Explore topic-wise InterviewSolutions in Current Affairs.

Let $f(x+y)=f\left(x\right)\cdot f\left(y\right)$ for all $x$ and $y$. If $f\left(3\right)=2$ and $f^{\prime }\left(0\right)=4$, then $f^{\prime }\left(3\right)$ is

If sinA + 2cosA = 1. Prove that 2sinA -cosA= 2.

The equations of the tangnets to the ellipse $4x^2+3y^2=5$ which are perpendicular to the line $3x-y+7=0$ are :

If A is a symmetric matrix, then matrix M'AM is

Find the value of k if the perpendicular distance of P (1, 2) from (4x - 3y + k) = 0 is 5 units.

What is the equation of the normal which is perpendicular to 3x + 4y = 5 for the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

If $z_1,z_{2}and{z}_3,z_4$ are two pairs of conjugate complex numbers, $arg\left(\frac{z_1}{z_4}\right)+arg\left(\frac{z_2}{z_3}\right)$ then equals

4x - 6 = 3x / 4 + 20

Let $A\left(Z_1\right),B\left(Z_2\right),C\left(Z_3\right)$ be the vertices of an equilateral triangle ABC, then the value of $arg\left(\frac{Z_2+Z_3-2Z_1}{Z_3-Z_2}\right)$ is equal to

${lim}_{n\to \infty }[\frac{1}{1-n^2}+\frac{2}{1-n^2}+\cdots +\frac{n}{1-n^2}]$ is equal to

If x=1/(2-√3),then the value of (x^3-2x^2-7x+5)

The directrix of the parabola $x^2-4x-8y+12=0$ is

If $sin\theta +cos\theta =m$, then prove that

$si{n}^6\theta +co{s}^6\theta =\frac{4-3(m^2-1{)}^2}{4}$, where $m^2\le 2$

$Thesolutionoftheequationco{s}^2\theta +sin\theta +1=0liesintheinterval$

If $a,b,c$ are in G.P., then ___.

If $f\left(x\right)={\int }_0^x\frac{dt}{2+t^4}$, then

The angle between the vectors $\overline{u}=<3,0>and\overline{v}=<5,5>$ is _____

If $f:R\to R$ be a continuos function such that $f\left(x\right)={\int }_1^{x}tf\left(t\right)dt,$ then correct statement is

The equation is $2co{s}^{-1}x+si{n}^{-1}x=\frac{11\pi }{6}$ has
[AMU 1999}

Which one of the following is not correct for the features of exponential function given by $f\left(x\right)=b^x$, where $b>1$

If $z$ and $\omega$ are two complex numbers such that $|z\omega |=1$ and $\arg \left(z\right)-\arg \left(\omega \right)=\frac{\pi }{2},$ then

If $f\left(x\right)=\left|\begin{array}{ccc}sinx& sina& sinb\\ cosx& cosa& cosb\\ tanx& tana& tanb\end{array}\right|,where0<a<b<\frac{\pi }{2}$
then the equation
$f^{\prime }\left(x\right)=0$ has in the interval $(a,b)$

For any two sets of A and B, prove that :

(i) $A^{\prime }\cup B=U\Rightarrow A\subset B$

(ii) $B^{\prime }\subset A^{\prime }\Rightarrow A\subset B$

The distance of the plane passing through (1,1,1) and perpendicular to the line $\frac{x-1}{3}=\frac{y-1}{0}=\frac{z-1}{4}$ from the origin is

Find the equations of the circles passing through two points on y-axis at distance $3$ from the origin and having radius $5$.

The value of $\sum _{i=1}^n\sum _{j=1}^i\sum _{k=1}^{j}1=220,$ then the value of $n$ equals

If $y=1+t^4$ and $x=3t^3+t$ then $\frac{dy}{dx}$ is equal to

If the curve $y=a{x}^2+bx+c,x\in R,$ passes through the point $(1,2)$ and the tangent line to this curve at origin is $y=x,$ then the possible values of $a,b,c$ are

If the difference between the number of subsets of two finite sets $A$ and $B$ is $120,$ then $n(A\times B)$ is

Total number of polynomials of the form $x^3+a{x}^2+bx+c,$ that are divisible by $x^2+1,$ where $a,b,c\in \{1,2,3,\dots ,9,10\}$ is

If $x^4+y^4+z^4=0,$ then $\left|\begin{array}{ccc}1& xy& yz\\ zx& 1& xy\\ yz& zx& 1\end{array}\right|=$ (where $x,y,z\in R)$

Prove that $(a+b).(a+b)=|a{|}^2+|b{|}^2$, if and only if a, b are perpendicular, given $a\ne 0$, $b\ne 0$

In answering a question on a multiple choice test a student either knows the answer or guesses. Let 3/4 be the probability that he knows the answer and 1/4 be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability 1/4 What is the probability that a student knows the answer given that the answered it correctly?

Using mathematical Induction, the numbers $a_n{}^{\prime }s$ are defined by $a_0=1,a_{n+1}=3n^2+n+a_n(n\ge 0)$ Then $a_n=$

If $y=(1+x)(1+x^2)(1+x^4).....(1+x^{2n}),\text{then}{\left(\frac{dy}{dx}\right)}_{x=0}=$

If the adjacent sides of a parallelogram are represented by $2x^2-5xy+3y^2=0$ and the equation of one diagonal is $x+y-2=0,$ then the equation of the other diagonal is

Let $\overrightarrow{a}=\hat{i}+\hat{j};\overrightarrow{b}=2\hat{i}-\hat{k}$. Then, vector $\overrightarrow{r}$ satisfying the equations $\overrightarrow{r}\times \overrightarrow{a}=\overrightarrow{b}\times \overrightarrow{a}$ and $\overrightarrow{r}\times \overrightarrow{b}=\overrightarrow{a}\times \overrightarrow{b}$ is