Explore topic-wise InterviewSolutions in Current Affairs.

If $(\cos p-1)x^2+\left(\cos p\right)x+\sin p=0,x\in R$ has real roots for $x$, then the range of $p$ is

If f(x) =cos x

Find f"(x) or double derivative

How many numbers are there between 100 and 1000 in which all the digits are distinct?

If $y=1+\frac{1}{x}+\frac{1}{x^2}+\frac{1}{x^3}+.....\infty$ with $|x|>1$ then $\frac{dy}{dx}=$

For which of the following functions the second derivative test for finding extremum fails at x = 0 ?

If normal at p to parabola $y^2=4ax$ meets parabola again at Q such that PQ subtends a right angle at the vertex of $y^2=4ax$ then p will be

The point $A$ divides the line segment joining the points $(-5,1)$ and $(3,5)$ in the ratio $k:1$. The coordinates of points $B$ and $C$ are $(1,5)$ and $(7,-2)$ respectively. If the area of $△ABC$ is $2$ square units, then the number of values of $k$ is

The domain of the function $\log |x^2-9|,$ is

I want some questions in that chapter

The value of $\sin ({45}^{\circ }+\theta )-\cos ({45}^{\circ }-\theta )$ is

If n be a positive integer, then in the trinomial expansion of$(x^2+2x+2{)}^n$ the coefficient of

Show that $f\left(x\right)=2x+co{t}^{-1}x+log(\sqrt{1+x^2}-x)$ is increasing in R.

The number of points with integer coordinates that lie inside a triangle with coordinates $(-50,0),(50,0)$ and $(0,50)$ are
(Note: Integral coordinates means both abscissa and ordinate are integral)

The value of $a$ if $\left[\begin{array}{ccc}1& a& 1\end{array}\right]\left[\begin{array}{c}2a\\ a\\ 2\end{array}\right]=\left[\begin{array}{c}1\end{array}\right]$

If $T_0,T_1,T_2,\cdots T_n$ represent the terms in the expansion of $(x+a{)}^n$, then the value of $(T_0-T_2+T_4-T_6+\cdots {)}^2+(T_1-T_3+T_5-\cdots {)}^2$ is

Find a particular solution of the differential equation $(x+1)\frac{dy}{dx}=2e^{-y}-1,$ given that y=0 when x=0.

If 3X + 2Y = I and 2X - Y = O, where I and O are unit and null matrices of order 3 respectively, then

For the differential equations in given question find the general solution.​​​​

$\frac{dy}{dx}+y=1(y\ne 1).$

Prove that the function f defined by $f\left(x\right)=\{\begin{array}{cc}\frac{x}{|x|+2x^2}& ifx\ne 0\\ k,& ifx=0\end{array}$
remains discontinuous at x=0, regardless the choice of k.

Evaluate the definite integrals.
${\int }_{\frac{\pi }{6}}^{\frac{\pi }{3}}\frac{sinx+cosx}{\sqrt{sin2x}}dx$

Form the differential equation for $y=(si{n}^{-1}x{)}^2+Aco{s}^{-1}x+B$ where A and B are arbitary constants, as its general solution.

If $P(A\cup B)=P(A\cap B)$ for any two events A and B. then

Prove that the function $f\left(x\right)=x^n$ is continuous at x=n, where n is a positive integer.

Find the maximum and minimum values, if any, of the following function given by,

$f\left(x\right)=-(x-1{)}^2+10$

The angle between the tangents drawn from the point (1, 4) to the parabola $y^2=4x$ is

Fine common tangent to hyperbola 9x^2 - 9y^2 = 8 and the parabola y^2 = 32x

9x+3y= 8

9x-3y= -8

9x-3y= -4

9x-3y= 8

If the statement $(p\to q)\to (q\to r)$ is false, then truth values of statement $p,q,r$ respectively, can be

The equation of a circle with centre $(2,2)$ and passes through the point $(4,5)$ is

Reduce the following equations into intercept form and find their intercepts on the axis.

(i) 3x + 2y - 1 2 = 0, (ii) 4x- 3y = 6, (iii) 3y + 2 = 0

Consider the hyperbola $H:x^2-y^2=1$ and a circle $S$ with center $N(x_2,0).$ Suppose that $H$ and $S$ touch each other at a point $P(x_1,y_1)\text{with}{x}_1>1\text{and}{y}_1>0.$ The common tangent to $H$ and $S$ at $P$ intersects the $x-$axis at point $M$. If $(l,m)$ is the centroid of the triangle $△PMN,$ then the correct expression(s) is (are)

1. *If R = {(x, y) : x + 2y = 8} is a relation on N, write the range of R.

The condition on a and b, such that the portion of the line ax + by – 1 = 0, intercepted between the lines ax + y = 0 and x + by = 0, subtends a right angle at the origin is

If $S=\frac{8}{5}+\frac{16}{65}+\frac{24}{325}+\dots +\frac{128}{4^9+1}$, then $S=$

The area shaded in the given figure can be calculated by which of the following definite integral?

The ratio of sum of n terms of 2 AP's is (7n+1):(4n+27).

Find the ratio of their m^th term.

show that:-

{cos²(45°-θ) +cos²(45°-θ)} /{tan(60°+θ) tan(30°-θ) } =1

Twelve persons are to be arranged around two round tables such that one table can accommodate seven persons and another table can accommodate five persons only.

The total number of possible arrangements if two particular persons $A$ and $B$ do not want to be on the same table is

Write the following sets in set builder form (1/4,2/5,3/6,4/7,5/8)

Let $f:R\to R,g:R\to R$, be two functions, such that f(x) =2x – 3, g (x) = $x^3$ + 5.
The function $(fog{)}^{-1}$ (x) is equal to

The sum of the squares of perpendicular on any tangent of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}$ = 1 from two points on the minor axis is