Explore topic-wise InterviewSolutions in Current Affairs.

Solve
system of linear equations, using matrix method.

x −
y + z = 4

2x
+ y − 3z = 0

x +
y + z = 2

The particular solution of the differential equation $x(y+2)y^{\prime }=\ln x+1,$ provided $y\left(1\right)=-1$, is

Each of the circles $|z-1-i|=1$ and $|z-1+i|=1$ where $z=x+iy,$ touches internally a circle of radius $2$ units. The equation of the circle touching all the three circles can be

If the area of a circle is $A_1$ and the area of the regular hexagon inscribed in the circle is $A_2,$ then the value of $\frac{A_1}{A_2}$ is

If $\tan x-{\tan }^{2}x>0$ and $|2\sin x|<1$ then the range of $x$ for which both conditions hold good is (where $n\in Z$)

Mohan posts a letter to Sohan. It is known that one letter out of $10$ letters does not reach its destination. It is certain that Sohan will reply if he receives the letter. If $A$ denotes the event that Sohan receives the letter and $B$ denotes the event that Mohan gets a reply, then

If $\text{tan}(x+y)=33$ and $x={\text{tan}}^{-1}3,$ then $y$ can be

If $x\in (0,\frac{\pi }{4}),$ then the derivative of ${\tan }^{-1}\left(\frac{\cos x+\sin x}{\cos x-\sin x}\right)$ with respect to $x$ is



[1 mark]

The value(s) of $x$ for which $\left|\begin{array}{cc}2x& 5\\ 8& x\end{array}\right|=\left|\begin{array}{cc}6& -2\\ 7& 3\end{array}\right|,$ is(are)

What is the parametric form of the equation of the ellipse given by,

x²/a² + y²/b² = 1

The value of ${\cos }^{-1}[-\sin \left(\frac{7\pi }{6}\right)]$ is

Prove the following question.

${\int }_0^{1}x{e}^{x}dx=1$

The value of $\int \frac{\sin 5x}{\sin x}dx$ is

(where $C$ is constant of integration)

If $\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...\infty =\frac{{\pi }^2}{6}$, then $\frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}+$.... equals

Using elementary transformations, find the inverse of the followng matrix.

$\left[\begin{array}{cc}2& 5\\ 1& 3\end{array}\right]$

If $y=x\left\{x\right\}-x\left[x\right],$ then $\frac{dy}{dx}$ is equal to

$($Where $x\ne Z,[\cdot ]$ denotes the greatest integer function and $\{\cdot \}$ denotes the fractional part function$)$

${lim}_{x\to \sqrt{2}}\frac{x^2-2}{x^2+\sqrt{2x}-4}$

If a = 2r for a simple cube, the volume of the unit cell will be:

A relationship between the sets P and Q. Write this relation in (i) set builder form

(ii) roster form. What is its domain and range ?

If $a_r=\cos \frac{2r\pi }{9}+i\sin \frac{2r\pi }{9},r=1,2,3,...,i=\sqrt{-1},$ then the determinant $\left|\begin{array}{ccc}{a}_1& a_2& a_3\\ a_4& a_5& a_6\\ a_7& a_8& a_9\end{array}\right|$ is equal to

Let $L_1$ and $L_2$ are two intersecting lines.
If the image of $L_1$ w.r.t. $L_2$ and $L_2$ w.r.t. $L_1$
coincide, then angle between $L_1$ and $L_2$ is-

Square roots of $-i$, where $i=\sqrt{-1}$, are

There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.