Explore topic-wise InterviewSolutions in Current Affairs.

Hydrogen rarely occurs in the free state because

The number of unordered pairs $(A,B)$ of subsets of the sets $S=\{1,2,3,4,5,6\}$ such that $A\cap B=\varphi$ and $A\cup B=S$ is

If $\sqrt{\frac{x^2-4x+3}{x^2-3x+2}}\le 1,$ then the interval(s) in which $x$ can not lie, is/are

If f(xy) = f(x)+f(y), and f(e) = 1, then find the value of $f\left(e^2\right)$

$\frac{3x-2}{5}\le \frac{4x-3}{2}$

Show that the four points A(4, 5, 1), B(0, -1, -1), C(3, 9, 4) and D(-4, 4, 4) are coplanar.

If $Z^2+kZ+1-2i=0$ has roots as $z_1$ and $z_2$, where $z_1=-i$ and $k\in R$, then the value of $k$ is

Question 91

A picture hall has seats for 820 persons. At a recent film show, one usher guessed it was $\frac{3}{4}$ full, another that it was $\frac{2}{3}$ full. The ticket office reported 648 sales. Which usher (first or second ) made the better guess?

Evaluate $\underset{x\to 0}{lim}\left(\frac{sin2x+sin6x}{sin5x-sin3x}\right)$

Select the correct structure of the sentence.

N = noun phrase; V = verb phrase; Adj = adjective phrase; p = prepositional phrase

The crowd dispersed.

Column 1 has the condition on circle and column 2 has the equation of circles.which one of them are matched correct?

Column 1 column 2

1) Centre of origin and radius = 10 P) $(x-8)(x+8)+(y-6)(y+6)=0$

2) Extremeties of diameter are (8,6) and (-8,-6) Q) $(x-6)(x+6)+(y-8)(y+8)=0$

3) Centre is (1,-2) and radius is 4 R) $x^2+y^2-2x+4y-11=0$

The vertices of a hyperbola are at $(0,0)$ and $(10,0)$ and one of its foci is at $(18,0)$. The equation of the hyperbola is

The sum of the series sin$\theta$.sec3$\theta$ + sin3$\theta$.$sec{3}^2$$\theta$ + $sin{3}^2$$\theta$.sec$3^3$$\theta$ + ...........n terms is

What is a locus? Explain elaborately

A differentiable function f(x) will have a local minimum at x = b if -

If $\alpha ,\beta$ are the real and distinct roots of $x^2$ + px + q = 0 and ${\alpha }^4,{\beta }^4$ are the roots of $x^2-rx+5=0$, then the equation $x^2-4qx+2a^2-r=0$ has always

Find the value of $\lambda$ if $\lambda$ $x^2$ + ( ${\lambda }^2$ - $\lambda$) x + 1 = 0 is an identity.

cos 10 cos 30 cos 50 cos 70 =

The volume of a sphere is increasing at a rate of $3$ cubic centimetres per second. How fast is the surface area increasing when the radius is $2$ centimetres ?

${\sum }_{r=1}^{16}\sqrt{1+cos4r}=$

A fair dice is rolled. If the number turned out is odd what is the probability that it is a prime number?

For $r=0,1,...,10$, let $A_r,B_r,$ and $C_r$ denote, respctively, the coefficient of $x^r$ in the expansions of $(1+x{)}^{10},(1+x{)}^{20}$ and $(1+x{)}^{30}$. Then ${\sum }_{r=1}^{10}{A}_r(B_{10}{B}_r-C_{10}{A}_r)$is equal to

cosA - cos3A=

A card is drawn from a deck of 52 cards. Find the probability of getting an ace or a spade card.

The product of r consecutive positive integers is divisible by

$Iff\left(x\right)+2f\left(\frac{1}{x}\right)=3x,x\ne 0,andS=\{xϵR:f(x)=f(-x\left)\right\};thenS:$

An ellipse whose axis is along $x$ axis and centre at origin. If the distance between focii is equal to length of minor axis, then the eccentricity of the ellipse is

Let A and B be two sets in the same universal set. Then, A- B =

If a variable plane forms a tetrahedron of constant volume $64k^3$ with the co-ordinate planes, then the locus of the centroid of the tetrahedron is

$\text{In any}\Delta ABC,\text{prove that :}asin\frac{A}{2}sin\left(\frac{B-C}{2}\right)+bsin\frac{B}{2}sin\left(\frac{C-A}{2}\right)+csin\frac{C}{2}sin\left(\frac{A-B}{2}\right)=0.$

Prove that the tetrahedron with vertices at the point O(0, 0, 0), A(0, 1, 1), B(1, 0, 1) and C(1, 1, 0) is a regular one.

Show that the relation R in the set R of real numbers defined as $R=\left\{\right(a,b):a\le b^2\}$ is neither reflexive nor symmetric nor transitive.

Find the separate equations of pair of straight lines $y^2-9xy+10x^2=0$

$1\times 1!+2\times 2!+3\times 3!+.....+n\times n!=(n+1)!-1$ for all N $ϵ$ N.

The intercepts on $x$-axis made by tangents to curve, $y=\underset{0}{\overset{x}{\int }}|t|dt,x\in R$, which are parallel to the line $y=2x$, are equal to:

$\text{If}\pi <\theta <2\pi andz=1+cos\theta +isin\theta ,\text{then write the value of}|z|$

Let $a_0=\frac{5}{2}$ and $a_k=a_{k-1}^2-2fork\ge 1,$ then the value of $\stackrel{\infty }{\underset{k=0}{\Pi }}(1-\frac{1}{a_k})$ is

${lim}_{x\to 27}\frac{(x^{\frac{1}{3}}+3)(x^{\frac{1}{3}}-3)}{x-27}$

If x, y and z are all different from zero and $\left|\begin{array}{ccc}1+x& 1& 1\\ 1& 1+y& 1\\ 1& 1& 1+z\end{array}\right|=0$,

then the value of $x^{-1}+y^{-1}+z^{-1}$ is

(a) $xyz$
(b) $x^{-1}{y}^{-1}{z}^{-1}$
(c) $-x-y-z$
(d) $-1$