Explore topic-wise InterviewSolutions in Current Affairs.

Two vertical poles are $150m$ apart and the height of one is three times that of the other. If from the middle point of the line joining their feet, an observer finds the angles of elevation of their tops to be complementary, then the height of the shorter pole (in meters) is:

If $|2^x-7|=|9-2^x|$, then the value of $x$ is

Find out the wrong number in the series given below :

$2,5,10,17,26,37,51$

Equation of the hyperbola passing through the point $(1,-1)$ and having asymptotes $x+2y+3=0$ and $3x+4y+5=0$ is :

The equation of the circle which passes through $(8,16)$ and touches the line $4x-3y=64$ at $(16,0)$ is

A line passing through the point $(4,6)$, then the locus of the mid point of the portion of line between the co-ordinate axes is

If $25$ blankets are distributed among $5$ persons then the probability that each person gets odd number of blankets is

If the equations $x^2+2xy+p{y}^2=0$ and $p{x}^2+2xy+y^2=0$ have one factor exactly in common, then the joint equation of their other two factors will be given by

(correct answer + 1, wrong answer - 0.25)

Three pipes $A,B$ and $C$ can fill a tank from empty to full in $30$ minutes, $20$ minutes, and $10$ minutes respectively. When the tank is empty, all the three pipes are opened. $A,B$ and $C$ discharge chemical solutions $P,Q$ and $R$ respectively. What is the proportion of the solution $R$ in the liquid in the tank after $3$ minutes?

Let $f:[-2,2]\to R$ be a continuous function such that $f\left(x\right)$ assumes only irrational values. If $f\left(\sqrt{2}\right)=\sqrt{2}$, then

The equation of the tangents to the circle $x^2+y^2=a^2$, which makes a triangle of area $a^2$ sq. units with coordinate axes, is/are

In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to:

If $\int \frac{x\cos \alpha +1}{(x^2+2x\cos \alpha +1{)}^{3/2}}dx=\frac{f\left(x\right)}{\sqrt{g\left(x\right)+1}}+C$, then $g\left(x\right)-2\cos \alpha f\left(x\right)$ is

(where $C$ is constant of integration)

The locus of the point of intersection of perpendicular tangents to the circles $x^2+y^2=a^{2}and{x}^2+y^2=b^{2}is$

The number of ways in which score of 11 can be made from a throw by three persons is throwing a single die once, is

(a) 45 (b) 18

(c) 27 (d) 68

An ideal gas undergoes a circular cycle centered at 4 atm, 4 lit as shown in the diagram. The maximum temperature attained in this process is close to

If $A=\left[\begin{array}{cc}1& tanx\\ -tanx& 1\end{array}\right],A^T{A}^{-1}=$ ___

The common tangent to the parabolas $y^2=4ax$ and $x^2=32ay$ has the equation

Find the second order derivative of the given functions.

$e^{6x}cos3x$

In the given figure, two circles of different radii are placed against a right angle. If the radius of the bigger circle is 1 unit, then the radius of the smaller circle is

The equation of plane whose foot of perpendicular from origin is $(-2,2,-1),$ is

If $\alpha$ is a non real root of $z=(1{)}^{1/5},$ then the value of $(1+\alpha +{\alpha }^2+{\alpha }^{-2}-{\alpha }^{-1})$ is

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Find the mean deviation about the median for the data

Consider the equation of curve $y=x^2-3x+3$ and $x\ne 3.$

Then slope of tangent at point, where its ordinate and abscissa are equal, is



[2 marks]

If $f\left(x\right)$ is a differentiable function and ${\int }_0^{t^2}xf\left(x\right)=\frac{2}{5}{t}^5$, then $f\left(\frac{4}{25}\right)$ equals

${lim}_{x\to 0}\frac{5^x+3^x+2^x-3}{x}$

If the line $2y=4x-6$ cuts the curve $y^2=-16x$ at points $A$ and $B$, then the equation of circle having $AB$ as diameter is

If $y=f\left(x\right)$ makes $+ve$ intercept of $2$ and $0$ unit on $x$ and $y$ axes respectively and enclosed an area of $\frac{3}{4}$ square unit in the first quadrant, then $\underset{0}{\overset{2}{\int }}x{f}^{\prime }\left(x\right)dx$ is equal to

${\left(ta{n}^{-1}x\right)}^2+{\left(co{t}^{-1}x\right)}^2=\frac{5{\pi }^2}{8}\Rightarrow x=$

If $I=\underset{-a}{\overset{a}{\int }}(\alpha {\sin }^{5}x+\beta {\tan }^{3}x+\gamma \cos x)dx$, where $\alpha ,\beta ,\gamma$ are constants, then the value of $I$ depends on

The value of $\underset{n\to \infty }{lim}\frac{(1^2+2^2+3^2+\cdots +n^2)(1^3+2^3+3^3+\cdots +n^3)}{1^6+2^6+3^6+\cdots +n^6}$ is