Explore topic-wise InterviewSolutions in Current Affairs.

Match the columns by referring to the definition given below.

"A conic is the locus of a point which moves in a plane so that its distance from a fixed point is in a constant ratio to its perpendicular distance from a fixed straight line”.

If n is a positive integer then $(1+i{)}^n+(1-i{)}^n$ =

If $\left|\begin{array}{cc}3x& 7\\ -2& 4\end{array}\right|=\left|\begin{array}{cc}8& 7\\ 6& 4\end{array}\right|$, find the value of x.

How many different words can be formed from the letters of the word GANESHPURI'? In how many of these words:
(i) the letter G always occupies the. first place?
(ii) the letters P and 1 respectively occupy first and last place ?
(iii) the vowels are always together ?
(iv) the vowels always occupy even places?

If in the expansion of $(1+x{)}^n$, the coefficients of three consecutive terms are 56, 70 and 56, then find n and the position of the terms of these coefficients.

Find the equation of a line which is perpendicular to the line joining (4, 2) and (3, 5) and cuts off an intercept of length 3 on y-axis.

The contrapositive of $p\to$ (~$p\wedge q)$ is

If $f\left(x\right)=\underset{n\to \infty }{lim}{\sum }_{r-=1}^n\frac{rx}{\mathrm{1.3.5}\dots (2r+1)}$, then ${\int }_0^3\left[f\right(x\left)\right]d(x-[x\left]\right)$ is equal to (where [.] denotes greatest integer function)

The equation ${\sin }^{-1}x=|x-a|$ will have atleast one solution if $a\in$

If $\alpha ,\beta$ are the roots of the quadratic equation $x^2+3x+6=0$ , then find the equation whose roots are $\frac{1+\alpha }{1-\alpha }$, $\frac{1+\beta }{1-\beta }$

Let f : $R\to R$ such that $f(x+2y)=f\left(x\right)+f\left(2y\right)+4xy,\forall x,yϵR$ and f(0) = 0.If $l_1={\int }_0^{1}f\left(x\right)dx,I_2={\int }_{-1}^{0}f\left(x\right)dx$, and $l_3={\int }_{-1}^{1}f\left(x\right)dx,$ then

Let $E=(2n+1)(2n+3)(2n+5)\cdots (4n–3)(4n–1)$ where $n>1$, then $2^n$ E is divisible by

If $f\left(x\right)={\cos }^{-1}\left(\frac{1-4^x}{1+4^x}\right),$ then $f^{\prime }\left(0\right)=$

Identify the missing one.
Father : Mother :: Uncle : ?

The two circles $x^2+y^2+2ax+c=0and{x}^2+y^2+2by+c=0$ touch if $\frac{1}{a^2}+\frac{1}{b^2}=$

Let $\overline{b}z+b\overline{z}=c,b\ne 0$ be a line in the complex plane. If a point $z_1$ is the reflection of a point $z_2$ through the line, then $c$ is

The curve $y\left(x\right)$ satisfying the differential equation $y-x\frac{dy}{dx}=a(y^2+\frac{dy}{dx})$ passes through $(1,1)$, then the possible of $a$ is
(assuming the constant of integration to be zero)

Let $\alpha ,\beta \in R$ be such that ${lim}_{x\to 0}\frac{x^{2}sin\left(\beta x\right)}{\alpha x-sinx}=1$. Then $6(\alpha +\beta )$ is equal to ___

$\begin{array}{cccc}& List-I& List-II& \\ & P\left(t\right)=(\frac{1}{t^2+1},\frac{t}{t^2+1}).IfP\left(\alpha \right),B\left(\beta \right).C\left(\gamma \right)& & \\ P.& areverticesofanequilateraltriangle& 1.& 0\\ & (\alpha ,\beta ,\gamma >0)anditscentroidis(a,b)then2a+b=& & \\ & IFacomplexnumber!zsatisfying|z-2+i|\le 1,& & \\ Q.& thenthemaximumdistanceoforiginfrom4+i(2-z)is& 2.& 1^2\\ & Considerthecurvexy=25!suchthat(\alpha ,\beta )isapointonthecurve.& & \\ R.& Thenthenumberofdistinctorderedpairs(\alpha ,\beta )& 3.& 2^2\\ & suchthatHCF(\alpha ,\beta )=1is{2}^{k}thenk=& & \\ S.& If{2}^{(1+cos\pi x)}lo{g}_2^5+2^{x^2-1}+2^{2(1-|x|)}=3,thensumoftherootsis& 4.& 3^2\end{array}$

A committee of 5 is to be chosen from a group of 9 people.The probability that a certain married couple will serve either together or not at all?

