Explore topic-wise InterviewSolutions in Current Affairs.

If $\left|\frac{2}{x-5}\right|>1,$ then $x$ belongs to the interval

If $\int \cos x\log \left(\tan \frac{x}{2}\right)dx=\sin x\log \left(\tan \frac{x}{2}\right)+f\left(x\right)$ then $f\left(x\right)$ is equal to, (assuming c is a arbitrary real constant)

${lim}_{x\to 0}\frac{tanx-sinx}{sin3x-3sinx}$

All linear programming problems have all of the following properties EXCEPT

xdy - ydx=$\sqrt{x^2-y^2}dx$ and y(1) = 0 then $y\left(e^{\frac{\pi }{2}}\right)$=

State and prove Lami's theorem.

If $i^2=-1$, then the sum $i+i^2+i^3+......$ upto 1000 terms is equal to

$\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+........+\frac{1}{n(n+1)}=\frac{n}{n+1}$

Two lines whose direction ratios are a₁, b₁, c₁ and a₂, b₂, c₂ are perpendicular, if

A ball is dropped from a balloon going up at a speed of 7 m/s. If the balloon was at a height 60 m at the time of dropping the ball, how long will the ball take in reaching the ground ?

If $A=\{x:x$ is a letter of the word 'RAMANA'$\}$,
$B=\{x:x$ is a letter of the word 'MISSISSIPPI'$\}$,
$C=\{x:x$ is a letter of the word 'NOOKBOOK'$\}$,
Then relation between cardinality of sets $A,B$ and $C$ is

Find the equation of the straight line passing through the point (6, 2) and having slope -3.

Answer Q.15 and Q.16 by appropriately matching the lists based on the information given in the paragraph.

Let $f\left(x\right)=\sin \left(\pi \cos x\right)$ and $g\left(x\right)=\cos \left(2\pi \sin x\right)$ be two functions defined for $x>0.$ Define the following sets whose elements are written in the increasing order:
$X=\{x:f(x)=0\},Y=\{x:f^{\prime }(x)=0\},$
$Z=\{x:g(x)=0\},W=\{x:g^{\prime }(x)=0\},$.
$List-I$ contains the sets $X,Y,Z$ and $W$. $List-II$ contains some information regarding these sets.

$\begin{array}{cccc}& ListI& & ListII\\ \left(i\right)& X& \left(P\right)& \supseteq \{\frac{\pi }{2},\frac{3\pi }{2},4\pi ,7\pi \}\\ \left(ii\right)& Y& \left(Q\right)& \text{an arithmetic progression}\\ \left(iii\right)& Z& \left(R\right)& \text{NOT an arithmetic progression}\\ \left(iv\right)& Z& \left(S\right)& \supseteq \{\frac{\pi }{6},\frac{7\pi }{6},\frac{13\pi }{6}\}\\ & & \left(T\right)& \supseteq \{\frac{\pi }{3},\frac{2\pi }{3},\pi \}\\ & & \left(U\right)& \supseteq \{\frac{\pi }{6},\frac{3\pi }{4}\}\end{array}$
Q.16 which of the following is the only CORRECT combination?

What will be the differenciation of sin²x using chain rule? Can you explain with detail?

Give the general solution of the equation tan 5x = cot 2x

$A(6,3),B(-3,5),C(4,-2)$ and $D(x,3x)$ are four points. If $\Delta DBC:\Delta ABC=1:2,$ then x is equal to

Find points on the curve $\frac{x^2}{9}+\frac{y^2}{16}=1$ at which the tangents are

(a) parallel to X-axis

(b) parallel to Y-axis.

Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.

Prove that $\frac{\left(2n\right)!}{2^{2n}(n!{)}^2}\le \frac{1}{\sqrt{3n+1}}$ for all $nϵN$.

The length of intercepts made by the circle $x^2+y^2-4x+6y+4=0$ on $X$ and $Y$ axis respectively, are

Find the locus of the mid-points of the portion of the line $xsin\theta +ycos\theta =p$ intercipted between the axes.

Equation of tangent to $x^2(x–y)+a^2(x+y)=0at(0,0)$ is

Write the value of $\frac{d}{dx}\left\{\right(x+|x|\left)|x|\right\}$

Prove that $\left|\begin{array}{ccc}bc-a^2& ca-b^2& ab-c^2\\ ca-b^2& ab-c^2& bc-a^2\\ ab-c^2& bc-a^2& ca-b^2\end{array}\right|$ is divisible by (a+b+c) and find the quotient.

Locus of the point of intersection of any two perpendicular tangents to the parabola $x^2=4ay$ is

For the set A = {1,2,3}, define the relation R on the set A as R = { (1,1), (2,2), (3,3) (1,3) }, the R is

For a circle $x^2+y^2=81,$ what is the equation of chord whose mid point is $(–2,3)$

If 1 $m^3$ = 750 kg for saw timber, find in which year was the difference in prices of saw timber and logs the least?

The number of solutions of equation $\pi co{t}^{-1}(x-1)+(\pi -1)co{t}^{-1}x=2\pi -1$ is

The value of $C$ in Mean value theorem for the function $f\left(x\right)=x^2$ in $\in [2,4]$ is

The general solution of differential equation $\frac{dy}{dx}=e^{x-y}+x^2{e}^{-y}$ is

If the mean deviation of the data $1,1+d,$ $1+2d,\dots ,1+100d$ from their mean is $255,$ then $d$ is equal to

$\text{In any}\Delta ABC,\text{prove that :}\frac{bsecB+csecC}{tanB+tanC}=\frac{csecC+asecA}{tanC+tanA}=\frac{asecA+bsecB}{tanA+tanB}$

${lim}_{x\to \frac{x}{4}}\frac{4\sqrt{2}-(cosx+sinx{)}^5}{1-sin2x}$ is equal to

For the following question verify that the given function (explicit or implicit) is a solution of the corresponding differential equation.

xy=logy +C and $y^{\prime }=\frac{y}{1-xy}(xy\ne 1).$

In any $\Delta ABC,$ prove that

$a(cosC-cosB)=2(b-c)co{s}^2\frac{A}{2}.$