Explore topic-wise InterviewSolutions in Current Affairs.

The value of the integral $\int \frac{dx}{x\sqrt{1+x^n}}$ is:

(where $c$ is integration constant)

$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots +\frac{1}{2^n}=1-\frac{1}{2^n}.$

If sin A = $\frac{4}{5}$ and cos B = - $\frac{12}{13}$, where A and B lie in first

and third quadrant respectively, then cos(A + B) =

The sum of the solutions of the equation

$2{\sin }^{-1}\left(\sqrt{x^2+x+1}\right)+{\cos }^{-1}\left(\sqrt{x^2+x}\right)=\frac{3\pi }{2}\mathrm{is}$

If a curve passes through the origin and the slope of the tangent to it at any point $(x,y)$ is $\frac{x^2-4x+y+8}{x-2}$, then this curve also passes through the point :

If the line $2x-y+1=0$ is a tangent to the circle $S\equiv 0$ at $P(2,5)$ and the centre of the circle lies on $x-2y=4,$ then the intercept made by the circle $S\equiv 0$ on the $x-$axis is equal to

The solution of the differential equation $(x+2y^3)\frac{dy}{dx}=y,y>0$ is

(where $c$ is integration constant)

Find the value of x if $x^2-4\left(x\right|+3=0$

1. 6

O is the circumcenter of $\Delta \mathrm{ABC}\mathrm{and}{R}_1,R_2\mathrm{and}{R}_3$are the radii of the circumcircles of the triangles OBC, OCA and OAB. Then $\frac{a}{R_1}+\frac{b}{R_2}+\frac{c}{R_3}=$ .

In the expansion of ${(x^3-\frac{1}{x^2})}^n,n\in N$, if the sum of the coefficients of $x^5$ and $x^{10}$ is $0$, then $n$ is

The value of $\sin {10}^{\circ }\sin {30}^{\circ }\sin {50}^{\circ }\sin {70}^{\circ }$ is :

A variable straight line through $A(-1,-1)$ is drawn to cut the circle $x^2+y^2=1$ at the points $B,C.$ If $P$ is chosen on the line $ABC$ such that $AB,AP,AC$ are in $A.P$ then the locus of $P$ is

If $||x-3|+4|\ge 2$, then $x$ belongs to

If set $A=\left\{\right(r,s)|r<s;r,s\in W\}$, then the number of elements in set $A$ such that ${}^7{C}_r+{}^7{C}_{r-1}={}^8{C}_s$ is

The range of $\lambda$ if the point $(\lambda ,\lambda +1)$ lies inside the parabola $y^2=14x$

The normal at any point $P$ on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b)$ meets the x-axis at $A$ and y-axis at $B$. If $PA:PB=1:4,$ then the eccentricity of the ellipse is

The vector(s) which is/are coplanar with vectors $\hat{i}+\hat{j}+2\hat{k}\text{and}\hat{i}+2\hat{j}+\hat{k}$ and perpendicular to the vector $\hat{i}+\hat{j}+\hat{k}$ is/are

Which of the following is not continuous for all x?

If $5x+9=0$ is the directrix of the hyperbola $16x^2-9y^2=144,$ then its corresponding focus is

If,
show that

Find the domain and range of the follwoing graph.

If $-2x^2+2x+\alpha <{\text{cosec}}^{-1}\left(\text{cosec 6}\right)+{\tan }^{-1}\left(\tan \right(-5\left)\right)\forall x\in R,$ then possible value(s) of $\alpha$ can be (where $\alpha \in Z$)

The period of the function $f\left(x\right)={\sin }^{3}x$ is

For any two sets A and B, prove that :

A' - B' = B- A

Find the four numbers in A.P. whose sum is 50 and in which the greatest number is 4 times the least.

If ${\sin }^4\theta +\frac{1}{{\sin }^4\theta }=194,\theta \ne n\pi ,n\in Z$, then the value(s) of $(2\text{cosec}\theta -\cot \theta \cos \theta )$ can be

A coin is tossed twice. The probability of getting head both the times is

[MNR 1978]