Explore topic-wise InterviewSolutions in Current Affairs.

The equation x log x = 3 - x has, in the interval (1, 3),

If $\alpha ,\beta$ be the roots of the equation $3\cos 2\theta +4\sin 2\theta =5$, then match the following from $\text{List I}$ to $\text{List II}$.

$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& \tan \alpha +\tan \beta & \text{(P)}& 0\\ \text{(B)}& \tan (\alpha +\beta )& \text{(Q)}& \frac{4}{3}\\ \text{(C)}& \tan (\alpha -\beta )& \text{(R)}& \frac{1}{4}\\ \text{(D)}& \tan \alpha \tan \beta & \text{(S)}& 1\end{array}$

The straight lines 3x-2y = 1, 3x + y = 13 and 6x-y = 5 form a triangle. Let the set $s=\left\{(\frac{3}{2},\frac{5}{2})(\frac{5}{2},\frac{21}{5})(\frac{3}{2},\frac{3}{2})(\frac{5}{2},\frac{14}{5})(\frac{11}{4},\frac{13}{2})\right\}$ then the number of points which lies in the interior of the triangle is ___

If $A=\left[\begin{array}{cc}1& tanx\\ -tanx& 1\end{array}\right],A^T{A}^{-1}=$ ___

If $A=\left[\begin{array}{cc}4& 2\\ -1& 1\end{array}\right]$ and I is the identity matrix of order 2, then (A - 2I)(A - 3I) =

If the mean of the set of numbers $x_1,x_2.x_3,.....,x_n$ is $\overline{x}$, then the mean of the numbers $x_1+2i,1\le i\le n$ is

If from the point P(a, b, c) perpendiculars PL, PM be drawn to YOZ and ZOX planes, then the equation of the plane OLM is

The value of
$sin\frac{\pi }{14}sin\frac{3\pi }{14}sin\frac{5\pi }{14}sin\frac{7\pi }{14}sin\frac{9\pi }{14}sin\frac{11\pi }{14}sin\frac{13\pi }{14}$ is equal to ___

The equation of the circle through the points of intersection of $x^2+y^2-1=0,x^2+y^2-2x-4y+1=0$

and touching the line x + 2y = 0, is

Let $f\left(x\right)=x^2-2x,xϵR$ and $g\left(x\right)=f\left(f\right(x)–1)+f(5–f(x\left)\right).$ Which of the following statements(s) is/are true?

The area bounded by $x=0,x=6+5y–y^2$ is

x and y are the sides of two squares such that $y=x-x^2$. The rate of change of area of the second square with respect to that of the first square is

If $\alpha ,\beta$ are the solutions of $\sin x=-\frac{1}{2}$ in $[0,2\pi ]$ and $\alpha ,\gamma$ are the solutions of $\cos x=-\frac{\sqrt{3}}{2}$ in $[0,2\pi ],$ then

${}^n{C}_r+{}^n{C}_{r-1}$ is equal to

${lim}_{x\to 0}\frac{e^{\tan x}-1}{\tan x}$

While apologizing to a subordinate, you must not:

The perimeter of a triangle PQR is six times the arithmetic mean of the sines of its angles. If a = 1, then $\angle A$ = .

PQ and PR are two infinite rays.QAR is an arc . point lying in the shaded region excluding the boundry satisfies

Find the perpendicular distance of the line joining the points $(cos\theta ,sin\theta )$ and $(cos\varphi ,sin\varphi )$ from the origin.

Suppose that water is emptied from a spherical tank of radius 10 cm. If the depth of the water in the tank is 4 cm and is decreasing at the rate of 2 cm/sec, them the radius of the top surface of water is decreasing at the rate of

Write which of the following statements are true ? Justify your answer.

(i) The set of all intergers is contained in the set of all rational numbers.

(ii) The set of all crows is contained in the set of all birds.

(iii) The set of all rectangles is contained in the set of all squares.

(iv) The set of all real numbers is contained in the set of all complex numbers.

(v) The sets P = {a} and B = {{a}} are equal.

(vi) The sets A = {x : x is a letter of the word "LITTLE"} and B = {x : x is a letter of the word "TITLE"} are equal.

