Explore topic-wise InterviewSolutions in Current Affairs.

The general solution of $\sin x+\cos x=1$ is

If $\frac{\log x}{b-c}=\frac{\log y}{c-a}=\frac{\log z}{a-b}$ , then which of the following is/are true?

Discuss the continuity and differentiability of the function f(x) = |x|+|x-1| in the interval (-1,2).

The product of non-real roots of the equation $(x^2+x-2)(x^2+x-3)=12$ is

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}, verify that

(i) $(A\cup B{)}^{\prime }=A^{\prime }\cap B^{\prime }$

(ii) $(A\cap B{)}^{\prime }=A^{\prime }\cup B^{\prime }$

If A is a square matrix such that $A^2=A$, then write the value of $7A-(1+A{)}^3$, where I is an identify matrix.

If A and B are any two events such that $P\left(A\right)=\frac{1}{2},P\left(B\right)=\frac{1}{3},andP(A\cap B)=\frac{1}{4},thenP\left(A^{\prime }/B^{\prime }\right)=$

The value of $2se{c}^{-1}2+si{n}^{-1}\left(\frac{1}{2}\right)$ is

(a) $\frac{\pi }{6}$ (b) $\frac{5\pi }{6}$ (c) $\frac{7\pi }{6}$ (d) 1

The sum of the solutions of the equation $|x^2-10x+21|=|x-3|$ is

${lim}_{x\to \infty }(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+....+\frac{1}{3^n})$

The coordinates of the focus of the parabola $y^2-x-2y+2=0$ are

$\text{Find the coordinates of the centre of the circle inscribed in a triangle whose vertices are A(-36,7),B(20,7)and C(0,-8).}$

If $5co{s}^{2}2x+4(co{s}^{2}x+si{n}^{4}x+co{s}^{6}x+si{n}^{6}x)=8$, then

If $y=sinx+e^x,then\frac{d^{2}x}{d{y}^2}=$

The range of $f\left(x\right)=\frac{x^2+14x+9}{x^2+2x+3},x\in R$ is

Find the equation of the curve passing through the point $(0,\frac{\pi }{3})$ and satisfying the differential equation $\sin x\cos ydx+\cos x\sin ydy=0,$ where$x,y\in (0,\frac{\pi }{2})$

Interval in which $‘a^{\prime }$ lies so that $x^3–3x+a=0$ has three real and distinct roots.

$If\frac{d}{dx}\left[\frac{1+x^2+x^4}{1+x+x^2}\right]=ax+bthen(a,b)=$

Evaluate $\left|\begin{array}{ccc}1& x& y\\ 1& x+y& y\\ 1& x& x+y\end{array}\right|$

If $\frac{(2x+3)(4-3x{)}^3(x-4)}{x^5(x+2{)}^2}\le 0$, then $x\in$

Let $f:R\to R$ be defined as $f\left(x\right)=x^4$. Choose the correct answer.
(a) f is one-one onto
(b) f is many-one onto
(c) f is one-one but not onto
(d) f is neither one-one nor onto

If one side of a triangle is double the other and the angles opposite to these sides differ by ${60}^0$, then the triangle is

The coefficient of$x^{103}$ in $(1+x+x^2+x^3+x^4{)}^{199}.(x-1{)}^{201}$ is

Select the conjunction which can be used to join the sentences.

I would be delighted to accept your application, ___ you should have come in early for it to be valid.

Total number of terms in the expansion of (1-x-x^2)^5 is ________

Show that (1+|a|^2) (1+|b|^2)=|1-a.b|^2+|a+b+a×b|^2 . For any 2 vectors a and b

${\int }_1^{a}x.a^{-\left[lo{g}_{a}x\right]}dx=\frac{e-1}{2},\text{where}a>1\text{and}[.]$ denotes the greatest integer function, then the value of $a^2$is

Solution to the differential equation $\frac{x+\frac{x^3}{3!}+\frac{x^5}{5!}+.......}{1+\frac{x^2}{2}+\frac{x^4}{4!}+......}=\frac{dx-dy}{dx+dy}$ is

Solution of $|x||x+1|=2$ is

The result of $21$ football matches (win,lose,draw) are to be predicted. The number of different forecasts that can contain $19$ wins is

Y= x-[x] defined for N>N

Is this function one,one or onto or both????

Identify the function from the description given.

1. Its an irrational function

2. Its graph is mirror image of y =$x^{2n}$ about y = x, for some n $\ge$ 1, n $\in$ I and x $\ge$ 0

3. x $\le$ f(x) $\le$ $x^{1/6}$ if x $\in$ [0, 1]

4. Its domain and range are [0, $\infty$)

If cos A= mcos B and cot$\frac{(A+B)}{2}=\lambda tan\left(\frac{B-A}{2}\right)$ and $\lambda$ is

Order and degree of differential equation are

[MP PET 1996]

If P $\equiv$ (0,1,0), Q $\equiv$ (0,0,1), then projection of PQ on the plane x+ y + z = 3 is
[EAMCET 2002]

Given that $tanA,tanB$ are the roots of the equation $x^2-px+q=0$, then the value of $si{n}^2(A+B)$ is

A single letter is selected at random from the word ‘PROBABILITY’. The probability that it is a vowel is

R = { (T1 , T2) : T1 , T2 ϵ A and T1 is congruent to T2} Then the relation R is______

Let $f\left(x\right)={\int }_0^1|t-x|tdt$ for all real x. Then the minimum value of f(x) is

A die is thrown twice. What is the probability that at least one of the two throws come up with the number 3?