Explore topic-wise InterviewSolutions in Current Affairs.

The sequence whose $n^{th}$ term is $\frac{3+(-1{)}^n}{3^n},$ is

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes $r.(\hat{i}-\hat{j}+2\hat{k})=5$ and $r.(3\hat{i}+\hat{j}+2\hat{k})=6$.

The function is defined by f(x) = $\{\begin{array}{c}kx+1,ifx\le \pi \\ cosx,ifx>\pi \end{array}$ at x = $\pi$.

Define a binary operation $\ast$ on the set {0,1,2,3,4,5}as $a\ast b$ $=\{\begin{array}{c}a+b,ifa+b<6\\ a+b-6,ifa+b\ge 6\end{array}$
Show that zero is the identity for this operation and each element $a\ne 0$ of the set is invertible with (6-a) being the inverse of a.

Vector(s) perpendicular to both the vectors
$\overrightarrow{A}=3\hat{i}+5\hat{j}+2\hat{k}$ and
$\overrightarrow{B}=2\hat{i}+4\hat{j}+6\hat{k}$ is/are

What is equivalence class? Explain with example and vedio.

Number of $4$ digit numbers using digits $0,1,2,3,4,5$ which are divisble by $9$, when each digit used at most once

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.
$x^2=-16y$

Set of value(s) of $\theta$ for which ${\sin }^{3}3\theta =0$ is

If $A=\{x:x^2-4\le 0,x\in Z\}$ and $B=\{y:y^2-9\ge 0,y\in Z\}$, then $n(A\cap B)$ is equal to

A farmer wants to buy some horses, and every horse he buys requires $2$ acres of land. If the farmer has $18$ acres of land, write an inequality representing the possible number of horses he can buy. (where $a$ is number of horses)

The curve y = ax³ + bx² + cx + 5 touches the x-axis at P(-2, 0) and cuts the y-axis at the point Q where its gradient is 3. the equation of the curve is... .

If the axes of the ellipse are coordinate axes and A and B are the ends of major axis and minor axis respectively.If the area of $△$OAB is 16 sq units, e = $\frac{\sqrt{3}}{2}$ then the equation of the ellipse is

What is the element in the 2^nd row and 1^stcolumn of a 2 x 2 Matrix A= [ a_ij], such that a ₌ (i + 3) (j - 1)

$ta{n}^{-1}\frac{a}{b}-ta{n}^{-1}\left(\frac{a-b}{a+b}\right)$ =

If $\frac{3\pi }{4}<\alpha <\pi$, then $\sqrt{cose{c}^2\alpha +2cot\alpha }$ is equal to

[Pb. CET 2000; AMU 2001; MP PET 2004]

If the curves $a{x}^2+4xy+2y^2+x+y+5=0$ and $a{x}^2+6xy+5y^2+2x+3y+8=0$ intersect at four concyclic points, then the value of $a$ is

The points $z_1=3+\sqrt{3}i\text{and}{z}_2=2\sqrt{3}+6i$ are given on a complex plane. The complex number lying on the bisector of the angle formed by the vector $z_1$ and $z_2$ is

PARAGRAPH
If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation $z=x/y$. If the errors in $x,y$ and $z$ are $\Delta x,\Delta y$ and $\Delta z$, respectively, then
$z\pm \Delta z=\frac{x\pm \Delta x}{y\pm \Delta y}=\frac{x}{y}(1\pm \frac{\Delta x}{x}){(1\pm \frac{\Delta y}{y})}^{-1}$.
The series expansion for ${(1\pm \frac{\Delta y}{y})}^{-1}$, to first power in $\Delta y/y$. is $1\mp \left(\Delta y/y\right)$. The relative errors in independent variables are always added. So the error in $z$ will be
$\Delta z=z(\frac{\Delta x}{x}+\frac{\Delta y}{y})$ .
The above derivation makes the assumption that $\Delta x/x\ll 1,\Delta y/y\ll 1$. Therefore, the higher powers of these quantities are neglected.

