Explore topic-wise InterviewSolutions in Current Affairs.

Let $P\left(z\right)=z^3+a{z}^2+bz+c,$ where $a,b,c\in R$. If there exists a complex number $w$ such that the three roots of $P\left(z\right)$ are $w+3i,w+9i$ and $2w-4$, where $i^2=-1$, then the value of $a+b+c$ is
​​​​​​​(correct answer + 1, wrong answer - 0.25)

1. 9

The values of x and y for which the numbers 3+i$x^2$y and $x^2$ +y+4i are conjugate complex are

Proof that the sum of in Arithmetic means between 2given number is n time singing Arithmetic mean between them

If equation $a{x}^2+bx+c$ = 0 has only imaginary roots and c < 0, then a is ______.

$A\left(\overrightarrow{a}\right),B\left(\overrightarrow{b}\right),C\left(\overrightarrow{c}\right)$ are the vertices of a triangle ABC and $R\left(\overrightarrow{r}\right)$ is any point in the plane of triangle ABC, then $\overrightarrow{r}.(\overrightarrow{a}\times \overrightarrow{b}+\overrightarrow{b}\times \overrightarrow{c}+\overrightarrow{c}\times \overrightarrow{a})$ is always equal to

In an A.P., if p^th
term is
and
q^th term is
,
prove that the sum of first pq terms is

The given graph shows a function representing the speed of a car with time. Find the domain where the speed is constant.

Let $T_n$ be the area bounded by $y={\tan }^{n}x,x=0,y=0$ and $x=\frac{\pi }{4}$ where $n$ is a integer greater than $2$, then $T_{100}$ is

Which of the following binary operations defined on the set of real numbers is not associative?

The value of $cos{52}^{\circ }+cos{68}^{\circ }+cos{172}^{\circ }$ is

Assume vector x & y to be of same magnitude

Which of the following approximately represent $\overrightarrow{x}-\overrightarrow{y}$

Which of the following is a null matrix?

Let slope of the tangent line to a curve at any point $P(x,y)$ be given by $\frac{x{y}^2+y}{x}$. If the curve intersects the line $x+2y=4\text{at}x=-2$, then the value of $y$, for which the point $(3,y)$ lies on the curve, is :

Inverse of a diagonal non-singular matrix is

Let p be a prime number. If p divides $a^2$ then _________, where a is a positive integer.

The range of $p$ for which the number $6$ lies between the roots of $x^2+2(p-3)x+9=0$ is

Find the angle in radians through which a pendulum swings if its length is 75 cm and the tip describes an arc of length (i) 10 cm (ii) 15 cm (iii) 21 cm

1/1+ x^a-b+ x^a-c+ 1/1+ x^b-c+ x^b-a+ 1/1+ x^c-a+ x^c-b = ?

(a)0. (b)1. (c)-1. (d)2

Let $S$ and $S^{\prime }$ be foci of an ellipse and $B$ be any one of the extremities of its minor axis. If $\Delta S^{\prime }BS$ is a right angled triangle with right angle at $B$ and area of $△S^{\prime }BS=8\text{sq. units}$, then the length of a latus rectum of the ellipse (in units) is :

The plane through the intersection of the planes $x+y+z=1$ and $2x+3y-z+4=0$ and parallel to $y$-axis also passes through the point:

The equation of the circumcircle of the triangle formed by the lines $xy-3x-2y+6=0$ and $x+y=0$ is

For any quadratic equation $y=a{x}^2+bx+c.$ Select the possible graphs for which $a>0.$

Which of the following statement is / are correct for equation 2x - 3y + 5 = 0

1. Slope of the straight line is $\frac{2}{3}$

2. x-intercept of the straight line is $\frac{-5}{2}$

3. y-intercept of the straight line is $\frac{5}{3}$

If $\overrightarrow{a}$ and $\overrightarrow{a}-\overrightarrow{b}$ making an angle ${60}^{\circ }$ with $\overrightarrow{a}\cdot \overrightarrow{b}=0,$ then which of the following is correct ?

Consider the parabola whose focus at $(0,0)$ and tangent at vertex is $x-y+1=0$.

The equation of the parabola is

Using
properties of determinants, prove that:

The solution set of $2lo{g}_{2}lo{g}_{2}x+lo{g}_{1/2}lo{g}_2\left(2\sqrt{2x}\right)=1$ is

The equation of the plane passing through the lines $\frac{x-4}{1}=\frac{y-3}{1}=\frac{z-2}{2}$ and $\frac{x-3}{1}=\frac{y-2}{-4}=\frac{z}{5}$ is

If $z$ is a complex number satisfying $|z|=1$, then the range of $\arg \left(\frac{1}{1-z}\right)$ is