Explore topic-wise InterviewSolutions in Current Affairs.

If a, b, c are positive numbers such that a>b>c and the equation $(a+b-2c)x^2+(b+c-2a)x+(c+a-2b)=0$ has a root in the interval (-1, 0), then

The range of the functions $f\left(x\right)={\int }_1^x|t|dt,xϵ[\frac{-1}{2},\frac{1}{2}]$ is

A value of b for which the equations $x^2+bx-1=0,x^2+x+b=0$ have one root in common is

The expression $\frac{36}{4\sin (x+\frac{\pi }{3})-4\sqrt{3}\cos x+8}$ lies in the interval

If $\theta ϵ[\frac{-\pi }{2},\frac{3\pi }{2}]$, then the probability that $cos\theta >sin\theta$ is

If one root of $5x^2+13x+k=0$ is reciprocal of the other, then k=

Let $y=g\left(x\right)$ be the inverse of a bijective mapping $f:R\to R,f\left(x\right)=3x^3+2x.$ The area bounded by the graph of $g\left(x\right),$ x-axis and the ordinate at $x=5$ is

The value of the expression $\frac{1}{cos{290}^{\circ }}+\frac{1}{\sqrt{3}sin{250}^{\circ }}$ is equal to

If x,y, z are non-zero real numbers, then the inverse of matrix

$A=\left[\begin{array}{ccc}x& 0& 0\\ 0& y& 0\\ 0& 0& z\end{array}\right]$ is

a) $\left[\begin{array}{ccc}{x}^{-1}& 0& 0\\ 0& y^{-1}& 0\\ 0& 0& z^{-1}\end{array}\right]$

b) $xyz\left[\begin{array}{ccc}{x}^{-1}& 0& 0\\ 0& y^{-1}& 0\\ 0& 0& z^{-1}\end{array}\right]$

c) $\frac{1}{xyz}\left[\begin{array}{ccc}x& 0& 0\\ 0& y& 0\\ 0& 0& z\end{array}\right]$

d) $\frac{1}{xyz}\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$

In a box of 10 electric bulbs, two are defective. Two bulbs are selected at random one after the other from the box. The first bulb after selection being put back in the box before making the second selection. The probability that both the bulbs are without defect is

[MP PET 1987]

The volume occupied by 2 mol of $N_2$ at 200 K and 10.1325 MPa pressure is

(Given that $\frac{P_c{V}_C}{R{T}_C}=\frac{3}{8}$ and $\frac{P_r{V}_r}{T_r}=2.21$ ), where $P_r,V_r$ and $T_r$ are reduced pressure, reduced volume and reduced temperature.

Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}, the relation R is

Two mole of ideal diatomic gas $(C_{v,m}=\frac{5}{2}R)$ at 300 K and 5 atm expanded irreversly and adiabatically to a final pressure of 2 atm against a constant pressure of 1 atm. Calculate q, w, $\Delta H$ and $\Delta U.$

Calculate the standard deviation for the following data :

$\begin{array}{cccccccc}Class:& 0-30& 30-60& 60-90& 90-120& 120-150& 150-180& 180-210\\ Frequency:& 9& 17& 43& 82& 81& 44& 24\end{array}$

${lim}_{x\to 1}\frac{x-1}{\sqrt{x^2+3}-2}$

The vector equation of the plane passing through the line $\overrightarrow{r}=\overrightarrow{a}+\lambda \overrightarrow{b}$ and parallel to the line $\overrightarrow{r}=\overrightarrow{c}+\mu \overrightarrow{d}$is

If $sin\alpha =\frac{4}{5}\text{and}cos\beta =\frac{5}{13}$, prove that $cos\frac{\alpha -\beta }{2}=\frac{8}{\sqrt{65}}$

Let $A,B\text{and}C$ be three events, which are pair-wise independent and $\overline{E}$ denotes the complement of an event $E$. If $P(A\cap B\cap C)=0$, then $P\left[\right(\overline{A}\cap \overline{B}\left)|C\right]$ is equal to:

Let $f\left(x\right)$ be a polynomial of degree $4$ having extreme values at $x=1$ and $x=2$. If $\underset{x\to 0}{lim}(\frac{f\left(x\right)}{x^2}+1)=3$ then $f(-1)$ is equal to :