Consider the ratio $r=\frac{(1-a)}{(1+a)}$ to be determined by measuring a dimensionless quantity $a$. If the error in the measurement of a is $\Delta a(\frac{\Delta a}{a}<<1)$, then what is the error $\Delta r$ in determining $r$?

The locus of centroid of a triangle whose vertices are $(a\cos t,a\sin t),(b\sin t,-b\cos t)$ and $(1,0),$ where $t$ is a parameter, is

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are perpendicular, then $\overrightarrow{a}\times (\overrightarrow{a}\times (\overrightarrow{a}\times (\overrightarrow{a}\times \overrightarrow{b})))$ is equal to :

The locus of the moving point $P$ such that $2PA=3PB$, where $A$ is $(0,0)$ and $B$ is $(4,-3)$, is

Without using the distance formula, show that points (-2, -1), (4, 0), (3, 3) and (-3, 2) are the vertices of a parallelogram.

Let $C$ be a circle passing through the origin and making an intercept of $\sqrt{10}$ on the line $y=2x+\frac{5}{\sqrt{2}}$. If the line subtends an angle of ${45}^{\circ }$ at the origin, then the equation of circle $C$ is/are

If $\frac{5x+8}{4-x}<2$, then

The equation of the circle with the center (-3,4) and the radius 5 units is .

$\text{If}\underset{0}{\overset{n}{\int }}f\left(x\right)dx=t\text{then evaluate}\sum _{r=1}^n{\int }_0^{1}f(r-1+x)dx$

Find the equation of the tangent and normal to the given curve at the given points

$y=x^4-6x^3+13x^2-10x+5at(1,3)$

Find $\frac{dy}{dx}$of the functions given in question.

$xy=e^{(x-y)}$.

$f\left(x\right)=\{\begin{array}{cc}{x}^{2}sin\frac{1}{x},& ifx\ne 0\\ 0,& ifx=0\end{array}$

Find the absolue maximum value and he absolute minimum value of the following functions in the given intervals:

$f\left(x\right)=x^3,xϵ[-2,2]$

$f\left(x\right)=sinx+cosx,xϵ[0,\pi ]$

$f\left(x\right)=4x-\frac{1}{2}{x}^2,xϵ[-2,\frac{9}{2}]$

$f\left(x\right)=(x-1{)}^2+3,xϵ[-3,1]$

Find the number of non-zero integral solutions of the equation $|1-i{|}^x=2^x$.

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that
first ball is black and second is red.

The line, $L1$ : $(2-\sqrt{3})x–y+\sqrt{3}=0$ passing through $A(1,2)$ is rotated about $A$ by an angle $\frac{\pi }{2}$ in counter clock wise direction to get line $L_2$. Let $B(h,k)$ and $C$ be the points on $L_1$ and $L_2$ respectively such that $AC=4$. If the area of the triangle $ABC$ is $\sqrt{8+4\sqrt{3}}$ square units, then the maximum value of $(2+\sqrt{3})h+k$ is

Prove that cos(A-B)-cos(A+B)=2sinAsinB

$If\frac{3\pi }{4}$ < $\alpha$ < $\pi$, then $\sqrt{2cot\alpha \frac{1}{si{n}^2\alpha }}$ is equal to

The ${13}^{th}$ term in the expansion of ${(x^2+\frac{2}{x})}^n$ is independent of x, then the sum of divisors of n is

Let $\overrightarrow{a}=\hat{i}+2\hat{j}+4\hat{k},\overrightarrow{b}=\hat{i}+\lambda \hat{j}+4\hat{k}$ and $\overrightarrow{c}=2\hat{i}+4\hat{j}+({\lambda }^2-1)\hat{k}$ be coplanar vectors. Then the non-zero vector $\overrightarrow{a}\times \overrightarrow{c}$ is :

($103{)}^{86}-(86{)}^{103}$ is divisible by

Integrate the following functions w.r.t. x.

$\int \frac{1}{x^2(x^4+1)}dx.$

For each of the differential equation in given question find the general solution.​​​​
$se{c}^{2}xtanydx+se{c}^{2}ytanxdy=0$