Explore topic-wise InterviewSolutions in Current Affairs.

The equation of the locus of the point of intersection of two normals to the parabola $y^2=4ax$ which are perpendicular to each other is

If $x\in R-\left\{3\right\},$ then the possible value(s) of the expression $\frac{\sqrt{x^2-6x+9}}{3-x}+2$ can be

Argument of the complex number $\frac{1}{(\sqrt{3}-i{)}^{25}}$ is

If acosθ+bsinθ=c ,then prove that asinθ–bcosθ=±√(a^{​​​​​​2}+b^{​​​​​​2} ​​​​-c^2)

How many A.P.'s with 10 temrs are there whose first term is in the set [1,2,3] and whose common difference is in the set [1,2,3,4,5] ?

Let $f\left(x\right)$ be a real valued function, then the domain of $f\left(x\right)=\sqrt{x-4-2\sqrt{x-5}}-\sqrt{x-4+2\sqrt{x-5}}$ is

Let $S$ and $S^{\prime }$ be two foci of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ . A circle is inscribed in the ellipse. If $S{S}^{\prime }$ is the diameter of the circle, then the eccentricity $e$ of the ellipse is

The angle between the lines whose direction cosines satisfy the equations
$l+m+n=0$ and $l^2=m^2+n^2$, is

Let the sequence $a_1,a_2,a_3.....a_n$ form an A.P. Then
$a_1^2-a_2^2+a_3^2-a_4^2+.....+a_{2n-1}^2-a_{2n}^2$ is equal to

If $P,Q$ and $R$ are foot of perpendiculars drawn from point $A(1,1,1)$ to planes $P_1:x+2y+2z=2$, $P_2:2x-2y+z=-8$ and to line of intersection of $P_1$ and $P_2$ respectively, then area of $\Delta PQR$ is -

If a variable takes the discrete values $\alpha +4,\alpha -\frac{7}{2},\alpha -\frac{5}{2},\alpha -3,\alpha -2\alpha +\frac{1}{2},\alpha -\frac{1}{2},\alpha +5(\alpha >0),$
then the median is

If A is a skew-symmetric matrix of order 3, then the matrix $A^4$ is

6 girls and 5 boys sit together randomly in a row, the probability that no two boys sit together, is

${lim}_{x\to \frac{\pi }{2}}\frac{\sqrt{2-sinx}-1}{(\frac{\pi }{2}-x{)}^2}$

$\mathrm{If}f\left(x\right)=\left(\begin{array}{ccc}x& \sin x& \cos x\\ x^2& \tan x& -x^3\\ 2x& \sin 2x& 5x\end{array}\right|,\mathrm{then}\underset{x\to 0}{\lim }\frac{f\text{'}\left(x\right)}{x}\mathrm{equals}$

The value of $x$ satisfying the equation ${\sin }^4\left(\frac{x}{3}\right)+{\cos }^4\left(\frac{x}{3}\right)>\frac{1}{2}$ is (where $n\in Z$)

If the solution of the differential equation $x\frac{dy}{dx}+y=x{e}^x$ be $xy=e^x\varphi \left(x\right)+c$ then $\varphi \left(x\right)$ is equal to

If the pair of straight lines $\sqrt{3}xy-x^2=0$ is tangent to the circle at $P$ and $Q$ from origin $O$ such that area of the smaller sector formed by $CP$ and $CQ$ is $3\pi$ sq. unit, where $C$ is the centre of circle, then $OP$ equals to

${lim}_{x\to \frac{\pi }{2}}\frac{\sqrt{3}-tanx}{\pi -3x}$

If an equilateral triangle is inscribed in a parabola $y^2=12x$ with one vertex at the vertex of the parabola, then its height is

In each of the following exercise, determine the direction cosines of the normal to plane and the distance from the origin:

z=2

x + y + z = 1

2x +3y -z = 5

5y + 8 = 0

Find the following integrals.
$\int \frac{x^3-x^2+x-1}{(x-1)}dx.$

Find $\frac{dy}{dx}$, if x and y are connected parametrically by the equations given in questions without eliminating the parameter.

x = sin t, y = cos 2t.

If in the expansion of $(1+x{)}^n,$the coefficient of pth and qth terms are equal and the relation between p and q is p-q =n . Find the value of $p^2+q^2$. where $p\ne q.$

Or

Find the term independent of x in the expansion of ${(2x-\frac{1}{x})}^{10}.$

Find the sum to n terms

$3\times 1^2+5\times 2^2+7\times 3^2+\dots \dots$

What volume of hydrogen measured at ${27}^{\circ }C$ and 776.7 mm pressure would be obtained by treating 0.65 g of pure zinc with sufficient amount of dilute hydrochloric acid? Aq. tension at ${27}^{\circ }C$ is 26.7 mm; At. mass of Zn is 65.

An anaoysis of the weekly wages paid to workers in two firms A and B, belonging to the same industry gives the following results:

$\begin{array}{ccc}& \text{Firm A}& \text{Firm B}\\ \text{Average weekly wages}& 586& 648\\ \text{Average weekly wages}& Rs.52.5& Rs.47.5\\ \text{Variance of the distribution of wages}& 100& 121\end{array}$

(i) Which firm A or B pays out larger amount as weekly wages ?

(ii) Which firm A or B has greater variability in individual wages ?

If the tangent and normal to a rectangular hyporbola $xy=c^2$ at a point cuts off intercepts $a_1$ and $a_2$ on $x-$axis and $b_1$, and $b_2$ on the $y-$axis, then $a_1{a}_2+b_1{b}_2=$

The derivative of $x^2+3x-2tan\left(x\right)$ will be equal to

Differentiate the following functions with respect to x :

$\frac{x^3}{3}-2\sqrt{x}+\frac{5}{x^2}$

If $e^{|\sin x|}+e^{-|\sin x|}+4a=0$ will have exactly $4$ different solutions in $[0,\pi ]$, then

Using vectors, prove that the parallelogram on the same base and between the same parallels are equal in area.

The set of all real values of $x$ which satisfies $(x-2)(x-3)\le 2\le (x-1)(x-2)$, is

For a square matrix $A,$ if $A^3=O,$ then $I+A+A^2$ is equal to

Match the List-I with List-II by using the postulates of VBT of complexes

List-I List-II

(P)$\left[Ni\right(CN{)}_4{]}^{2-}$ (1) $s{p}^3$hybridization

(Q)$\left[Ni\right(CO{)}_4]$ (2) $ds{p}^2$ hybridization

(R) $\left[Cu\right(N{H}_3{)}_4{]}^{2+}$ (3) $\mu$ = 0 BM

(S)$\left[Pd\right(Cl{)}_4{]}^{2-}$ (4) $\mu$ =1.732 BM

The sum of 10 terms of the series $\sqrt{2}+\sqrt{6}+\sqrt{18}+...$

Let $A=\{x:x\text{is a prime factor of}240\}$ and $B=\{y:y\text{is the sum of any two prime factors of}240\}$. Then which of the following options is true?

For any two sets A and B, $(A-B)\cup (B-A)=$