Explore topic-wise InterviewSolutions in Current Affairs.

If a, b $\in$ R distinct numbers satisfying $|a-1|+|b-1|=|a|+|b|=|a+1|+|b+1|$, then the minimum value of $|a-b|$ is

The number of ways can $4$ men, $3$ boys, $2$ women be seated in a row so that the men, the boys and the women are not seperated is

The points (3, 9), (4, 8) and (5, 7) are

An expert burglar has 8 master keys to open several new houses of a mansion.Only one master key will open a given house.If $40\%$ of these houses remain unlocked the probability that the burglar will break open the treasury house on selecting 3 master keys at random is?

${lim}_{x\to 1}\frac{x^{15}-1}{x^{10}-1}$

The foci of the hyperbola are $S(5,6),S^{\prime }(-3,-2)$. If its eccentricity is $2$, then the equation of its directrix corresponding to focus $S$ is

The sets of real values of x for which
$lo{g}_{2x+3}{x}^2<lo{g}_{2x+3}(2x+3)$
includes

Let * be an operation on Z be defined on Z as a* b = a^b for all a,b ϵ Z. Then which one of these options is correct?

The sum of the series $S=1+2\left(\frac{10}{11}\right)+3{\left(\frac{10}{11}\right)}^2+\cdots \text{upto}\infty$ is equal to

Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys.

$\text{Find what the following equations become when the origin is shifted to the point(1,1)}?\left(i\right)x^2+xy-3y^2-y+2=0\left(ii\right)xy-y^2-x+y=0\left(iii\right)xy-x-y+1=0\left(iv\right)x^2-y^2-2x+2y=0$

If $\alpha ,\beta and\gamma$ are the roots of the equation $x^3+2x^2+3x+1=0$ . Find the equation whose roots are ${\alpha }^3$, ${\beta }^3$ and ${\gamma }^3$.

Find the sum of the terms of an infinity decreasing G.P. in which all the terms are positive, the first term is 4, and the difference between the third and fifth term is equal to $\frac{32}{81}$.

If the lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to a circle, then find the radius of the circle.

If $f\left(x\right)=\left(lo{g}_{cotx}tanx\right)(lo{g}_{tanx}cotx{)}^{-1}+ta{n}^{-1}(\frac{x}{\sqrt{4-x^2}})$ , then f’(0) is equal to

If $A=\{5,6,7\},B=\{1,2,3,4\}$, then number of elements in set $(A-B)\times B$ is

$x_1,x_2$ are the roots of $x^2-3x+a=0$ and $x_3,x_4$ are the roots of $x^2-12x+b=0.$ If $x_1,x_2,x_3,x_4$ form an increasing G.P. then ordered pair (a,b) is :

If $\alpha$ is a repeated root of $a{x}^2+bx+c=0$ then $\underset{x\to \alpha }{lim}\frac{\sin (a{x}^2+bx+c)}{(x-\alpha {)}^2}$ is

Let $f\left(n\right)=\left|\begin{array}{ccc}n& n+1& n+2\\ {}^n{P}_n& {}^{n+1}{P}_{n+1}& {}^{n+1}{P}_{n+2}\\ {}^n{C}_n& {}^{n+1}{C}_{n+1}& {}^{n+1}{C}_{n+2}\end{array}\right|$
Then, f(n) is divisible by

The points (0, 0), (a, 0) and $(\frac{a}{2},\frac{a\sqrt{3}}{2})$ are vertices of

The number of words that can be formed by using the letters of the word $MATHEMATICS$ that start as well as end with $T$ are

The set of values of x which satisfy 5x + 2 < 3x + 8 and $\frac{x+2}{x-1}$ < 4 , is

A straight line joining the points $(1,1,1)$ and $(0,0,0)$ intersects the plane $2x+2y+z=10$ at

The probability that a student will pass the final examination in both

English and Hindi is 0.5 and the probability of passing neither is 0.1. If the

probability of passing the English examination is 0.75. What is the

probability of passing the Hindi examination ?

If either a = 0 or b = 0, then a.b = 0. But the converse need not to be true. Justify your answer with an example.

Prove that the product of the lengths of the perpendiculars drawn from the points $(\sqrt{(a^2-b^2},0)$ and $(-\sqrt{(a^2-b^2},0)$ to the line
$\frac{x}{a}cos\theta +\frac{y}{b}sin\theta =1$ is $b^2$

for $x>1$, If $(2x{)}^{2y}=4e^{2x-2y}$, then
$(1+{\log }_{e}2x{)}^2\frac{dy}{dx}$ is equal to :

$cos{6}^{\circ }cos{42}^{\circ }cos{66}^{\circ }cos{78}^{\circ }=\frac{1}{16}$

A plane passes through the points P (1,1,1) , Q (3, -1, 2) and R (-3, 5 , -4). The equation of the plane is .

If the line $y-\sqrt{3}x+3=0$ cuts the parabola $y^2=x+2$ at A and B, then PA. PB is equal to (where $P\equiv (\sqrt{3},0)$

If $A_1,A_2,.....,A_n$ are n independent events such that $P\left(A_i\right)=\frac{1}{i+1},i=1,2,....,n$. The probability that none of $A_1,A_2,....A_n$ occurs is

If $X=\{1,2,3,4,5\},Y=\{1,3,5,7,9\},$ then which among the following is not a relation from $X$ to $Y$

If $A=\{y:y={\log }_2|x-2|,x<5,x\text{is a whole number}\},B=\{y:y=|x-2|,x\in [0,1],y\in N\},C=\{1,3,5\}$
, then $n\left(\right(A\times B)\cap (B\times C\left)\right)$ is

Which of the following represents identity function?

Let $\overrightarrow{A}=2\hat{i}+3\hat{j}-\hat{k}$ and $\overrightarrow{B}=\hat{i}-\hat{j}$, then component of $\overrightarrow{A}$ perpendicular to $\overrightarrow{B}$ is

Write the value of ${lim}_{x\to 0}\frac{sinx}{\sqrt{1+x-1}}.$

Find the equations of two straight lines passing through (1, 2) and making an angle of ${60}^{\circ }$ with the line $x+y=0$. Find also the area of the triangle formed by the three lines.

If $a,b$ and $c$ are non-zero numbers, then the value of the determinant, $D=\left|\begin{array}{ccc}{b}^2{c}^2& bc& b+c\\ c^2{a}^2& ca& c+a\\ a^2{b}^2& ab& a+b\end{array}\right|$ is

A discrete random variable x has following probability distribution

$x:11234567P\left(x\right):k2k2k3k{k}^{2}2k^{2}7k^2+k$

Then k=

If a is a non-zero vector of magnitude a and $\lambda$ is a non-zero scalar, then $\lambda$ a is unit vector if

a) $\lambda =1$

b) $\lambda =-1$

c) $a=|\lambda |$

d) $a=\frac{1}{|\lambda |}$

${lim}_{n\to \infty }[\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}+\cdots +\frac{1}{2n}]=$ [Karnataka CET 1999]

Write the negation of each of the following statement :

(i) For every $xϵN,x+3<10$

(ii) There exists $xϵN,x+3=10$