Explore topic-wise InterviewSolutions in Current Affairs.

The mid point of line joining the common points of the line $2x-3y+8=0$ and $y^2=8x,$ is

If the normals at $A\left(t_1\right)$ and $B\left(t_2\right)$ meet again at $C\left(t_3\right)$ on the parabola $y^2=4ax,$ then the locus of the mid point of $AB$ is

If $x=a(\cos \theta +\theta \sin \theta )$ and $y=a(\sin \theta -\theta \cos \theta ),$ then $a\theta \frac{d^{2}y}{d{x}^2}=$

Total number of $4$ digit numbers that can be formed using digits $0,1,3,4,7$ without repetition such that it should be a multiple of $6$ are

Let $P$ and $Q$ be distinct points on the parabola $y^2=2x$ such that a circle with $PQ$ as diameter passes through the vertex $O$ of the parabola. If $P$ lies in the first quadrant and the area of the triangle $△OPQ$ is $3\sqrt{2}\text{sq. units}$, then which of the following is/are the coordinates of $P$?

Show that the straight lines whose direction cosines are given by 2l+2m-n=0 and mn+nl+lm=0 are at right angles.

Examine if Rolle's theorem is applicable to any of the following functions. Can you say something about the converse of Rolle's theorem from these example ?

(iii) $f\left(x\right)=x^2-1forxϵ[5,9]$.

Let $f:R-\{-\frac{4}{3}\}\to R$ be a function defined as $f\left(x\right)=\frac{4x}{3x+4},x\ne -\frac{4}{3}$. The inverse of f is the map g: Range $f\to R-\{-\frac{4}{3}\}$ is given by
$\left(a\right)g\left(y\right)=\frac{3y}{3-4y}\left(b\right)g\left(y\right)=\frac{4y}{4-3y}\left(c\right)g\left(y\right)=\frac{4y}{3-4y}\left(d\right)g\left(y\right)=\frac{3y}{4-3y}$

Let $S_1,S_2,S_3$ and $S_4$ be four sets defined as
$S_1=\{y:y\in Z\text{and}y=\frac{x^2+4x+3}{x^2+7x+14}\text{for}x\in R\}$
$S_2=\{x:x\in Z\text{and}|1-\frac{|x|}{1+|x|}|\ge \frac{1}{3}\}$
$S_3=\left\{x:x^2-3x+2\text{sgn}\left(x\right)=0\right\},$ where $\text{sgn}\left(x\right)$ represents the signum function.
$S_4=\left\{\right(x,y):x,y\in Z,x^2+y^2\le 4\}$.

$\text{List I}$ has four entries and $\text{List II}$ has five entries. Each entry of $\text{List I}$ is to be correctly matched with a unique entry of $\text{List II}.$

$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& n\left(S_1\Delta S_2\right)& \text{(P)}& 9\\ \text{(B)}& n((S_1\times S_2)\cap (S_2\times S_1))& \text{(Q)}& 12\\ \text{(C)}& n(S_1\cap S_2\cap S_3^{\prime })& \text{(R)}& 36\\ \text{(D)}& n(S_4\times S_3)& \text{(S)}& 2\\ & & \text{(T)}& 0\end{array}$

Which of the following is the only CORRECT combination?

For the following question verify that the given function (explicit or implicit) is a solution of the corresponding differential equation.

$x+y=ta{n}^{-1}yand{y}^2{y}^{\prime }+y^2+1=0$

The value of x in the expression $(x+x^{lo{g}_{10}x}{)}^5$ if the third term in the expansion is ${10}^6$:

Find the point on the straight line 3x+y+4=0 which is equidistance from the points (-5,6)and(3,2)

Find x if

2^x-7 × 5^x-4 = 1250

show that sin⁶A+cos⁶A=1-3sin²A.cos²A.

The numerically greatest term in the expansion of $(2+3x{)}^{12}$ when $x=\frac{5}{6}$ is:

Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in $A\times B,$ find A and B, where x, y and z are distinct elements.

A feasible solution of a LPP if it also optimizes the objective function is called

Given that $\alpha ,\beta ,a,b$ are in A.P. ; $\alpha ,\beta ,c,d$ are in G.P. and $\alpha ,\beta ,e,f$ are in H.P. If $b,d,f$ are in G.P., then the value of $\frac{{\beta }^6-{\alpha }^6}{\alpha \beta ({\beta }^4-{\alpha }^4)}$ is

CosA/1-tanA + sinA/1-cotA = cosA+sinA

Prove it

If x is real and $k=\frac{x^2-x+1}{x^2+x+1}$ then

abc $\ne$ 0 & a, b, c $ϵ$ R. If $x_1$ is a root of $a^2{x}^2+bx+c=0,x_2$ is a root of $a^2{x}^2-bx-c=0$ and $x_1>x_2>0$, then the equation $a^2{x}^2+2bx+2c=0$ has a root $x_3$ such that

The value of $\frac{\tan {53}^{\circ }}{\cot {37}^{\circ }}-\frac{\cot {40}^{\circ }}{\tan {50}^{\circ }}+2$ is

If f(x) is defined in [a,b] where $ab\ge 0$, then the even extemsion of f(x) is

The remainder when $(2222{)}^{5555}$ is divided by 7

A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, p people chose the first picture in the set. If more than $20\%$ of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of p?

Graph of $y=3|\frac{1}{2}x+2|-9$ is

What is the sentence type?

Atul got a raise, yet he doesn’t seem satisfied.

If the ratio of the lengths of tangents from a point to the circles $x^2+y^2+4x+3$ = 0,$x^2+y^2-6x+5$ = 0 is 1:2 then the locus of P is a circle whose centre is

Let $a=p+2$ and $b=3-2p$. If $a$ and $b$ have same absolute value, then the value(s) of $p$ is/are

If the sides of a right angled triangle are in A.P., the ratio of the sides are:

The equation of the lines joining the vertex of the parabola $y^2=6x$ to the point on it whose abscissa is 24 , is

Four fair dice $D_1,D_2,D_{3}and{D}_4$ each having six faces numbered 1, 2, 3, 4, 5 and 6 are rolled simultaneously. The probability that $D_4$ shows a number appearing on one of $D_1,D_{2}and{D}_3$, is ?

Find the total number of ways of selecting five letters from the letters of the word INDEPENDENT.___

If ${\log }_{10}(x^3+y^3)-{\log }_{10}(x^2-xy+y^2)\le 2\forall x>0,y>0$, then the maximum value of $x+y$ is

Evaluate: $\underset{x\to 0}{lim}\frac{cos2x-1}{cosx-1}$