Explore topic-wise InterviewSolutions in Current Affairs.

A non-zero polynomial $f\left(x\right)$ of degree $3$ has roots at $x=1,x=2$ and $x=3$. Which one of the followinng must be TRUE?

The equation of the directrix of the parabola with vertex at the origin and having the axis along $x$ − axis and a common tangent of slope $2$ with the circle $x^2+y^2=5$ is⁄are

If $y=[x{]}^2+2\{x\left\}\right[x]+\frac{\sum _{r=1}^{100}\{x+r{\}}^2}{100}$, then $\int y\cdot dx=$

(where [.] and {.} are greatest integer function and fractional part function respectively and $c$ is integration constant)

For every natural number n

$\underset{x\to 0}{lim}\frac{8}{x^8}[1-cos\frac{x^2}{2}-cos\frac{x^2}{4}+cos\frac{x^2}{2}cos\frac{x^2}{4}]\text{is equal to}$

Let $A$ and $B$ be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that $A$ or $B$ occurs is $\frac{1}{2}$, then the probability of both of them occur together is :

${lim}_{x\to \frac{\pi }{6}}\frac{co{t}^{2}x-3}{cosecx-2}$

If $f\left(x\right)=x-x^2+x^3-x^4\cdots \infty$ and $|x|<1,$ then $f^{\prime }\left(x\right)=$

If the image of the point $(2,1)$ with respect to a line mirror is $(5,2),$ find the equation of the mirror.

Quadratic equation $x^2+(a-1)ix+5=0(a\in R)$ will have a pair of conjugate complex roots, if

The maximum value of $(se{c}^{-1}x{)}^2+(cose{c}^{-1}x{)}^2$ is equal to

Number of $4$ digit numbers that can be formed using digits $0,1,2,3,4,5$ which are divisible by $8,$ when each digit is used at most once is

The length of the latus-rectum of the parabola $x^2-4x-8y+12=0$ is

3<sup>2n
+ 2</sup> – 8n – 9 is divisible by 8.

If the locus of the mid-point of the line segment from the point $(3,2)$ to a point on the circle , $x^2+y^2=1$ is a circle of the radius $r$ then $r$ is equal to :

Solve the equation –x² + x – 2 = 0

A radioactive nucleus can decay by two different processes. The half life for the first process is $t_1$ and that for the second process is $t_2$. If effective half life is $t$, then

The Laplace transform of a function f(t) is $\frac{1}{s^2(s+1)}$. The function f(t) is

Let $f\left(x\right)=x^2-6x+5$ and $m$ is the number of points of non derivability of $y=|f\left(|x|\right)|$. If $|f\left(|x|\right)|=k,k\in R$ has atleast $m$ distinct solution(s), then the number of integral values of $k$ is

State the parts of speech of the underlined words.

The people in the restaurant seemed as lonely as the place itself.

Answer each of the following questions in one word or one sentence or as per exact requirement of for question:

$\text{Find the are of the triangle}\Delta ABCinwhicha=1,b=2and\angle c={60}^{\circ }.$

Prove the following;

$2si{n}^{-1}\frac{3}{5}=ta{n}^{-1}\frac{24}{7}$

Which of these is the length of the interval $(-12,21)$?

A line cuts the x-axis at $A(5,0)$ and the y-axis at $B(0,–3)$. A variable line $PQ$ is drawn perpendicular to $AB$ cutting the x-axis at $P$ and the y-axis at $Q$. If $AQ$ and $BP$ meet at $R$, then the locus of $R$ is

The value of $si{n}^{-1}\left[cot(si{n}^{-1}\sqrt{\frac{2-\sqrt{3}}{4}}+co{s}^{-1}\frac{\sqrt{12}}{4}+se{c}^{-1}\sqrt{2})\right]$ is

If $|z+2-i|=5,$ then the maximum value of $|3z+9-7i|$ is

If $z_1$ and $z_2$ are two non zero complex numbers, satisfying the equation $\arg \left({\overline{z}}_1\right)=\arg \left(z_2\right),$ then which of the following is/are true?

If a convex polygon has $35$ diagonals, then the number of points of intersection of diagonals which lies inside the polygon is

The line $2x-y+1=0$ is tangent to a circle at point $(2,5)$ and the centre of the circle lies on $x-2y=4.$ Then the radius of the circle is ____ units.

A variable straight line through $A(-1,-1)$ is drawn to cut the circle $x^2+y^2=1$ at the points $B,C.$ If $P$ is chosen on the line $ABC$ such that $AB,AP,AC$ are in $A.P$ then the locus of $P$ is

The value of $\lambda$ for which the lines 3x – 4y – 13 = 0, 8x – 11y – 33 = 0 and 2x – 3y + $\lambda =0$ are concurrent is

Which among the following functions is not an injective function?