Explore topic-wise InterviewSolutions in Current Affairs.

If $x^2-(a-3)x+a=0$ has atleast one positive root, then $a\in$

If${\theta }_1\text{and}{\theta }_2$ satisfy the equation $\cos {\theta }_1+\cos {\theta }_2=\sqrt{3}(\sin {\theta }_1-\sin {\theta }_2),$ then $({\theta }_1>{\theta }_2\text{and}0>{\theta }_1,{\theta }_2<\frac{\pi }{2})$

If the curves $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and
​$\frac{x^2}{{\alpha }^2}+\frac{y^2}{{\beta }^2}=1$

Principal solutions are ______

The length of normal to the curve $x=a\left(\theta +\sin \theta \right),y=a\left(1-\cos \theta \right)\mathrm{at}\theta =\frac{\pi }{2}$ is .

Each set X, contains 5 elements and each set Y, contains 2 elements and ${\bigcup }_{r=2}^{20}{X}_r=S={\bigcup }_{r=1}^n{Y}_r$. If each element of S belongs to exactly 10 of the $X_r^{{}^{\prime }s}$ and to exactly 4 of $Y_r^{{}^{\prime }s}$ then find the value of n.

1. 6

The ratio in which $x-$ axis divides the line segment joining $(3,-4)$ and $(-5,6)$ is

Find the equation of the plane which is at a distance of $\frac{6}{\sqrt{29}}$ from the origin and its normal vector from the origin is $2\hat{i}-3\hat{j}+4\hat{k}$

A dice is thrown, what is the probability of getting an even number?

If ${\Delta }_1=\left|\begin{array}{ccc}1& 0& 2\\ 0& 2& -1\\ 0& -1& 3\end{array}\right|$ and ${\Delta }_2=\left|\begin{array}{ccc}2& -1& 0\\ 3& 1& 0\\ 0& 0& 2\end{array}\right|,$ then the value of ${\Delta }_1{\Delta }_2$ is

If $g\left(x\right)=\frac{1}{x\sqrt{x^2+1}},$ then $g^{\prime }\left(x\right)=$

Using Binomial Theorem, evaluate (99)⁵

Why do we consider length and breadth in the layer formed by Oliver acid on water ?

The layer is circle in shape which means it should have radius not length and breadth.......

And it's area will be 2πR

The domain of the definition of the function $f\left(x\right)=\frac{1}{4-x^2}+{\log }_{10}(x^3-x)$ is :

An electric dipole is placed in an uniform electric field of magnitude $40\text{N/C}$. The graph given below represents the magnitude of the torque on dipole versus the angle $\theta$ between field and dipole moment. The magnitude of dipole moment is equal to

Select the correct graph of the quadratic polynomial $y=-x^2-x+2.$

If atleast one of the root of the equation $x^2-(a-3)x+a=0$ is greater than $2$, then $a$ lies in the interval

The general solution of $\frac{dy}{dx}+ytanx=secx$ is
(a) y secx=tanx+C
(b) y tanx=secx+C
(c) tanx=y tanx+C
(d) x secx=tany+C

Find the length of direct common tangent for circles $x^2+y^2-20x+64=0$and $x^2+y^2+30x+144=0$

If $x$ and $y$ hold good with the equations

${\log }_{10}(x-2)+{\log }_{10}y=0$ and $\sqrt{x}+\sqrt{y-2}=\sqrt{x+y},$ then which of the following option is correct?

If $I_{m,n}=\underset{0}{\overset{\pi /2}{\int }}{\cos }^{m}x\sin nxdx$, then $7I_{4,3}-4I_{3,2}$ is equal to

Number of ordered pairs $(x,y)$ which satisfies $\frac{x^4+1}{8x^2}={\sin }^{2}y{\cos }^{2}y;$ where $y\in [0,2\pi ]$ is

If the equation of the line passing through $M(1,1,1)$ and intersecting at right angle to the line of intersection of the planes $x+2y-4z=0$ and $2x-y+2z=0$ is $\frac{x-1}{a}=\frac{y-1}{b}=\frac{z-1}{c},$ then $a:b:c$ equals

The roots of $(2-2i{)}^{\frac{1}{3}}$

Insert 2 no.s between 1 & $\frac{1}{3}$ so that the sequence becomes an Harmonic progression --

Let $f\left(x\right)=x^2+ax+3,g\left(x\right)=x+b$ and $F\left(x\right)=\underset{n\to \infty }{lim}\frac{f\left(x\right)+x^{2n}g\left(x\right)}{1+x^{2n}}$. If $F\left(x\right)$ is continuous $\forall x\in R,$ then

Let $\overrightarrow{A}$ be vector parallel to line of intersection of planes $P_1$ and $P_2$ through origin. $P_1$ is parallel to the vectors $2\hat{j}+3\hat{k}$ and $4\hat{j}-3\hat{k}$ and $P_2$ is parallel to $\hat{j}-\hat{k}$ and $3\hat{i}+3\hat{j},$ then the angle between vector $\overrightarrow{A}$ and $2\overrightarrow{i}+\overrightarrow{j}-2\hat{k}$ is

The value of $tan[co{s}^{-1}\left(\frac{-2}{7}\right)-\frac{\pi }{2}]$ is

If f, g, h are real functions given by $f\left(x\right)=x^2,g\left(x\right)=tanx$ and $h\left(x\right)=lo{g}_{e}x$, then write the value of $hogof\left(\sqrt{\frac{\pi }{4}}\right)$

The lateral edge of a regular hexagonal pyramid is 1 cm. If the volume is maximum, then its height is

If $\int \frac{4x+1}{x^2+3x+2}dx=2\log |x^2+3x+2|+f\left(x\right)+C$, then $f\left(x\right)$ is

(where $C$ is integration constant)