Explore topic-wise InterviewSolutions in Current Affairs.

The slope of the normal at the point with abscissa x = – 2 of the graph of the function $f\left(x\right)=|x^2-|x||$ is

1. 2

Write the order and degree of the given differential equation:

Show that the three
lines with direction cosines

are mutually perpendicular.

Which of the following limit is not in the indeterminant form ?

If a and b are the roots $x^2-3x+p=0$ and c, d are roots of $x^2-12x+q=0$, where a, b, c, d form a G.P. Prove that $(q+p):(q-p)=17:15$.

The angles A, B, and C of a triangle are in A.P. and

b:c = $\sqrt{3}:\sqrt{2},then\angle A=$ .

Sum upto $n$ terms for series $\frac{C_0}{1\cdot 2}+\frac{C_1}{2\cdot 3}+\frac{C_2}{3\cdot 4}+\cdots$ is
( where $C_r={}^n{C}_r$)

The value of the determinant
$\left|\begin{array}{ccc}lo{g}_a\left(\frac{x}{y}\right)& lo{g}_a\left(\frac{y}{z}\right)& lo{g}_a\left(\frac{z}{x}\right)\\ lo{g}_b\left(\frac{y}{z}\right)& lo{g}_b\left(\frac{z}{x}\right)& lo{g}_b\left(\frac{x}{y}\right)\\ lo{g}_c\left(\frac{z}{x}\right)& lo{g}_c\left(\frac{x}{y}\right)& lo{g}_c\left(\frac{y}{z}\right)\end{array}\right|$ is

The area of the triangle formed with the coordinate axes and the tangent at the point $(x_1,y_1)$ on the circle $x^2+y^2=a^2$ is

The zeroes of the polynomial $f\left(x\right)=x^2-3$ is

Using the letters of the given word, make three words. One is done for you.

Look at these words in the poem.

Here are their full forms:

i. Now write the full forms of the following words.
Can’t __________ It’s ____________ Isn’t __________
What's __________ That's ____________
ii. Make sentences using the following

iii. Now write about two things you'll do when you grow up. You can begin like this :
When I grow up I'll _________________________________________
____________________________________________________________
____________________________________________________________

A family of lines is given by $(1+2\lambda )x+(1-\lambda )y+\lambda =0,$ $\lambda$ being the parameter. The line belonging to this family at the maximum distance from the point $(1,4)$ is

$si{n}^{-1}$x + $si{n}^{-1}$y = $\frac{\pi }{2}$, then $\frac{dy}{dx}$ =

Area of the region in which point $p(x,y),\{x>0\}$ , lies; such that $y\le \sqrt{16-x^2}$ and $\left|ta{n}^{-1}\left(\frac{y}{x}\right)\right|\le \frac{\pi }{3}$ is

If $f_{n-1}\left(x\right)=\ln \left(f_n\right(x\left)\right)\forall n\in N$ and $f_0\left(x\right)=x-1$, then $\frac{d}{dx}(f_n\left(x\right))$ is

The total number of terms in the expansion of $(x+a{)}^{100}+(x-a{)}^{100}$ after simplification is

If the circles $x^2+y^2-8x-6y+21=0$ and $x^2+y^2+ay-15=0$ are orthogonal then the value of $a$ is

If the line $y=4x-2$ cuts the curve $y^2=8x$ at points $A$ and $B,$ then the equation of circle having $AB$ as a diameter, is

The value(s) of $\lambda$ for which the system of equations $x+y-3=0,(1+\lambda )x+(2+\lambda )y-8=0$ and $x-(1+\lambda )y+(2+\lambda )=0$

is consistent, is:

If ${lim}_{x\to \infty }(\frac{x^2+x+1}{x+1}-ax-b)=4$, then

Find the shortest distance (in units) between the lines 2y = -2x - 4 and -3y = 3x - 6.

Select the right options about a hyperbola.

If the coefficient of $x^2$ and $x^3$ are both zero, in the expansion of the expression $(1+ax+b{x}^2)(1-3x{)}^{15}$ in powers of $x$, then the ordered pair $(a,b)$ is equal to :

If $f\left(x\right)=\left|\begin{array}{ccc}2& \sin 2x& -2\\ 3& x^2+3x& \pi +3\\ 5& 5x+\cos x& 4\end{array}\right|,$ then which of the following(s) is a solution of $f^{\prime }\left(x\right)=0$

The value of $\int \frac{\ln \left(\tan x\right)}{\sin 2x}dx$ is

(where $C$ is constant of integration)

Consider the matrix $A=\left[\begin{array}{cc}3& 2\sin x\\ 1& -2\end{array}\right],$ where $x\in R.$ Then the maximum value of sum of minors of all elements of $A$ is



[2 marks]

The value of $I={\int }_0^{\pi }x\left({\sin }^2\right(\sin x)+{\cos }^2(\cos x\left)\right)dx$ is

$\int \frac{se{c}^2\left(x\right)}{4ta{n}^2\left(x\right)+9}dx$

Probability
of solving specific problem independently by A and B
arerespectively.
If both try to solve the problem independently, find the probability
that

(i) the
problem is solved (ii) exactly one of them solves the problem.

The value of ${\cos }^{-1}\left(\cos {680}^{\circ }\right)$ is

Write
Minors and Cofactors of the elements of following determinants:

(i) (ii)

In the figure, length of subnormal is the length P1N (tangent and normal is drawn at the point P)

1. T

Select the appropriate verb for the blank.

You need to _________ your studies seriously.