Explore topic-wise InterviewSolutions in Current Affairs.

If $S_n=\sum _{r=1}^n\frac{1}{\sqrt{4n^2-r^2}},$ then which of the following statement(s) is(are) correct ?

The angle between the straight lines, whose direction cosines are given by the equations $2l+2m-n=0$ and $mn+nl+lm=0,$ is

Consider the binary relation:

$S=\left\{\right(x,y)|y=x+1\text{and}x,yϵ\{0,1,2,\dots \dots \left\}\right\}$

The reflexive transitive closure of $S$ is

The two parabolas $y^2=4ax$ and $y^2=4c(x-b)$ cannot have a common normal, other than the axis unless, if

The general solution(s) of $\theta$ satisfying the equation ${\tan }^2\theta +\sec 2\theta =1$ can be (where $n\in Z$)

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are non-zero vectors such that $\overrightarrow{a}\cdot (\overrightarrow{b}+\overrightarrow{c})=\overrightarrow{c}\cdot (\overrightarrow{a}+\overrightarrow{b}),$ then which of the following can be true ?

If |x| < 1 then the coefficient of $x^n$ in the expansion

of $(1+x+x^2+.......{)}^2$ will be

The locus of the orthocentre of the triangle formed by the lines $(1+p)x-py+p(1+p)=0,$$(1+q)x-qy+q(1+q)=0$ and $y=0,$ where $p\ne q,$ is

The letters of the word "RANDOM" are arranged in all possible ways. The number of arrangements in which there are $2$ letters between 'R' and 'D' is

If the equation $si{n}^{-1}(x^2+x+1)+co{s}^{-1}(ax+1)=\frac{\pi }{2}$ has exactly two solutions, then a cannot have the integral value/s

The number of chords can be drawn through 21 points on the circle is

Consider the following system of equations :
$ax+by+cz=0az+bx+cy=0ay+bz+cx=0$
$\begin{array}{cccc}& \text{List - I}& & \text{List - II}\\ \text{(I)}& \text{If}a+b+c\ne 0\text{and}& \text{(P)}& \text{Planes meet only at one point}\\ & (a-b{)}^2+(b-c{)}^2+(c-a{)}^2=0.& & \\ \text{(II)}& \text{If}a+b+c=0\text{and}& \left(Q\right)& \text{Equations represent the line}x=y=z\\ & (a-b{)}^2+(b-c{)}^2+(c-a{)}^2\ne 0& & \\ \text{(III)}& \text{If}a+b+c\ne 0\text{and}& \text{(R)}& \text{Equations represent identical planes}\\ & (a-b{)}^2+(b-c{)}^2+(c-a{)}^2\ne 0& & \\ \text{(IV)}& \text{If}a+b+c=0\text{and}& \text{(S)}& \text{The solution of the system represents}\\ & (a-b{)}^2+(b-c{)}^2+(c-a{)}^2=0& & \text{whole of the three dimensional space}\end{array}$


Which of the following is the "INCORRECT" option?

A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is $‘a^{\prime }$, the closest approach between two atoms in a metallic crystal will be:

If the foot of perpendicular drawn from origin to a plane is $(1,2,-3),$ then the equation of the plane is

If $PQ$ is a normal chord of the parabola $y^2=4ax$ at $P(a{t}^2,2at).$ Then the axis of the parabola divides $\overline{PQ}$ in the ratio

Respected Sir,

Please help me in solving my below mentioned doubt,

If a + b + c = 0, then find one of the roots of quadratic equation ax² + bx + c = 0

The solution of the differential equation $\frac{dy}{dx}-\frac{y+3x}{{\log }_e(y+3x)}+3=0$ is

(where $c$ is a constant of integration)

The value of integral $\underset{0}{\overset{\infty }{\int }}\frac{z{e}^{-z}}{\sqrt{1-e^{-2z}}}dz$ is

[Hint:
multiply numerator and denominator by x^{n
− 1} and put xⁿ = t]

If $\Delta ABC$ is right angled at $A$, then the value of $r_2+r_3$ is:

If $\frac{3+2isin\theta }{1-2isin\theta }$ is a real number and 0 < $\theta <2<2\pi \text{then}\theta$

A plane meets the coordinate axes in A, B, C such that the centroid of the triangle ABC is the point (a, a, a).

Then the equation of the plane is x + y + z = p, where p is

If $\underset{0}{\overset{10}{\int }}f\left(x\right)dx=5$ and $\sum _{k=1}^{10}\underset{0}{\overset{1}{\int }}f(k-1+x)dx=R,$ then the value of $R$ is

The ratio in which the area enclosed by the curve $y=\cos x(0\le 0\le \frac{\pi }{2})$ in the first quadrant is divided by the curve $y=\sin x$, is:

A rectangle with sides 2m -1 and 2n -1 is divided into squares of unit length by drawing parallel lines as shows in the diagram, then the number of rectangles possible with odd side lengths is

For
the matrix,
verify that

(i)

is a symmetric matrix

(ii)

is a skew symmetric matrix