Explore topic-wise InterviewSolutions in Current Affairs.

The number of four-letter words that can be formed with letters $a,b,c$ such that all three letters occur is

The value of limit n tends to infinity ((1.5)ⁿ + {(1+0.0001)¹⁰⁰⁰⁰}ⁿ)^1/n

^{{} denotes Greatest Integer function is?}

^{Options: A.1 B.1/2 C.Does not exist D.2}

If $z$ is a point on the circle $|z–1|=1,$ then $argz=$

The solution set of the inequality ${\log }_3(x+2)(x+4)+{\log }_{1/3}(x+2)<\frac{1}{2}{\log }_{\sqrt{3}}7$ is

The prefix used for 10^-18 is:

There was a survey in a city about number of people reading newspaper A, B and C. there are 42% of people read newspaper A; 51% of people read newspaper B and 68% of people read paper C. 30% of people read both newspaper A and B. 28% reads B and C and 36% read C and A. 8% do not read any newspaper. Find the percentage of people read all the three newspaper.

The least value of $\alpha \in R$ for which $4\alpha x^2+\frac{1}{x}\ge 1,\text{for all}x>0$, is:

Coefficient of $t^{24}$ in $(1+t^2{)}^{12}(1+t^{12}\left)\right(1+t^{24})$ is

A line l passing through the origin is perpendicular to the lines
$l_1:(3+t)\hat{i}+(-1+2t)\hat{j}+(4+2t)\hat{k},-\infty <t<\infty l_2:(3+2s)\hat{i}+(3+2s)\hat{j}+(2+s)\hat{k},-\infty <s<\infty$
Then, the coordinate(s) of the point(s) on $l_2$ at a distance of $\sqrt{17}$ from the point of intersection of l and $l_1$ is (are)

If the normal’s at $(x_i,y_i)$ where $i=1,2,3,4$ to the rectangular hyperbola $xy=2$ meet at the point (3, 4), then

Vertex of the parabola $x^2+4x+2y-7=0$ is

Solve the system of equations.

$\frac{2}{x}+\frac{3}{y}+\frac{10}{z}=4;\frac{4}{x}-\frac{6}{y}+\frac{5}{z}=1$ and $\frac{6}{x}+\frac{9}{y}-\frac{20}{z}=2$

For the straight lines 4x + 3y – 6 = 0 and 5x + 12y + 9 = 0, the equation of the bisector of the angle which contains the origin is

Write the coordinates of the orthocentre of the triangle formed by the lines xy=0 and x+y=1.

Let X = {1,2,3,…,50}. A subset A of X is chosen at random. The set X reconstructed by replacing the elements of A, and another set B of X is chosen at random. The probability that A B contains exactly 5 elements is

If x is positive, the first negative term in the expansion of ${(1+x)}^{\frac{27}{5}}$

Show that the function given by $f\left(x\right)=sinx$ is

strictly decreasing in $(\frac{\pi }{2},\pi )$

The area (in sq. units) of the region bounded by the parabola, $y=x^2+2$ and the lines $y=x+1,x=0$ and $x=3,$ is:

The solution set of $x^3-10x^2+21x>0$ is

The number of ways of choosing $10$ objects out of $31$ objects of which $10$ are identical and the remaining $21$ are distinct, is

Let n ³ 3 .A list of numbersx_1, x₂,.........x_n has mean m and standard deviation s . A new list of numbers y₁, y₂,..........y_n is made as follows : and y_j = x for j = 3,4,.......n . The mean and the standard deviation of the list are. Then which of the following is necessarily true?

Prove that $7+77+777+......+777\underset{n-digits}{.............}7=\frac{7}{81}({10}^{n+1}-9n-10)$

Prove that $1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+.....+\frac{1}{n^2}<2-\frac{1}{2}$ for all $n>2$, n $ϵ$ N.

