Explore topic-wise InterviewSolutions in Current Affairs.

Let A = {$\varphi$ {$\varphi$}, 1, {1, $\varphi$}, 2}. Which of the following are true ?

(i) $\varphi ϵA$ (ii) {$\varphi$} $ϵ$ A

(iii) {1} $ϵ$ A (iv) {2, $\varphi$} $\subset$ A

(v) 2 $\subset$ A (vi) {2, {1}} $⊈$ A

(vii) {{2}, {1}}, $⊈$ A

(viii) { $\varphi$, {$\varphi$} , {1, $\varphi$}} $\subset$ A

(ix) {{ $\varphi$}} $\subset$ A.

The locus of a point which divides the line segment joining the point $(0,-1)$ and a point on the parabola, $x^2=4y$, internally in the ratio $1:2$, is:

There are $8$ events that can be scheduled in a week. Then total number of ways that these $8$ events are scheduled on exactly $6$ days of a week is given by $266\times k!,$ where $k\in N.$ The value of $k$ is

The number of solutions of ${\cos }^{2}x+\frac{\sqrt{3}+1}{2}\sin x-\frac{\sqrt{3}}{4}-1=0$, where $x\in [-\pi ,\pi ]$ is

The value of expression
$3(1!)-4(2!)+5(3!)-6(4!)+.....-2008(2006!)+(2007!)$ is

Which of the following is "CORRECT" option?

$$\begin{array}{cc}\text{List I}& \text{List II}\\ \text{(a) The coordinates of a point on the line}& \\ x=4y+5,z=3y-6\text{at a distance}3\text{from}& \\ \text{the point}(5,3,-6)\text{is/are}& \text{(p)}(-1,-2,0)\\ \text{(b) The plane containing the lines}& \\ \frac{x-2}{3}=\frac{y+3}{5}=\frac{z+5}{7}& \\ \text{and parallel to}\hat{i}+4\hat{j}+7\hat{k}\text{has}& \\ & \text{(q)}(5,0,-6)\\ \text{(c) A line passes through two points}A(2,-3-,1)& \\ \text{and}B(8,-1,2)\text{. The coordinates of a point}& \\ \text{on this line farthest to the origin and at a}& \\ \text{distance of}14\text{units from}A\text{is}& \text{(r)}(2,5,7)\\ \text{(d) The coordinates of the foot of the perpendicular}& \\ \text{from the point}(3,-1,11)\text{on the line}& \\ \frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}\text{is/are}& \text{(s)}(14,1,5)\end{array}$$

The value of $\sqrt{\frac{1+\sin A}{1-\sin A}}$ where $A\in [0,2\pi ]-\left\{\frac{\pi }{2}\right\}$ is

Let $f\left(x\right)=x,g\left(x\right)=\frac{1}{x}$ and $h\left(x\right)=f\left(x\right)g\left(x\right)$. Then, $h\left(x\right)=1$ for

The value of $\sum _{n=1}^{100}\underset{n-1}{\overset{n}{\int }}{e}^{x-\left[x\right]}dx,$ where $\left[x\right]$ is the greatest integer $\le x,$ is :

The equation of a line parallel to the line $3x+4y=0$ and touching the circle $x^2+y^2=9$ in the first quadrant is

The polar coordinates of the point whose Cartesian coordinates are $(-\frac{1}{\sqrt{2}},\sqrt{2})$, are

Let $A=\left(\begin{array}{ccc}3-t& 1& 0\\ 1& 3-t& 1\\ 0& -1& 0\end{array}\right)$ and det $A=5$ , then

If $f\left(x\right)=64x^3+\frac{1}{x^3}$ and $\alpha ,\beta$ are the roots of $4x+\frac{1}{x}=3$. Then,

Write the set of all vowels in the English alphabet which precede q.

