Explore topic-wise InterviewSolutions in Current Affairs.

${lim}_{x\to 0}\frac{3x+1}{x+3}$

The sum of the series $\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}\cdots$ up to $\infty$ is equal to

The value of ${\text{cosec}}^{-1}(-\sqrt{2})$ is

Solution of the equation $xdy=(y+x\frac{f\left(\frac{y}{x}\right)}{f^{\prime }\left(\frac{y}{x}\right)})dx$

Find the distance of (3,4,5) from Z- axis

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three vectors such that $(\overrightarrow{a}+\overrightarrow{b})\cdot \overrightarrow{c}=(\overrightarrow{a}-\overrightarrow{b})\cdot \overrightarrow{c}=0,$ then the resultant of the vector $(\overrightarrow{a}\times \overrightarrow{b})\times \overrightarrow{c}$ is

If $i{j}^{th}$ element of matrix A is $2+3i,$ then the corresponding element in conjugate of A is .

If $(1+x+x^2{)}^n=a_0+a_{1}x+a_2{x}^2+...+a_{2n}{x}^{2n}$, and $E_1=a_0+a_3+a_6+...$,
$E_2=a_1+a_4+a_7+...$,
$E_3=a_2+a_5+a_8+...$, then

If $x={\sin }^{-1}\left(\sin 10\right)$ and $y={\cos }^{-1}\left(\cos 10\right)$, then $y-x$ is equal to :

The set of values of $x$ for which $\frac{\tan 3x-\tan 2x}{1+\tan 3x\cdot \tan 2x}=1$ is (where $n\in Z$)

Find the
degree measures corresponding to the following radian measures

.

(i) (ii) –
4 (iii) (iv)

The symmetric form of the equation of the line x + y – z = 1, 2x – 3y + z = 2 is

Three circles touch one another externally. If the tangents at their points of contact meet at a point whose distance from a point of contact is $4$, then the ratio of product of radii to the sum of the radii of the circles, is

Three integers $a,b,c$ are in $G.P.$ If $a,b,c-64$ are in $A.P.$, and $a,b-8,c-64$ are in $G.P.$, then $(a+b+c)$ is equal to

Which of the following points lies on the line passing through $2\hat{i}-\hat{j}$ and $3\hat{i}-2\hat{k}$ is?

The value of ${\cos }^{-1}\sqrt{\frac{2}{3}}-{\cos }^{-1}\frac{\sqrt{6}+1}{2\sqrt{3}}$ is equal to

If ${}^{20}{C}_1+(2^2{)}^{20}{C}_2+(3^2{)}^{20}{C}_3+.....+({20}^2{)}^{20}{C}_{20}=A(2^{\beta })$, then the ordered pair $(A,\beta )$ is equal to:

If the coordinates of the points A, B, C, be (4,4), (3,-2) and (3,-16) respectively, then the area of the triangle ABC is

The value of $(2\cdot {}^1{P}_0-3\cdot {}^2{P}_1+4\cdot {}^3{P}_2-\cdots \cdots \text{up to}{51}^{\text{th}}\text{term})+(1!-2!+3!-4!+\cdots \cdots \text{up to}{51}^{\text{th}}\text{term})$ is equal to

$$\left[\begin{array}{cc}2x+y& 4x\\ 5x-7& 4x\end{array}\right]$$ = $$\left[\begin{array}{cc}7& 7y-13\\ y& x+6\end{array}\right]$$, then the value of x + y is
(a) x = 3, y = 1
(b) x = 2, y = 3
(c) x = 2, y = 4
(d) x = 3, y = 3

If the lines represented by $4x^2+12xy+9y^2-6x-9y$ = 1 are 2 tangents to a circle then its area is

If the angles of a triangle ABC be in A.P., then

Latus rectum of the parabola $y^2-4y-2x-8=0$ is

Let $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ be 2 sets of solution satisfying the following equations:

${\log }_{10}\left(2xy\right)=4+({\log }_{10}x-1)({\log }_{10}y-2)$

${\log }_{10}\left(2yz\right)=4+({\log }_{10}y-2)({\log }_{10}z-1)$

${\log }_{10}\left(zx\right)=2+({\log }_{10}z-1)({\log }_{10}x-1)$

such that $(x_1>x_2)$,

then match the elements of List - I with the correct answer in List -II.



$\begin{array}{cc}\text{List -I}& \text{List -II}\\ \left(I\right)\frac{y_1}{x_1}& \left(P\right)2\\ \left(II\right)\frac{z_1}{x_2}& \left(Q\right)100\\ \left(III\right)\frac{z_1{x}_2}{z_2}& \left(R\right)1000\\ \left(IV\right)\frac{y_2+z_1}{x_2}& \left(S\right)150\end{array}$



Which of the following is the only 'CORRECT' combination?

If $f\left(x\right)=\frac{2{\sin }^{2}x+2\sin x+3}{{\sin }^{2}x+\sin x+1},$ then the number of integer(s) in the range of $f$ is