The direction ratios of two lines AB,AC are 1, -1, -1 and 2, -1,1. The direction ratios of the normal to the plane ABC are

In a triangle $ABC\angle A={60}^{\circ },\angle B={40}^{\circ }$ and $\angle C={80}^{\circ }$ If P is the centre of the circumcircle of triangle $ABC$ with radius unity, then the radius of the circumcircle of triangle $BPC$ is

The two curves $x^3-3x{y}^2+2=0$ and $3x^{2}y-y^3=2$

If two adjacent sides of a cyclic quadrilateral are $2$ and $5$ and the angle between them is ${60}^{\circ }$. If the third side is $3$, then the remaining fourth side is

How many ways are there to arrange the letters in the WORD “GARDEN ” with the vowels in alphabetical order ?

If $\overrightarrow{x}$ is a vector in the direction of $(2,-2,1)$ of magnitude $6$ and $\overrightarrow{y}$ is a vector in the direction of $(1,1,-1)$ of magnitude $\sqrt{3}$, then $|\overrightarrow{x}+2\overrightarrow{y}|$ is equal to

${lim}_{x\to \pi }\frac{\sqrt{2+cosx}-1}{(\pi -x{)}^2}$

For the given table choose the correct option
$\begin{array}{cccc}& & & \\ & \text{Column I}& & \text{Column II}\\ \left(a\right)& \text{The value of}\cot \left(\frac{41\pi }{4}\right)\text{is}& \left(p\right)& 1\\ \left(b\right)& \text{The value of}\sec (-{600}^{\circ })\text{is}& \left(q\right)& 2\\ \left(c\right)& \text{The value of}{\text{cosec}}^2\left(\frac{41\pi }{4}\right)\text{is}& \left(r\right)& -2\\ \left(d\right)& \text{The value of}\tan \left(\frac{19\pi }{4}\right)\text{is}& \left(s\right)& -1\end{array}$

$a^2(co{s}^{2}B-co{s}^{2}C)+b^2(co{s}^{2}C-co{s}^{2}A)+c^2(co{s}^{2}A-co{s}^{2}B)=0$

By giving a counter example, show that the following statement is not true.

p : " If all the angles of a triangle are equal then the triangle is an obtuse angled triangle "

The least value of $f\left(x\right)=|x-a|+|x-b|+|x-c|+|x-d|$, where $a<b<c<d$ are fixed real numbers, is

The maximum possible area bounded by the parabola $y=x^2+x+10$ and a chord of the parabola of length $1$ is.

The general solution of $8\cos x\cdot \cos 2x\cdot \cos 4x=\frac{\sin 6x}{\sin x}$ is

\(\text {ABC is an isosceles triangle inscribed in a circle of radius r. If AB = AC and h is the altitude from A to BC, then the triangle has area A is equal to

the set values of'a 'for which the $f\left(x\right)=a{x}^2+2x(1-a)-4$ is negative for exactly three integral value of $x$, is

Let $z=x+iy$ be a complex number such that $|z|=1$, where $i=\sqrt{-1}$. Match List - I with List - II.

$\begin{array}{cccc}\text{List-I}& & \text{List - II}& \\ \text{(I)}& \text{Re}\left(\frac{iz}{1+z^2}\right)\text{is equal to}& \text{(P)}& 0\\ \text{(II)}& \text{Im}\left(\frac{iz}{1+z^2}\right)\text{can be equal to}& \text{(Q)}& 1\\ \text{(III)}& \text{Number of integers NOT in the}& \text{(R)}& \frac{1}{2}\\ & \text{range of}\text{Im}\left(\frac{iz}{1+z^2}\right)\text{is equal to}& & \\ \text{(IV)}& \frac{1}{2\pi }\arg \left(\frac{iz}{1+z^2}\right)\text{is equal to}& \text{(S)}& -\frac{1}{2}\\ & (\text{where}-\pi <\arg (z)\le \pi )& & \\ & & \text{(T)}& -\frac{1}{4}\\ & & \text{(U)}& \frac{1}{4}\end{array}$

Which of the following is only CORRECT combination?