A chord $ax+y=1$ subtends ${90}^{\circ }$ at the center of the circle $x^2+y^2=\frac{3}{2}.$ Then the value of $a$ is

$\text{In a triangle ABC, the sides b and c are the roots of the equation}{x}^2-61x+820=0\text{and}A=ta{n}^{-1}\frac{4}{3}\text{then}{a}^2\text{is equal to}$

$\frac{d}{dx}\left[log\left(\sqrt{\frac{1-cosx}{1+cosx}}\right)\right]=$

Solve the following system of linear equations, using matrix method

$2x+y+z=1,x-2y-z=\frac{3}{2},3y-5x=9$

If $(co{t}^{-1}x{)}^2–3(co{t}^{-1}x)+2>0$, then x lies in

Find the approximate value of $(1.999{)}^5$

The equation of two equal sides $AB$ and $AC$ of isosceles triangle $ABC$ are $x+y=5$ and $7x-y=3$, respectively. Then the equation of the side $BC$ if are of $△ABC=5{\text{unit}}^2$, is/are

A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.

$A=\left[\begin{array}{ccc}1& 2& -3\\ 5& 0& 2\\ 1& -1& 1\end{array}\right],B=\left[\begin{array}{ccc}3& -1& 2\\ 4& 2& 5\\ 2& 0& 3\end{array}\right],C=\left[\begin{array}{ccc}4& 1& 2\\ 0& 3& 2\\ 1& -2& 3\end{array}\right]$ compute (A+B) and (B-C). Also verify that A+(B-C)=(A+B)-C.

Let $\overrightarrow{a}=4\hat{i}+5\hat{j}-\hat{k},\overrightarrow{b}=\hat{i}-4\hat{j}+5\hat{k},$ and $\overrightarrow{c}=3\hat{i}+\hat{j}-\hat{k}$. Find a vector $\overrightarrow{d}$ which is perpendicular to both $\overrightarrow{c}$ and $\overrightarrow{b}$ and $\overrightarrow{d}$.$\overrightarrow{a}=21$.

Let A ={1,2,3},B={4,5,6,7} and let f={(1,4),(2,5),(3,6)} be a function from A to B. Show that f is one-one.

Which among the functions are continuous throughout its domain?

$S_n=\sum log\frac{(n-1)}{(n-2)}(n>2),thenthevalueof{S}_{19}$

The normal form of the line $\frac{x}{2}+\frac{y}{3}=2$ is

If the equation $|x+1|+|x-3|=k$ has exactly two solution then $k$ lies in

If $\sum _{r=1}^n{t}_r=\sum _{k=1}^n\sum _{j=1}^k\sum _{i=1}^j\left(2\right)$, then $\sum _{r=1}^n{\frac{1}{t}}_r$ is

In a survey it was found that, the number of people who like only What’s app, only Facebook, both What’s app and Facebook and neither of them are $2n,3n,\frac{69}{n},\frac{69}{3n}$
respectively. What is the number of people who like facebook?

Minimum value of $Z=x-5y+20$ under the given conditions
$$x-y\ge 0-x+2y\ge 2x\ge 3,y\le 4x,y\ge 0$$
is

The point on the curve $y^2=x$ where the tangent makes an angle of $\frac{\pi }{4}$ with $X$-axis is

If $f\left(x\right)=3x-2$ and $(gof{)}^{-1}=x-2$, then $\int g\left(x\right)dx$ is (where $C$ is constant of integration)

The solution set of the equation ${\log }_{x}3{\log }_{3x}3={\log }_{9x}3$ is similar to which of the following options :

Determine whether the relation R defined on the set R of all real numbers as R = {(a, b) ; a, b $ϵ$ R and a-b + $\sqrt{3}ϵ$ S, where S is the set of all irrational numbers}, is reflexive, symmetric and transitive.

OR

Let A = $R\times R$ and $\ast$ be the binary operation on A defined by (a,b) $\ast$ (c, d) - (a + c, b + d).

Prove that $\ast$ is commutative and associative. Find the identity element for $\ast$ on A. Also write the inverse element of the element (3, -5) in A.

The locus of center of the circle which cuts the circles $x^2+y^2+2g_{1}x+2f_{1}y+c_1=0$ and $x^2+y^2+2g_{2}x+2f_{2}y+c_2=0$ orthogonally is

Differentiate the given functions w.r.t. x.

${(x+\frac{1}{x})}^x+x^{(1+\frac{1}{x})}$