Domain of $f\left(x\right)=si{n}^{-1}\left(\frac{2x-\left[x\right]}{\left[x\right]}\right)$ , where $[\cdot ]$ denotes the greatest integer function, is

The value(s) of $p$ for which the quadratic equation $2x^2+px+8=0$ has equal roots is/are

Find the value of $\cos \left(1.74\right)$ from the table
$\begin{array}{cccccc}x:& 1.7& 1.74& 1.78& 1.82& 1.86\\ \sin x:& 0.9916& 0.9857& 0.9781& 0.9691& 0.9584\end{array}$

An equation of the curve in which subnormal varies as the square of the ordinate is (k is constant of proportionality)

If $z=3+2i$, then value of $3z^3-13z^2+9z+65$ is

Find the term independent of $x$ in the expansion of $(1+x+2x^3){(\frac{3x^2}{2}-\frac{1}{3x})}^9$

If $x^2+y^2=1$, then

If the function f (x) = x² - 8x + 12 satisfies the condition of Rolle's Theorem on (2, 6), find the value of c such that f '(c) = 0

An urn contains marbles of four colours : red, white, blue and green. When four marbles are drawn without
replacement, the following events are equally likely :
(1) the selection of four red marbles;
(2) the selection of one white and three red marbles;
(3) the selection of one white, one blue and two red marbles;
(4) the selection of one marble of each colour.
The smallest total number of marbles satisfying the given condition is

If $l(m,n)={\int }_0^1{t}^m(1+t{)}^{n}dt$, then the expression for $l(m,n)$ in terms of $l(m+1,n-1)$ is

If the chord of contact of tangents from 3 points A,B,C to the Circle $x^2+y^2=a^2$ are concurrent, then A,B,C will be

The angle between the lines 3x + 2y + z = 0 = x + y – 2z and 2x – y – z = 0 = 7x + 10y – 8z is :

${lim}_{x\to a}{\left\{\frac{\sin x}{\sin a}\right\}}^{\frac{1}{x-a}}$

${lim}_{x\to \frac{\pi }{4}}\frac{1-tanx}{1-\sqrt{2}sinx}$

If n geometric means between a and b be $G_1,G_2,....G_n$ and a geometric mean of a and b be G, then the true relation is

A and B toss a coin alternatively, the first to show a head being the winner. If A starts the game, the chance of his winning is [MP PET 1987]

A farmer is testing a new piece of equipment he has for determining whether an animal is a cow or a sheep. If a cow walks through the machine, $90\%$ of the time it says it is a cow and $10\%$ of the time it says it is a sheep. If a sheep walks through the machine, $95\%$ of the time it says it is a sheep and $5\%$ of the time it says it is a cow. The farmer has 5 cows and 36 sheep. If an animal walks through and the machine claims it is a cow, the probability that it actually is a cow is?

The number of ways in which the letters of the word 'Constant' can be arranged without changing the relative positions of the vowels and consonants is

The value of $\underset{n\to \infty }{lim}\frac{1}{n^2}\{{\sin }^2\frac{\pi }{4n}+2{\sin }^2\frac{2\pi }{4n}+\cdots +n{\sin }^2\frac{4\pi }{4n}\}$ is

A student obtained the mean and standard deviation of 100 observations as 40 and 5.1 respectively. It was late found that one observation was wrongly copied as 50, the correct figure being 40. Find the correct mean and S. D.

TanA and tanB are the roots of $x^2-5x+\frac{1}{2}$=0 . Find the value of tan (A+B)

If $\theta$ denote the acute angle between the line
$\overrightarrow{r}=(\hat{i}+2\hat{j}-\hat{k})+\lambda (\hat{i}-\hat{j}+\hat{k})$ and the plane $\overrightarrow{r}.(2\hat{i}-\hat{j}+\hat{k})=4$, then $\sin \theta +\sqrt{2}\cos \theta =$

The line $x=y$ touches a circle at the point $(1,1).$ If the circle also passes through the point $(1,-3),$ then its radius(in units) is :