Explore topic-wise InterviewSolutions in Current Affairs.

If $f\left(x\right)={\log }_x\left(\ln x\right)$, then

The point of intersection of tangents at the points on the parabola $y^2=4x$ whose ordinates are $4$ and $6$ is

Consider $I_n=\underset{0}{\overset{\infty }{\int }}\frac{dx}{{(x+\sqrt{1+x^2})}^n},$ where $n>1$, then which of the following statement(s) is/are true ?

Choose the correct pair of quadratic equations with roots with opposite sign.

In how many different ways ,can $3$ persons $A,B,C$ having $6$ one rupee coin, $7$ one rupee coin, $8$ one rupee coin, respectively donate $10$ one rupee coin collectively ?

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are unit vectors, then the vector $(\overrightarrow{a}+\overrightarrow{b})\times (\overrightarrow{a}\times \overrightarrow{b})$ is parallel to the vector:

The equation of circle with centre (1, 2) and tangent x + y - 5 = 0 is

Which of the following is/are the roots of $(x-1)(x-2)(3x-1)(3x-2)=8x^2$ ?

If $b,k$ are the intercepts of the focal chord of $y^2=4ax$, $a\ne b$ then $k$ is

For any three vectors, $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$, the value of $(\overrightarrow{a}-\overrightarrow{b})\cdot (\overrightarrow{b}-\overrightarrow{c})\times (\overrightarrow{c}-\overrightarrow{a})$ is:

Let $u=\frac{2z+i}{z-ki},z=x+iy$ and $k>0.$ If the curve represented by $Re\left(u\right)+Im\left(u\right)=1$ intersects the $y$-axis at the points $P$ and $Q,$ Where $PQ=5,$ then the value of $k$ is

$\Delta LMN\sim \Delta PQR$, $9Ar\left(\Delta PQR\right)=16Ar\left(\Delta LMN\right)$. If $QR=20$ then Find $MN$.

If A and G be A.M. and
G.M., respectively between two positive numbers, prove that the
numbers are.

The acute angle between the curves $y=\frac{x^2-7x+11}{x-1}$ and $y=\frac{x+3}{x^2+1}$ at $(2,1)$ is

A bag consists of $10$ balls each marked with one of the digits $0$ to $9$. If four balls are drawn successively with replacement from the bag, then the probability that no ball is marked with the digit $0$ is:

The value of $\underset{0}{\overset{\pi /2}{\int }}\frac{{\tan }^{2}x}{1+{\tan }^{2}x}dx$ is

Let $\alpha$ and $\beta (\beta <\alpha )$ be the roots of equation $x^2-6x+8=0$. If

$A$ denotes the number of ways of dividing $(\alpha +\beta )$ people in groups of $\beta ,(\beta +1)$ and $(\beta -1)$ people,

and $B$ denotes the number of ways of dividing $(\alpha \cdot \beta )$ people in groups of $2$ people, then

$ta{n}^{-1}\left[\frac{3sin2\alpha }{5+3cos2\alpha }\right]+ta{n}^{-1}\left[\frac{tan\alpha }{4}\right]=\frac{\lambda \alpha }{4}$ where $-\frac{\pi }{2}<\alpha <\frac{\pi }{2},then\lambda$is ___.

If the equation $||x-1|+a|=4$ has a real soltuion then $a$ belongs to

The area between x = y²
and x = 4 is divided into two equal parts by the line x
= a, find the value of a.

Given standard equation of ellipse,

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b$,

with eccentricity $e$

Match the following

$\begin{array}{cc}\text{a) Focus}& i\left)\right(ae,0)\\ \text{b) Directrix}& ii\left)\right(a,0)\\ \text{c) Eccentricity}& iii)x=\frac{a}{e}\\ \text{d) Vertices}& iv\left)\right(-ae,0)\\ & v)x=\frac{-a}{e}\\ & vi)\sqrt{1-\frac{b^2}{a^2}}\end{array}$

1. 0

If the sum of the slopes of the lines represented by the equation $x^2-2xytanA-y^2=0$ be 4, then $\angle A$ =

If $2f\left(xy\right)={\left(f\right(x\left)\right)}^y+{\left(f\right(y\left)\right)}^x\forall x,y\in R$ and $f\left(1\right)=3,$ then the value of $\sum _{r=1}^{10}f\left(r\right)$ is equal to

If $lo{g}_{0.5}(x-1)<lo{g}_{0.25}(x-1),$ then x lies in the interval.