The tangent to the curve $x^2+y^2=25$ parallel to the line 3x-4y=7 exist at the point

A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the probability

(i) All the three balls are while.

(ii) All the three balls are red.

(iii) One ball is red and two balls are white.

In a right angled triangle ABC, write the value of $si{n}^{2}A+si{n}^{2}B+si{n}^{2}C$.

If $\alpha \&\beta$ are the roots of equation. $x^2+px+q=0$, then - $-\frac{1}{\alpha },-\frac{1}{\beta }$ are the roots of the equation.

If A and B are two given sets, then $A\cap (A\cap B{)}^c$ is equal to

If $\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k},\overrightarrow{b}=\hat{i}+\hat{j}-2\hat{k}$ and $\overrightarrow{c}=\hat{i}+3\hat{j}-({\lambda }^2+3\lambda )\hat{k}$, where $\lambda$ is a constant and $\overrightarrow{a}$ is perpendicular to $\overrightarrow{c}-\lambda \overrightarrow{b}$, then sum of the different values of $\lambda$ is

If A and B are acute angles such that sin (A - B)= cos(A+B) = 1/2, find A and B

The eccentricity of the ellipse which meets the straight line $\frac{x}{7}+\frac{y}{2}=1$ on the axis of x and the straight line $\frac{x}{3}-\frac{y}{5}=1$ on the axis of y and whose axes lie along the axes of coordinates, is

If the function f(x) defined by $f\left(x\right)=\frac{x^{100}}{100}+\frac{x^{99}}{99}+\cdots +\frac{x^2}{2}+x+1,then{f}^{\prime }\left(0\right)=$

If f : D $\to$R $f\left(x\right)=\frac{x^2+bx+c}{x^2+b_{1}x+c_1},where\alpha ,\beta$ are th roots of the equation $x^2+bx+c=0$ and ${\alpha }_1,{\beta }_1$ are the roots of $x^2+b_{1}x+c_1=0$. Now, answer the following question for f(x). A combination of graphical and analytical approach may be helpful in solving these problems. If ${\alpha }_{1}and{\beta }_1$ are real, then f(x) has vertical asymptote at $x=({\alpha }_1,{\beta }_1$).
If ${\alpha }_1<{\beta }_1<\alpha <\beta$, then

If $n>3$ and $a,bϵR,$ then the value of $ab-n(a-1)(b-1)+\frac{n(n-1)}{1.2}(a-2)(b-2)-......+(-1{)}^n(a-n\left)\right(b-n)$ is equal to

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

The number of five letter words containing 3 vowels and 2 consonants that can be formed using the letters of the word EQUATION so that two consonants occur together is

${lim}_{x\to 0}\frac{sin{x}^2(1-cos{x}^2)}{x^6}$

Solve the following system of equations in R.
$\frac{|x+2|-x}{x}<0$

Let $y=y\left(x\right)$ be the solution of the differential equation $\frac{dy}{dx}+2y=f\left(x\right),$ where $f\left(x\right)=\{\begin{array}{c}1,x\in [0,1]\\ 0,\text{otherwise}\end{array}$
If $y\left(0\right)=0$, then $y\left(\frac{3}{2}\right)$ is

A data consists of $n$ observations:
$x_1,x_2,....,x_n$. If $\sum _{i=1}^n(x_i+1{)}^2=9n$ and $\sum _{i=1}^n(x_i-1{)}^2=5n$, then the standard deviation of this data is :

A box contains 100 bulbs, 20 of which are defective. 10 bulbs are selected for inspection. Find the probability that :

(i) all 10 arc defective

(ii) all 10 are good

(iii) at least one is defective

(iv) None is defective

For two complex numbers $z_1$ and $z_2;(a{z}_1+b\overline{z_1})(c{z}_2+d\overline{z_2})=(c{z}_1+d\overline{z_1})(a{z}_2+b\overline{z_2})$ $b\ne 0,d\ne 0$ if

If α = sin^{-1 then}