Explore topic-wise InterviewSolutions in Current Affairs.

If a < 0 and D < 0, what can be inferred about $f\left(x\right)$ = $a{x}^2+bx+c$?

If in a triangle $△ABC,a^2{\cos }^{2}A-b^2-c^2=0,$ then

The coefficient of $x^{50}$ in $(1+x{)}^{1000}+x(1+x{)}^{999}+x^2(1+x{)}^{998}+...+x^{1000}$is

The value of $x$ for $\sin x+\sqrt{3}\cos x\ge 1$ in the interval $-\pi <x\le \pi$ is

The sum of the series ${\sum }_{k=1}^{360}\frac{1}{k\sqrt{k+1}+(k+1)\sqrt{k}}$ is

The value of $\log \tan {17}^{\circ }+\log \tan {37}^{\circ }+\log \tan {53}^{\circ }+\log \tan {73}^{\circ }$ is

The area bounded by the parabolas $y^2=4x$ and $x^2=4y$ is

The chord $x+y=1$ of the curve $y^2=12x$ cuts it at the points $A$ and $B.$ The normals at $A$ and $B$ intersect at $C.$ If a third line from $C$ cuts the curve normally at $D,$ then the co-ordinates of $D$ are

If $\frac{1+\sin 2x}{1-\sin 2x}={\cot }^2(a+x)$$\forall x\in R-(n\pi +\frac{\pi }{4}),$ $n\in N$ then the possible value of $a$ is

Let E and F be events with P(E)=$\frac{3}{5},P\left(F\right)\frac{3}{10}$ and P$(E\cap F)=\frac{1}{5}$. Are E anf F independent?

Let A and B be independent event with P (A ) = 0.3 and P (B) = 0.4. find
$P\left(\frac{B}{A}\right)$

Two groups are competing for the position on the board of directors of a corporation. The probability that the first and the second groups will win are 0.6 and 0.4, respectively. Further, if the first group wins the probability of introducing a new product is 0.7 and the corresponding probability is 0.3, if the second group wins. Find the probability that the new product introduce was by the second group.

The domain of the definition of the function $f\left(x\right)=\frac{1}{4-x^2}+{\log }_{10}(x^3-x)$ is :

Total number of solutions of sinx = $\frac{|x|}{10}$ is

If $\alpha ,\beta$ are the roots of the equation $x^2-px+r=0$ and $\frac{\alpha }{2},2\beta$ are the roots of the equation $x^2-qx+r=0$, then the value of $r$ in terms of $p$ and $q$ is

If $si{n}^{-1}(1-x)-2si{n}^{-1}x=\frac{\pi }{2}$ , then x =

Determine $P\left(\frac{E}{F}\right)$
A coin is tossed three times
E: Atleast two heads F : atmost two heads

Prove the following theorem:

The total number of subsets of a finite set containing n elements is 2ⁿ.

In which step, the elements ‘72 today required 44’ are in the same order?

$co{t}^{-1}\left(\frac{\sqrt{1+sinx}+\sqrt{1-sinx}}{\sqrt{1+sinx}-\sqrt{1-sinx}}\right)=\frac{x}{2},xϵ(0,\frac{\pi }{4})$

Differentiate $e^{\sqrt{c}otx}$

The coordinates of the feet of the perpendiculars from the vertices of a triangle on the opposite sides are $(20,25),(8,16)$ and $(8,9)$. The coordinates of a vertex of the triangle are

$\text{If}{z}_1\text{and}{z}_2$ are two complex numbers such that $|z_1|=|z_2|\text{and}\left(z\right)+arg\left(z_2\right)=\pi ,\text{then show that}{z}_1=-\overline{z_2}.$

From a committee of 8 persons,in how many ways can we choose a chairman and a vice chairman assuming one person can not hold more than one position ?

An item is manufactured by three machines A, B and C. Out of the total number of items manufactured during a specified period, 50% are manufactured on A, 30% on B and 20% on C. 2% of the items produced on A and 2% of items produced on B are defective and 3% of these produced on C are defective. All the items are stored at one godown. One item is drawn at random and is found to be defective. What is the probability that was manufactured on machine A ?

Let f = { (1,3), (2,1) , (3,2)} and g= {(1,2), (2,3) , (3,1)} . What is gof(2)?

If A and B are two events such that P (A) $\ne 0$ and

$P\left(\frac{B}{A}\right)=t,$ then

(a) $A⊏B$ (b) $B⊏A$
(c) $B=\varphi$ (d) $A=\varphi$

Solve the following equation for x:

$ta{n}^{-1}\frac{1-x}{1+x}=\frac{1}{2}ta{n}^{-1}x,(x>0)$.

The solution of $\frac{dy}{dx}+1=e^{x+y}$ is

If $i=\sqrt{-1}$, then $4+5{(-\frac{1}{2}+\frac{\sqrt{3}}{2}i)}^{334}+3{(-\frac{1}{2}+\frac{\sqrt{3}}{2}i)}^{365}$ is equal to

In an A.P. the value of the common difference d is

Matrix $A_r=\left[\begin{array}{cc}r& r-1\\ r-1& r\end{array}\right];r=1,2,3,...$. If $\sum _{r=1}^{100}|A_r|=(\sqrt{10}{)}^k$, where $|A_r|$ is determinant of $A_r$, then the value of $k$ is

If a,b be positive real numbers such that $a^2$ + $b^2$ = 8, then maximum value of a+b is _____.

If A and B are the sunsets of the universal set U, then show that

1. A is a subset of A union B

If f(x) = x^2 -5x +7 and let A be a matrix . f(A) is written as A^2 -5A +7I where I is an Identity matrix .Why 7 is written as 7I as It is a scalar and multiplying by matrix makes it a matrix .

The signs of the X, Y and Z coordinates of a point that lies in the octant OXYZ' is

The value of $Sec{0}^{\circ }Sec{5}^{\circ }Sec{10}^{\circ }$....................$Sec{170}^{\circ }Sec{175}^{\circ }Sec{180}^{\circ }$ is,

A mirror in the first quadrant is in the shape of a hyperbola whose equation is xy = 1. A light source in the second quadrant emits a beam of light that hits the mirror at the point $(2,\frac{1}{2})$. If the reflected ray is parallel to the y-axis the slope of the incident beam is

If sec$\theta$ = 1 $\frac{1}{4}$, then tan $\frac{\theta }{2}$ =