Explore topic-wise InterviewSolutions in Current Affairs.

Find the component statements of the following compound statements.
'It is raining and it is cold'.

If $(1+x+x^2{)}^{20}=a_0+a_{1}x+a_2{x}^2+\cdots +a_{40}{x}^{40},$ then the value of $a_0+a_1+a_2+\cdots +a_{19}$ is

If A = $\left[\begin{array}{ccc}1& 2& -1\\ -1& 1& 2\\ 2& -1& 1\end{array}\right]$, then det (Adj (Adj A)) is

Determine the points in

(i) xy-plane

(ii) yz-plane and

(iii) zx-plane which are equidistant from the points A(1,-1,0), B(2, 1, 2) and C(3, 2, -1)

If $z_1,z_2,z_3$ represent the vertices of an equilateral $\Delta ABC$ and $\sqrt{\frac{|z_2-z_1{|}^2+|z_3-z_1{|}^2}{|z_2+z_3-2z_1{|}^2+|z_3-z_2{|}^2}}=sin\theta$ (where $0<\theta <\pi$) then $\theta$ is

Findf(x),
where f(x) =

Solve the following system of equations in $R$.

$2x-3<7,2x>-4$

Evaluate.

If $\frac{3\pi }{4}<\alpha <\pi$ then, $\sqrt{2cot\alpha +\frac{1}{si{n}^2\alpha }}$ is equal to

Find the integrals of the functions.
$\int \frac{si{n}^{2}x}{1+cosx}dx.$

For any quadratic expression $f\left(x\right)=a{x}^2+bx+c,a>0$ and if $(v,f(v\left)\right)$ is it's vertex, then $y\in$

Two real numbers $x,y$ are chosen from the interval $[0,8]$ then the probability that $y^2>2x$ is

A customer forgets a four-digit code for an Automatic Teller Machine (ATM) in a bank However, he remembers that this code consists of digits 3,5,6 and 9. Find the largest possible number of trials necesssary to obtain the correct code.

If $7x^2+x^{2a-6}+3x+13$ is a quadratic polynomial, then the value of $a$ can be:

If $M(x_0,y_0)$ is the point on the curve $3x^2-4y^2=72,$ which is nearest to the line $3x+2y+1=0,$ then the value of $(x_0+y_0)$ is equal to

The value of $\underset{-\pi /2}{\overset{\pi /2}{\int }}(x^3+x\cos x+{\tan }^{5}x+1)dx$ is

Let $g\left(x\right)$ be a continuous function satisfying $g(x+a)+g\left(x\right)=0,\forall x\in R,a>0.$ If $\underset{b}{\overset{2k}{\int }}g\left(t\right)dt$ is independent of $b$ and $b,k,c$ are in A.P. ,then the least positive value of $c$ is

The length of chord of circle $x^2+y^2+6x+9y+8=0$ intercepted by $x$ axis is

If $x=\frac{4\lambda }{1+{\lambda }^2}$ and $y=\frac{2-2{\lambda }^2}{1+{\lambda }^2}$ where $\lambda$ is a real parameter and $x^2–xy+y^2$ lies between $[a,b]$ then $(a+b)$ is

$\sqrt{3}+i=(a+ib)(c+id),then{\tan }^{-1}\frac{b}{a}+{\tan }^{-1}\frac{d}{c}$

has the value

Find the intersection of each pair of sets:

(i) X = {1, 3, 5} Y = {1, 2, 3}

(ii) A = {a, e, i, o, u} B = {a, b, c}

(iii) A = {x: x is a natural number and multiple of 3}

B = {x: x is a natural number less than 6}

(iv) A = {x: x is a natural number and 1 < x ≤ 6}

B = {x: x is a natural number and 6 < x < 10}

(v) A = {1, 2, 3}, B = Φ

$cosA=-\frac{12}{13}$ and $cotB=\frac{24}{7},$ where A lies in the second quadrant and B in the third quadrant, find the values of the following:
(i)sin(A+B)
(ii)cos(A+B)
(iii)tan(A+B)

The number of points (x,y) having integral coordinates satisfying the condition x^{​​​​​​2} + y^{​​​​​​2} <25 is?

Two cards are drawn at random from a pack of 52 cards. What is the probability that both the drawn cards are aces ?

If the equation $(a-2)(x-[x]{)}^2+2(x-\left[x\right])+a^2=0,a\in R$ has no integral solution and has exactly one solution in $[2,3)$, then $a$ lies in the interval

(where $\left[x\right]$ denotes the greatest integer function)

The value of $k$ in order that $f\left(x\right)=\sin x-\cos x-kx+5$ decreases for all positive real values of $x$ is given by