Explore topic-wise InterviewSolutions in Current Affairs.

${lim}_{x\to 2}\frac{x-2}{lo{g}_a(x-1)}$

If $U=1,2,3,4,5,6,7,A=1,2,3,4,5$, and $B=1,3,5,7$, then $A^{\prime }–B^{\prime }$ is equal to:

Solve the following equation for x:
$2ta{n}^{-1}\left(cosx\right)=ta{n}^{-1}\left(2cosecx\right)$

If $cos\alpha +cos\beta =\frac{1}{3}andsin\alpha +sin\beta =\frac{1}{4}$, prove that $cos\frac{\alpha -\beta }{2}=\pm \frac{5}{24}$

If second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first term is

For the given differential equation find the general solution.

$x\frac{dy}{dx}+y-x+xycotx=0(x\ne 0)$

If the expression $a{x}^4+b{x}^3-x^2+2x+3$ has remainder $4x+3$ when divided by $x^2+x-2$, then which of the following is/are true?

If $\sqrt{a+ib}$ = x+iy, then possible value of $\sqrt{a-ib}$ is

If $7^x=3^{{\log }_{9}7}\cdot 5^{{\log }_{25}49}$, then the value of $x$ is

The differential equation of the family of parabolas with focus at the origin and the x-axis as axis is

[EAMCET 2003]

A group of $10$ persons including ''Manager'', ''Assistant manager'' and ''Secretory'' are to be seated around a circular table.

The total number of possible arrangements, if ''Manager'' and ''Secretory'' had to sit together and ''Assistant manager'' had to sit opposite to ''Manager'' is

If the area enclosed by the curve $y^2=x$ and ordinates $x=0,x=1$ is divided by the line $x=\alpha$ in two equal areas. Then which of the following statement(s) is/are correct ?

If one root of the equation $x^4+4x^3+6x^2+4x+5$ is $\sqrt{-1}$ . Find the sum of the squares of other three roots.

Let $PQR$ be a triangle of area $△$ with $a=2,b=\frac{7}{2}$ and $c=\frac{5}{2},$ where $a,b$ and $c$ are the lengths of the sides of the triangle opposite to the angles at $P,Q$ and $R$ respectively. Then $\frac{2\sin P-\sin 2P}{2\sin P+\sin 2P}$ equals

Find the values of x for which $y=\left[x\right(x-2){]}^2$ is an increasing function.

OR

Find the equation of tangent and normal to the curve $\frac{x^2}{a}-\frac{y^2}{b^2}=1$ at the point $(\sqrt{2}a,b)$.

The set of exhaustive values of $x$ which satisfying the equation $|x^2-5x+4|+|x^2-7x+10|=2|x-3|$ is given by

A variable line having negative slope and passing through the point $(8,2)$ meets the axes at $A$ and $B$. Find the minimum value of the sum $OA+OB$ where $O$ is the origin.

If $\Delta =\left|\begin{array}{ccc}5& 3& 8\\ 2& 0& 1\\ 1& 2& 3\end{array}\right|$, then the co-factor of the element $a_{23}$ is

The area enclosed by the curve $y=\sqrt{4-x^2},y\ge \sqrt{2}\sin \left(\frac{x\pi }{2\sqrt{2}}\right)$ and the x-axis divided by the y - axis in the ratio

If $\underset{0}{\overset{x}{\int }}f\left(t\right)dt=x+\underset{x}{\overset{1}{\int }}tf\left(t\right)dt,$ then the value of $f\left(1\right)$ is

The differential equation whose solution is $(x-h{)}^2+(y-k{)}^2=a^2$ is (a is a constant)

The locus of the mid points of the chords of the hyperbola $x^2-y^2=4,$ which touch the parabola $y^2=8x,$ is

If A is a symmetric matrix, then B' AB is

The value of $\Delta =\left|\begin{array}{ccc}1& 2& 4\\ -1& 3& 0\\ 4& 1& 0\end{array}\right|$ is

Write the function in
the simplest form:

A survey conducted in a city reveals that $48$% children like cricket while $77$% children like football. Then the percentage of children who like both cricket and football can be

If the middle term in the expansion of ${(\frac{p}{2}+2)}^8$ is $1120$, then the value of $p$ is

Solve the given inequality for real x:

The number of integer values of $k$ for which the equation $x^2+y^2+(k-1)x-ky+5=0$ represent a circle whose radius cannot exceed $3,$ is

For a biased die, the probability of getting an even number is twice the probability of getting an odd number. The die is thrown twice and the sum of the outcomes is even. Then the probability that both the outcomes on the die is an odd number is

The value of $\int \frac{(x+1{)}^2}{x(x^2+1)}dx$ is equal to

Let $L_1$ be a straight line passing through the origin and $L_2$ be the straight line x + y = 1. If the intercepts made by

the circle $x^2+y^2-x+3y=0$ on $L_1$ and $L_2$ are equal, then which of the following equations can represent $L_1$