then $P\left(A^{\prime }|B\right)=$

The coefficient of $x^6$ in the expansion of ${(1+\frac{x}{\angle 1}+\frac{x^2}{\angle 2}+\frac{x^3}{\angle 3}+\frac{x^4}{\angle 4}+\frac{x^5}{\angle 5})}^2$ is

General solution of a differential equation is $y=k{e}^x$. Find the particular solution if the curve passes through $(0,1)$

Evaluate the following limits:

${lim}_{x\to 0}\frac{\sqrt{1+x+x^2}-1}{x}$

Let $A=Q\times Q$, where Q is the set of all rational numbers, and * be a binary operation on A defined by (a, b) * (c, d) = (ac, b + ad) for $(a.b),(c,d)ϵA$. Then find

(i) The identity element of * in A.

(ii) Invertible elements of A, and hence write the inverse of elements (5, 3) and. $(\frac{1}{2},4)$.

OR

Let f : $W\to W$ be defined as

$f\left(n\right)\{\begin{array}{cc}n-1,& \text{if n is odd}\\ n+1,& \text{if n is even}\end{array}$
Show that f is invertible and find the inverse of f. Here, W is the set of all whole numbers.

Determine the point on yz-plane which is equidistant from points A(2, 0, 3), B(0, 3, 2) and C(0, 0, 1).

Let $a,b,c$ and $d$ be non-zero numbers. If the point of intersection of the lines $4ax+2ay+c=0$ and $5bx+2by+d=0$ lies in the fourth quadrant and is equidistant from the two axes then:

Find the coefficient of variation for the following data :

$\begin{array}{ccccccc}\text{Size (in cms ):}& 10-15& 15-20& 20-25& 25-30& 30-35& 35-40\\ \text{No of items}:& 2& 8& 20& 35& 20& 15\end{array}$

$ta{n}^{-1}\frac{x}{y}-ta{n}^{-1}\frac{x-y}{x+y}$ is equal to (where x>y>0)

${lim}_{n\to \infty }[\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}\cdots \frac{1}{(2n+1)(2n+3)}]$ is equa to

$\int co{s}^{3}x{e}^{logsinx}dx$

In triangle $ABC,\frac{\sin A+\sin B+\sin C}{\sin A+\sin B-\sin C}$ is equal to

If $B=\left[\begin{array}{ccc}5& 2\alpha & 1\\ 0& 2& 1\\ \alpha & 3& -1\end{array}\right]$ is the inverse of a $3\times 3$ matrix $A,$ then the sum of all values of $\alpha$ for which $det\left(A\right)+I=0,$ is

If $(p+q{)}^{th}$ and (p - q)th terms of a G.P. are m and n respectively, then write its pth term.

$\text{The general solution of the equation 7}co{s}^2\theta +3si{n}^2\theta =4is$

The derivative of $\frac{d}{dx}\left(\frac{1}{x\sqrt{x}}\right)=$ .

A vertical lamp foot of height $10$m stands at the corner of the rectangular field. The angle of elevation of its top from the farthest corner is ${30}^{\circ }$ while from one of the other two corners it is ${45}^{\circ }$, then the area of the field is

The coefficient of $x^{28}$ in the expansion of $(1+x^3-x^6{)}^{30}$ is

A tangent to the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ at any point $P$ meets the line $x=0$ at a point $Q.$ Let $R$ be the image of $Q$ in the line $y=x$, then the circle whose extremities of a diameter are $Q$ and $R$ passes through a fixed point. The fixed point is

find the value of : 5sin² + cos² 45`- 4tan<sup>2</sup> 30`/ 2sin30 cos30 + tan45

Let $A(a,b)$ and $B(0,0)$ be two fixed points. If $M_1$ is the mid point of line segment $AB$, $M_2$ is the mid point of line segment $A{M}_1$ and $M_3$ is the mid point of line segment $A{M}_2$ and so on, then which of the following is/are true?

Prove that :

$(9^{\frac{1}{3}}{.9}^{\frac{1}{9}}{.99}^{\frac{1}{27}}{.169}^{\frac{1}{32}}.....\infty )=3.$

Let f and g be two real functions given by
f = {(0, 1), (2, 0), (3, -4), (4, 2), (5, 1)} and
g = {(1, 0), (2, 2), (3, -1), (4, 4), (5, 3)}.
Find the domain of fg.

Straight lines are drawn by joining $m$ points on a straight line to $n$ points on another line. Then excluding the given points, the number of point of intersections of the lines drawn is (no two lines drawn are parallel and no three lines are concurrent)

Let $A$ and $B$ (where $A>B$), be acute angles. If $\sin (A+B)=\frac{12}{13}$ and $\cos (A-B)=\frac{3}{5}$, then the value(s) of $\sin \left(2A\right)$ is/are
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If a coin is tossed two times, describe the sample space associated to this experiment.

Let f(x) = 2x + 1. Then the number of real values of x for which the three numbers f(x), f(2x), f(4x) are in G.P. is

In a $△ABC$, if $tan\frac{A}{2}=\frac{5}{6}andtan\frac{B}{2}=\frac{20}{37}$,then

Miss $X$ takes either tea or coffee at morning break. If she had tea one morning, the probability that she has tea the next morning is $\mathrm{0.4.}$ If she had coffee one morning, the probability that she has coffee the next morning is $\mathrm{0.3.}$ Suppose she has coffee on a Monday morning. The probability that she has tea on the following Wednesday morning, is

If f and g two functions such that they are one-one then g o f is:

If $5p^2-7p-3=0$ and $5q^2-7q-3=0$, $p\ne q$, then the equation whose roots are $5p-4q$ and $5q-4p$ is :