Explore topic-wise InterviewSolutions in Current Affairs.

Let $M=\left\{(x,y)\in R\times R:x^2+y^2\le r^2\right\}$, where $r>0$. Consider the geometric progression $a_n=\frac{1}{2^{n-1}},n=1,2,3,\dots .$ Let $S_0=0$ and, for $n\ge 1$, let $S_n$ denote the sum of the first $n$ terms of this progression. For $n\ge 1$ let $C_n$ denote the circle with center $(S_{n-1},0)$ and radius $a_n$ and $D_n$ denote the circle with center $(S_{n-1},S_{n-1})$ and radius $a_n$.



Consider $M$ with $r=\frac{(2^{199}-1)\sqrt{2}}{2^{198}}$. The number of all those circles $D_n$ that are inside $M$ is

If $I=\int (\sqrt{\cot x}-\sqrt{\tan x})dx$ equals $\sqrt{2}\log |f\left(x\right)+\sqrt{g\left(x\right)}|+C$, then which of the following is/are correct ?

Let $x=\underset{0}{\overset{\cos t}{\int }}(z^2-1){\cos }^{2}zdz$ and $y=\underset{0}{\overset{{\sin }^{2}t}{\int }}{z}^2\left({\sin }^2\sqrt{1-z}\right)dz,t\in (0,\frac{\pi }{2}),$ then $\frac{dy}{dx}$ is equal to

A box contains $15$ red and $10$ blue balls. If $10$ balls are randomly drawn one by one with replacement then the variance of the number of red balls is

If 1/a + 1/b + 1/c = 1/(a+b+c), where a+b+c and a*b*c is not equal to zero then what's the value of

(a+b)(b+c)(c+a)

If the diagonals of the parallelogram whose sides are $lx+my+n=0,lx+my+n^{\prime }=0$ and $mx+ly+n=0,mx+ly+n^{\prime }=0$ includes an angle $\theta$, then the value of $\theta$ is

The solution of differential equation $(x^2-xy)dy=(xy+y^2)dx,$ is

(where $c$ is integration constant)

If one of the root of the qudratic polynomial $f\left(x\right)=a{x}^2+bx+c;a>0$ is greater than $k_1$ and other root is less than $k_2$. Then select the correct statement(s) for $k_1<k_2$.

How many values of $xϵ[0,2\pi ]$ satisfies the equation sin 2x + 5 sin x + 1 + 5 cos x = 0?

If sin x+siny =$\frac{1}{2}$ and cosx+cosy = 1, then tan (x+y) = ……..

For $\alpha ϵR$ (the set of all real numbers), $a\ne -1$,
${lim}_{n\to \infty }\frac{(1^a+2^a+\dots +n^a)}{(n+1{)}^{a-1}[(na+1)+(na+2)+\dots +(na+n)]}=\frac{1}{60}$

Let $S$ be the circle in $xy$-plane which touches the $x$-axis at point $A$, the $y$-axis at point $B$ and the unit circle $x^2+y^2=1$ at point C externally. If $O$ denotes the origin, then the angle $OCA$ equals

If the letters of the word $MAHARASTRA$ are permuted at random, then the probability that the two $R^{\prime }s$ come together and no two $A^{\prime }s$ come together is:

Which of the following represent the collection of all the real numbers on a number line?

Let $U=\{x\in N\mid x<20\}$ be the universal set. Let $A=\{x\in N\mid x\text{is prime less than}20\}$,

$B=\{x\in N\mid x\text{is}3n,n\in N,n\le 6\}$,

$C=\{x\in N\mid x=2n–1,n\in N,n\le 10\}$. Then $n\left[\right(A\cup B{)}^{\prime }\cup (A\cap C)]=$

If $\alpha ,\beta ,\gamma$ are the roots of $x^3+lx+m=0$, then the value of ${\alpha }^3+{\beta }^3+{\gamma }^3$ is

Let $F\left(x\right)$ be a non-negative continuous function and $F\left(x\right)=\underset{0}{\overset{x}{\int }}f\left(x\right)dx\forall x\ge 0.$ If for some $c>0,f\left(x\right)\le cF\left(x\right)$ for all $x\ge 0,$ then which of the following is/are always correct ?

If $5^{40}$ is divided by $11,$ then remainder is $\alpha$ and if $2^{2003}$ is divided by $17,$ then remainder is $\beta .$ Then the value of $(\beta -\alpha )$ is

The ratio of area of a regular polygon of $n$ sides inscribed in a circle to that of the polygon of same number of sides circumscribing the same circle is $3:4$. Then the value of $n$ is

If $A=\left[\begin{array}{cc}sin\alpha & cos\alpha \\ -cos\alpha & sin\alpha \end{array}\right]$, then verify that A'A=I.

Which of the following is correct?
a) Determinant is a square matrix
b) Determinant is a number associated to a matrix
c) Determinant is a number associated to a square matrix
d) None of the above

If $|x-7{|}^2-3|x-7|-10=0$, then value(s) of $x$ can be equal to

Solve the given inequality for real x:

If $I_1=\underset{0}{\overset{\frac{\pi }{2}}{\int }}\frac{{\cos }^{2}x}{1+{\cos }^{2}x}dx,I_2=\underset{0}{\overset{\frac{\pi }{2}}{\int }}\frac{{\sin }^{2}x}{1+{\sin }^{2}x}dx,I_3=\underset{0}{\overset{\frac{\pi }{2}}{\int }}\frac{1+2{\cos }^{2}x{\sin }^{2}x}{4+2{\cos }^{2}x{\sin }^{2}x}dx,$ then

The shaded region in the figure is the solution set of the inequations





[1 mark]

If the roots of $x^2-(a-3)x+a=0$ are such that at least one of the root(s) is greater than $2,$ then find the range of $a.$

The value of the integral $\int \frac{x^2+x+1}{(x+2)(x^2+1)}dx$

(where $m$ is integration constant)

If p is the perimeter of the $△ABC$ then $bco{s}^2\frac{C}{2}+cco{s}^2\frac{B}{2}$ is equal to