Explore topic-wise InterviewSolutions in Current Affairs.

If $a{x}^2+bx+c=0$ and $b{x}^2+cx+a=0$ have a common root

a ≠ 0, then $\frac{a^3+b^3+c^3}{abc}=$

The value of Expression $(cos\frac{\pi }{2}+isin\frac{\pi }{2})$

$(cos\frac{\pi }{2^2}+isin\frac{\pi }{2^2})$...........to $\infty$is

There are three bags $B_1,B_2,\text{and}{B}_3$ containing $2$ red & $3$ white, $5$ red & $5$ white, $3$ red & $2$ white balls respectively. A ball is drawn from bag $B_1$ and placed in $B_2$. Then a ball is drawn from bag $B_2$ and placed in $B_3$. Then a ball is drawn from bag $B_3$. The number of ways in which this process can be completed, if same colour balls are used in the first and the second transfers is (assuming all balls are different)

A business man hosts a dinner to 21 guests. He is having 2 round tables which can accommodate 15 and 6 persons each. In how many ways can he arrange the guests ?

If $y=(a-2)x^2+(b-3)x,$ where $a,b\in R$ is a linear function and $|a-b|=4$, then the possible value(s) of $b$ is/are

Write the values of the square root of -i.

Differentiate the following questions w.r.t. x.

$\sqrt{e^{\sqrt{x}}}$

If $\sin \theta =-\frac{4}{5}$ and $\pi <\theta <\frac{3\pi }{2}$, then $\tan \theta +\cos \theta =$

The corner points of the feasible region determined by the following system of linear inequalities :

$2x+y\ge 10,x+3y\ge 15,x,y\ge 0are(0,0),(5,0),(3,4)and(0,5).$ Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is

(a) p = q

(b) p = 2q

(c) p = 3q

(d) q = 3p

If $\sqrt{2}$ and $3i$ are two roots of a biquadratic equation with rational coefficients, then its equation is, (where $i^2=-1$)

Evaluate the definite integrals.
${\int }_2^3\frac{1}{x}dx.$

Find the area bounded by the curves $(x-1{)}^2+y^2=1$ and $x^2+y^2=1$.

State whether the given table is not the probability distributions of a random variable. Give reasons for your answer.
$$\begin{array}{cccccc}x& 0& 1& 2& 3& 4\\ P\left(X\right)& 0.1& 0.5& 0.2& -0.1& 0.3\end{array}$$

Differentiate given problems w.r.t.x.
cos(a cos x+b sin x),for some constants a and b.

Show that the function f(x)=$x^3-3x^2+6x-100$ is increasing on R.

If $p$ is the length of the perpendicular from origin to the line $\frac{x}{a}+\frac{y}{b}=1$, then the correct relation between $a,b$ and $p$ is

Find the general situation of $si{n}^{-1}\left(dy/dx\right)=x+y$ using variable separable method.

If two of the lines given by $3x^3+3x^{2}y-3x{y}^2+d{y}^3=0$ are at right angles then the slope of one of them is

If the tangent at the point P(2, 4) to the parabola $y^2=8x$ meets the parabola $y^2=8x+5$ at Q and R,
then the midpoint of QR is

What is the inverse of the matrix $\left[\begin{array}{cc}-3& 2\\ 5& -1\end{array}\right]$

$\sum _{m-1}^n{\tan }^{-1}\left(\frac{2m}{m^v+m^2+2}\right)$ is equal to

Two cards are drawn from the standard deck of 52 playing cards without replacement. Find the probability of getting first card as queen and second as an ace.

The general solution of $\tan x+\tan 2x+\sqrt{3}\tan x\cdot \tan 2x=\sqrt{3}$ is
$(\text{where}n\in Z)$

In $R^3$, consider the planes $P_1:y=0$ and $P_2:x+z=1$. Let $P_3$ be a plane , different from $P_1$ and $P_2$, which passes through the intersection of $P_1$ and $P_2$. If the distance of the point (0, 1, 0) from
$P_3$ is 2, then which of the following relation(s) is/are true?

An unbalanced dice (with six faces numbered from $1$ to $6$) is thrown. The probability that the face value is odd is $90$% of the probability that the face value is even. The probability of getting any even numbered face is the same. If the probability that the face is even given that it is greater than $3$ is $0.75$, then the probability that the face value exceeds $3$ is

Circles $x^2+y^2-2x-4y=0and{x}^2+y^2-8y-4=0$

The angle between the planes $r.(2\hat{i}-\hat{j}+2\hat{k})=3$ and $r.(3\hat{i}-6\hat{j}+2\hat{k})=4$

Let $f:R\to R$ be defined as $f\left(x\right)=\frac{sin\pi \left\{x\right\}}{x^2-x+1}\forall xϵR$, where {x} is the fractional part of x, then

If $g$ is the inverse of a function $f$ and $f^{\prime }\left(x\right)=\frac{1}{1+x^5}$, then $g^{\prime }\left(x\right)$ is equal to:

In an A.P the sum of the first n terms bears a constant ratio λ with the sum of the next n terms, then $\lambda =$

Two integers x and y are chosen with replacement out of the set {0, 1, 2, 3, . . . .10}. Then find the probability that |x - y|>5

Two vertices of an equilateral triangle are (–1, 0) and (1, 0) and its third vertex lies above the x-axis, the equation of the circumcircle is

The area in the first quadrant enclosed by the axis, the line $x=y\sqrt{3}$ and the circle $x^2+y^2=4$ is

A function f such that $f\left(a\right)=f^{\prime \prime }\left(a\right)=......f^{2n}\left(a\right)=0$ and f has a local maximum value b at x = a, if f (x) is

In a $△ABC,AB=ri+j,AC=si-j$ if the area of triangle is of unit magnitude, then

Two plants A and B of a factory show following results about the number of workers and the wages paid to them

$\begin{array}{ccc}& \text{Plants A}& \text{Plant B}\\ \text{No. of workers}& 5000& 6000\\ \text{Average monthly wages}& Rs.2500& Rs.2500\\ \text{Variance of distribution of wages}& 81& 100\end{array}$

In which plant A or B is there greater variability in individual wages ?

Let z and w betwo complex numbers such that $|z|\le 1,|w|\le 1and|z+iw|=|z-\overline{iw}|=2$ Then z is equal to

Number of values of $k$ so that the equations $x^2+kx+(k+2)=0\text{and}{x}^2+(1-k)x+3-k=0$ have exactly one common root, is -

The value of $\frac{\cos {58}^{\circ }}{\sin {32}^{\circ }}+\frac{\sin {22}^{\circ }}{\cos {68}^{\circ }}-\frac{\cos {38}^{\circ }\text{cosec}{52}^{\circ }}{\tan {18}^{\circ }\tan {35}^{\circ }\tan {72}^{\circ }\tan {55}^{\circ }}$
is

The distance between the directrices of the ellipse $\frac{x^2}{36}+\frac{y^2}{20}=1$ is

If -1+$\sqrt{-3}$=r$e^{i\theta }$, then $\theta$ is equal to