Explore topic-wise InterviewSolutions in Current Affairs.

lim ₓ→_-2 (x³ - 7x -6)÷(x⁴+ 5x-6)

Find the value of x, if the expression $\frac{(2x-4)+y\alpha }{(x-2)+2y}$ is independent as y.

The temperature at which the R.M.S. speed of $C{O}_2$ becomes equal to that of nitrogen at ${21}^{\circ }$c is

If ${\sin }^3\theta \cos \theta -{\cos }^3\theta \sin \theta =\frac{1}{4},$ then the values of $\theta$ which satisfy the equation is

Show that $si{n}^{-1}\frac{5}{13}+co{s}^{-1}\frac{3}{5}=ta{n}^{-1}\frac{63}{16}.$

Let A =R -{3}, B=R -{1}. If $f:A\to B$ be defined by $f\left(x\right)=\frac{x-2}{x-3},\forall x\in A$. Then, show that f is bijective.

If $A=\left[\begin{array}{ccc}2& -1& 1\\ -1& 2& -1\\ 1& -1& 2\end{array}\right]$ verify that $A^3-6A^2+9A-4I=0$ and hence, find $A^{-1}$

For the given differential equation find the general solution.
$xlogx\frac{dy}{dx}+y=\frac{2}{x}logx$

Solve the equation cos$\left(ta{n}^{-1}x\right)=sin\left(co{t}^{-1}\frac{3}{4}\right).$

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

log(log x), x>1.

The general solution of the equation ${\sin }^{100}x-{\cos }^{100}x=1$ is
(where $n\in Z$ )

The least positive value of $t$ so that the lines $x=t+\alpha ,y+16=0$ and $y=\alpha x$ are concurrent is

Which carbon atom will show minimum electronegativity -

H ${}^{1}C$ $\equiv$ ${}^{2}C$ - C${}^{3}H$ - C${}^{4}H$ - C${}^{5}H$

The portion of the tangent at any point on the curve $x=a{t}^3$, $y=a{t}^4$ between the axes is divided by the abscissa of the point of contact externally in ratio

If $2sec2\alpha =tan\beta +cot\beta ,$ then one of the values of
$\alpha +\beta$ is

In a precision bombing attack, there is $50\%$ chance that any one bomb will strike the target. Two precise hits are required to destroy the target completely. The number of bombs which should be dropped to give a $99\%$ chance or better of completely destroying the target can be

If the two equations $x^2-cx+d=0$ and $x^2-ax+b=0$ have one common root and the second has equal roots, then $2(b+d)=$)

If (b + c), (c + a), (a + b) are in H.P., then which of the following hold(s) good?

‘n’ whole numbers are randomly chosen and multiplied, then probability that

$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \left(a\right)& \text{The last digit is 1,3,7 or 9}& \left(p\right)& \frac{8^n-4^n}{{10}^n}\\ \left(b\right)& \text{The last digit 2,4,6,8}& \left(q\right)& \frac{5^n-4^n}{{10}^n}\\ \left(c\right)& \text{The last digit is 5}& \left(r\right)& \frac{4^n}{{10}^n}\\ \left(d\right)& \text{The last digit is zero}& \left(s\right)& \frac{{10}^n-8^n-5^n+4^n}{{10}^n}\end{array}$

Find the centre of the sphere
$x^2+y^2+z^2+2z-x=0$

Given that the equation $z^2+(p+iq)z+r+is=0$where p,q,r,s are real and non-zero has a real root, then

Twenty tickets are marked the numbers 1, 2, ..... 20. If three tickets be drawn

at random, then what is the probability that those marked 7 and 11 are

among them

The area in the first quadrant bounded by the parabola $y=x^2+1$, the tangent to it at the point (2, 5) and the coordinate axes is sq. units.

${lim}_{x\to 0}\frac{sin2x(cos3x-cosx)}{x^3}$

If odds against an event be 7 : 9, find the probability of non-occurrence of this event.

Given $\overrightarrow{\alpha }=3\hat{i}+\hat{j}+2\hat{k}$ and $\overrightarrow{\beta }=\hat{i}-2\hat{j}-4\hat{k}$ are the position vectors of the points $A$ and $B.$ Then the distance of the point $-\hat{i}+\hat{j}+\hat{k}$ from the plane passing through $B$ and perpendicular to $AB$ is

The image of a point $(3t+1,1-4t),\forall t\in R-\left\{0\right\}$ in a line, lies on $3x-4y+1=0.$ Then the slope of line(s) is (are)

The function f(x) =$x{e}^x$ is strictly increasing in the interval

${lim}_{x\to 1}\frac{x^7-2x^5+1}{x^3-3x^2+2}$

Let $X$ and $Y$ be two events such that $P\left(X\right)=\frac{1}{3},P\left(X|Y\right)=\frac{1}{2}$ and $P\left(Y|X\right)=\frac{2}{5}$. Then

Let E and F be two independent events. The probability that exactly one of them occurs is$\frac{11}{25}$ andthe probability that none of them occurs is $\frac{2}{25}$ .Then $P(E\bigcap F)=$

$Thefociofthehyperbola2x^2-3y^2=5are$

Mr Seth and his wife had booked business class tickets for an Air Mindo flight from New York to Mumbai on 14th, October, 2011 and paid a total of Rs 2,43,241. The complainants had paid for business class seats, but had been provided the defective seats. As a result, they had to bear physical discomfort and mental harassment.

The Air Mindo was found guilty of deficiency in service. The Consumer Disputes Redressal Forum, Ahmedabad (Rural), allowed Mr Tarun Seth and Mrs Prathibha Seth to file a complaint by Consumer Education and Research Society (CERS), Ahmedabad against the regional manager - Air Mindo. Ahmedabad and the commercial director - Air Mindo, Mumbai.

It was observed by the forum that the airline was guilty of deficiency in service and directed it to refund the Seth's Rs 2,43,241 with $9\%$ interest from the date of complaint.

(i) Is the step taken by them appreciable or not?

(ii) Which values of a customer satisfied in this case?

$\frac{2x-3}{3x-7}>0$

The term independent of $x$ in the expansion of $(\frac{1}{60}-\frac{x^8}{81})\cdot {(2x^2-\frac{3}{x^2})}^6$ is equal to:

If $|x+2|\le 9$,then

Which of the following equations are quadratic?

Solution set of $\frac{x^2-4x+3}{x^2-8x+15}\le 0$ is

Let $a,b,c,d\in R^{+}$ and $256abcd\ge (a+b+c+d{)}^4$ and $3a+b+2c+5d=11$ then $a^3+b+c^2+5d$ is

The maximum value of |z| satisfying the equation $\frac{1}{12}(z+\overline{z}{)}^2=1-\frac{1}{3}|z{|}^2$ is:

Given the parabola $y^2=4ax,$ find the locus of intersection of pair of tangents that are perpendicular to each other