Explore topic-wise InterviewSolutions in Current Affairs.

Express $(sin\theta +icos\theta {)}^5$ in Eulers form.

The set of values of $k$ for which roots of the quadratic equation $-x^2-2(k-1)x-(k+5)=0$ are less than \(1)\ is

If
A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D =
{15, 17}; find

(i) A
∩
B

(ii) B
∩
C

(iii) A
∩
C ∩
D

(iv)
A ∩
C

(v) B
∩
D

(vi) A
∩
(B ∪
C)

(vii)
A ∩
D

(viii) A
∩
(B ∪
D)

(ix) (A
∩
B) ∩
(B ∪
C)

(x) (A
∪
D) ∩
(B ∪
C)

Find Ceff

The negation of the compound proposition $p\vee (\sim p\vee q)$ is

Sum of n terms of series
ab+(a+1)(b+1)+(a+2)(b+2)+....+(a+(n-1))(b+(n-1))
if $ab=\frac{1}{6}and(a+b)=\frac{1}{3},is$

If $A=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 2015& 2016& -1\end{array}\right],$ then $(2A^2+4A^4+6A^6)$ is equal to

$($Here, $I_3$ is unit matrix of order $3)$

If $y\left(x\right)={\cot }^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right),x\in (\frac{\pi }{2},\pi ),$ then $\frac{dy}{dx}$ at $x=\frac{5\pi }{6}$ is

If $a=\cos x-\sin x$, then in the interval $[-\pi ,\pi ],a>0\forall a\in$

The equation of a circle which touches both axes and the line 3x – 4y + 8 = 0 and whose centre lies in the third quadrant is

If A is square matrix of order 3 and |A| = 7 then |A ^T| = ______

The value of $\cos (\frac{\pi }{4}+A)\cos (\frac{\pi }{4}-B)-\sin (\frac{\pi }{4}+A)\sin (\frac{\pi }{4}-B)$ is

The number of possible straight lines, passing through $(2,3)$ and forming a triangle with co-ordinate axis, whose area is $12$ sq. units is______.

The value of $\sin {10}^{\circ }\sin {30}^{\circ }\sin {50}^{\circ }\sin {70}^{\circ }$ is :

The polar coordinates of the point whose Cartesian coordinates are $(-1,-\sqrt{3})$, are

If $U=\{1,3,5,7,9,11,13\}$, then which of the following is/are the subsets of $U$?

Find the mean and
standard deviation using short-cut method.

Let $\left|\begin{array}{cc}2\cos x& 3\sin x\\ e^x& 5\end{array}\right|=A+Bx+C{x}^2+\cdots (A,B,C\text{are real constants}),$ then which of the following(s) is/are true

If $A=\frac{\cos 9^{\circ }-\sin 9^{\circ }}{\cos 9^{\circ }+\sin 9^{\circ }},B=\frac{\cos {21}^{\circ }+\sin {21}^{\circ }}{\cos {21}^{\circ }-\sin {21}^{\circ }}$ and $C=\tan {20}^{\circ }+\tan {40}^{\circ }+\sqrt{3}\tan {20}^{\circ }\tan {40}^{\circ }$, then the correct relation between $A,B,C$ is

The vectors, $\overrightarrow{P}=a\hat{i}+a\hat{j}+3\hat{k}$ and $\overrightarrow{Q}=a\hat{i}-2\hat{j}-\hat{k}$ are mutually perpendicular. The value of $a$ will be -

The number of $A$ in $T_p$ such that det $\left(A\right)$ is not divisible by $p$ is

Evaluate the following definite integrals as limit of sums.
${\int }_0^5(x+1)dx.$

The value of $\frac{q}{p}$, if $\frac{p+q}{p-q}=7$ is

$\int \frac{secx(2+secx)}{(1+2secx{)}^2}dx=f\left(x\right)+c$, where C is constant of integration and f(0) = 0, then ${\int }_0^{\pi }f\left(x\right)dx$ is equal to

Suppose $f$ and $g$ are differentiable functions on $(0,\infty )$ such that $f\text{'}\left(x\right)=-\frac{g\left(x\right)}{x}$ and $g\text{'}\left(x\right)=-\frac{f\left(x\right)}{x}$, for all $x>0$. Further, $f\left(1\right)=3$ and $g\left(1\right)=-1$.



If $f\left(x\right)-g\left(x\right)=B{x}^m,$ for all $x>0$ and some constant $B$, then the value of $m$ equals

In a class of $40$ students, $12$ enrolled for both English and German. $22$ enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for English but not German ?

If $|z-3+2i|$ = 4, then sum of max|z| and min|z| is:

Domain of the function $f\left(x\right)=si{n}^{-1}(1+3x+2x^2)$ is

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are non-zero vectors such that $\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})$ is perpendicular to $(\overrightarrow{a}\times \overrightarrow{b})\times \overrightarrow{c},$ then which of the following is/are true $?$

In the expansion of ${(x-\frac{1}{3x^2})}^9$, the term independent of x is

What is the range of cos function?

1. -2.25

If, $I_n=\underset{0}{\overset{\pi /4}{\int }}{\tan }^{n}xdx,n>1\text{and}n\in N,$ then which of the following option(s) is/are true

Match the following:

$\begin{array}{cccc}\left(P\right)& Thestraightlinejoiningthepointsandisa& \left(1\right)& -4\\ & tangenttothecurvey=\frac{C}{x+1}thenC=& & \\ \left(Q\right)& Foreachparabolay=x^2+px+q(p,qare& \left(2\right)& 2\\ & parameters)meetingcoordinateaxesat3distinctpoints,& & \\ & ifcirclesaredrawnthroughthesepoints,andthefamily& & \\ & ofcirclespassesthroughthefixedpoint(h,k)thenh+4k=& & \\ \left(R\right)& IfOBisonesideofarhombusofarea2\sqrt{3}sq.units& \left(3\right)& 0\\ & whereO=(0,0)andB=(2,0)andtheothervertices& & \\ & are(x_1,y_1),(x_2,y_2)inthefirstquadrantthen{x}_1+x_2+y_1-y_2=& & \\ \left(S\right)& Thedistancebetweenthelines& \left(4\right)& 4\\ & (x+7y{)}^2+4\sqrt{2}(x+7y)-42=0& & \end{array}$