Let $\alpha ,\beta$ be the roots of the quadratic equation $3x^2+10x+2=0$, then the quadratic equation whose roots are $\frac{\alpha }{\alpha +5},\frac{\beta }{\beta +5}$, is

$li{m}_{\pi \to \infty }{\sum }_{k=1}^n\frac{k}{n^2+k^2}$ is equals to [Roorkee 1999]

The order of the differential equation whose general solution is given by is

[AMU 2000]

If ${\tan }^{-1}\left(\frac{a}{x}\right)+{\tan }^{-1}\left(\frac{b}{x}\right)=\frac{\pi }{2},$ then $x$ is equal to

Let $P=\sum _{r=1}^{50}\frac{{}^{50+r}{C}_r(2r-1)}{{}^{50}{C}_r(50+r)},Q=\sum _{r=0}^{50}{(}^{50}{C}_r{)}^2$ and $R=\sum _{r=0}^{100}(-1{)}^r{(}^{100}{C}_r{)}^2$. Then

For any two sets A and B, show that the following statements are equivalent :

(i) $A\subset B$ (ii) $A-B=\varphi$

(iii) $A\cup B=B$ (iv) $A\cap B=A.$

Number of distinct rational numbers $x$ such that $0<x<1$ and $x=p/q,$ where $p,q\in \{1,2,3,4,5,6\}$ is

In a self there are $2$ different physics books and $3$ different chemistry books. The number of ways in which a student can select a physics book and chemistry book is:

Let ${\lambda }_1$ be the area of the region on the plane bounded by $max(\left|x\right|,\left|y\right|)\le 1$ and $xy\le \frac{1}{2},$ and ${\lambda }_2$ be the length of $y-$intercept of the plane which is passing through the intersection of the planes $x+2y+3z+5=0$ and $2x-3y+7z+1=0$ and is parallel to the line $\overrightarrow{r}=\overrightarrow{i}+2\hat{j}+t(8\hat{i}-7\hat{j}-4\hat{k}),$ where $t\in R.$ Then $\left[{\lambda }_1\right]+\left[{\lambda }_2\right]$ equals
($[.]$ denotes the greatest integer function)

The value of $\frac{\tan {225}^{\circ }-\cot {81}^{\circ }\cot {69}^{\circ }}{\cot {261}^{\circ }+\tan {21}^{\circ }}$ is

The point of concurrency of the altitudes drawn from the vertices $A(a{t}_1{t}_2,a(t_1+t_2\left)\right),B(a{t}_2{t}_3,a(t_2+t_3\left)\right)$ and $C(a{t}_3{t}_1,a(t_3+t_1\left)\right)$ of the triangle $ABC$ (where $t_1\ne t_2\ne t_3)$is

If $J=\underset{\pi /6}{\overset{\pi /3}{\int }}\frac{dx}{\sqrt{\cos x}+\sqrt{\sin x}}$ then $\underset{\pi /6}{\overset{\pi /3}{\int }}\frac{xdx}{\sqrt{\cos x}+\sqrt{\sin x}}$ equals

The set of all real values of $a$ for which the function $f\left(x\right)=(a+2)x^3-3a{x}^2+9ax-1$ decreases monotonically throughout for all real $x,$ is

Verify $A\left(adj\right)\left(A\right)-\left(adjA\right)A=|A|I_n|)in$
$\left[\begin{array}{ccc}1& -1& 2\\ 3& 0& -2\\ 1& 0& 3\end{array}\right]$

Find the area of the smaller part of the circle $x^2+y^2=a^2$ cut-off by the line $x=\frac{a}{\sqrt{2}}.$

Let A and B be sets. Show that $f:A\times B\to B\times A$ such that f(a,b)=(b,a) is bijective function.

The value of $tan\alpha +2tan\left(2\alpha \right)+4tan\left(4\alpha \right)+.....+2^{n-1}tan\left(2^{n-1}\alpha \right)+2^{n}cot\left(2^n\alpha \right)$ is

Show that $f:[-1,1]\to R$, given by $f\left(x\right)=\frac{x}{(x+2)},x\ne -2$, is one-one. Find the inverse of the function $f:[-1,1]\to$ Range f.

The inequality $lo{g}_2\left(x\right)<si{n}^{–1}$ (sin(5)) holds true if x $ϵ$

By using properties of definite integrals, evaluate the integrals
${\int }_0^{\frac{\pi }{2}}co{s}^{2}dx.$