Explore topic-wise InterviewSolutions in Current Affairs.

A dice is thrown (2n + 1) times. The probability of getting 1, 3 or 4 at most n times, is

If $A,B,C$ are square matrices of same order such that $AB=BA,C^2=B,$ then $(A^{-1}CA{)}^2$ is equal to

$\int \frac{\sqrt{x^2+1}\left[log\right(x^2+1)-2logx]}{x^4}dx$

One card is drawn at random from a well- shuffled deck of 52 cards. In which of the following cases are the events E and F independent?
E: the card drawn is a king or queen
F: the card drawn is a queen or jack

Let $f:X\to Y$ be an invertible function. Show that the inverse of $f^{-1}$ is f i.e., $(f^{-1}{)}^{-1}=f.$

If p: Ridhi did not eat lunch q: Azad did not have lunch. Then which of the following denotes the compound statement: "Both Ridhi and Azad did not have lunch.”

The value of $P$ for which the equation $(P^3-3P^2+2P)x^2+(P^3-P)x+P^3+3P^2+2P=0$ has both the roots at infinity is

Which of the following is a identity function?

Find the determinant value of an orthogonal matrix.

Find the direction cosines of the side AB of the triangle whose vertices are A(3, 5, -4), B(-1, 1, 2) and C(-5, -5, -2)

The system of linear equations

$x+\lambda y-z=0\lambda x-y-z=0x+y-\lambda z=0$

has a non-trivial solution for :

Which of the following is/are correct?

A value of $\theta$ for which $z=\frac{2+3isin\theta }{1-2isin\theta }$ is purely imaginary, is

An experiment succeeds twice as often as it fails. Find the probability that in the next six trials there will be atleast 4 successes.

Use HM $\le$ AM and find maximum value of $\frac{xy}{x+y}$ + $\frac{yz}{y+z}$ + $\frac{xz}{x+z}$

Statements: B # F, F $ H, H © K

Conclusions:

a) H B

b) K $ B

If $2a=\sqrt{64},then\frac{a}{4}$ is equal to

Find the length of the longest rod that can be placed in a room 16 m long, 12 m broad and $10\frac{2}{3}$ m high.

If α,β are roots of $x^2$- 3ax + $a^2$ = 0 such that $a^2$+ $b^2$ = 1.75, then possible values of a are

Two tangents are drawn to end points of the latus rectum of the parabola $y^2=4x$. The equation of the parabola which touches both the tangents as well as the latus rectum is

If $\alpha ,\beta \ne 0$ and $f\left(n\right)={\alpha }^n+{\beta }^n$ and $\left|\begin{array}{ccc}3& 1+f\left(1\right)& 1+f\left(2\right)\\ 1+f\left(1\right)& 1+f\left(2\right)& 1+f\left(3\right)\\ 1+f\left(2\right)& 1+f\left(3\right)& 1+f\left(4\right)\end{array}\right|=K(1-\alpha {)}^2(1-\beta {)}^2(\alpha -\beta {)}^2$, then K is equal to

The values of $x$ satisfying $x^{{\log }_{5}x}>5$ lie in the interval

For all permissible values of $A,2A$, following holds true.
$\left(i\right)\cot A+\tan A=\frac{1}{\sin A\cos A}=2\text{cosec}2A\left(ii\right)\cot A-\tan A=\frac{{\cos }^{2}A-{\sin }^{2}A}{\sin A\cos A}=2\cot 2A\left(iii\right)2\cot A=2(\text{cosec}2A+\cot 2A)\Rightarrow \text{cosec}2A+\cot 2A=\cot A$

Also to evaluate a series of form $f\left(x\right)+f\left(2x\right)+f\left(4x\right)+\cdots +f\left(2^{n}x\right)$ when $f\left(x\right)$ can be expressed as $g\left(x\right)-g\left(2x\right)$, we can use the following technique,
$f\left(x\right)+f\left(2x\right)+f\left(4x\right)+\cdots +f\left(2^{n}x\right)=\left(g\right(x)-g(2x\left)\right)+\left(g\right(2x)-g(4x\left)\right)+\cdots \left(g\right(2^{n}x)-g(2^{n+1}x\left)\right)=g\left(x\right)-g\left(2^{n+1}x\right)$

Based on the above information, solve the following questions for all permissible values of $x$.

The value of $\cot 37{\frac{1}{2}}^{\circ }$ is

Find the values of y for which the following will be positive, negative or zero. $y=x-6\sqrt{x}+8$

In $△$ ABC, if cot A, cot B, cot C be in A. P. then $a^2,b^2,c^2$ are in

The coefficient of x in the quadratic equation $x^2+px+q=0$ was taken as -14 in place of -10, its roots were found to be 6, 4. If α, β are the roots of correct equation, then the value of ${\alpha }^2+{\beta }^2$ must be equal to

In acute angled triangle $ABC,r=r_2+r_3-r_1$ and $\angle B>\frac{\pi }{3}$ then exhaustive range of $\frac{a-c}{b}$ is

Number of value(s) of $x$ which disobey(s) the condition ${\log }_3(2x^2+6x-5)>1,x\in N$ is

If $S_n=(\frac{n}{1})\sin a+(\frac{n}{2})\sin 2a+\cdots +(\frac{n}{n})\sin na$ and $T_n=(\frac{n}{1})\cos a+(\frac{n}{2})\cos 2a+\cdots +(\frac{n}{n})\cos na$
where $n\in N$ and $a$ be the non-zero real number such that $a\ne (2n-1)\frac{\pi }{2}$, then which of the following is/are CORRECT?
$(\text{Here},(\frac{n}{r})={}^n{C}_r)$

${lim}_{x\to 0}\frac{1-cos2x}{x}$ is

If AB is a double ordinate of the hyperbola such that ∆ OAB (O is the origin) is an equilateral triangle, then the eccentricity e of the hyperbola satisfies

Find the number of ways in which :

(a) a selection (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.

Let $f$ be a differentiable function from $R$ to $R$ such that $|f\left(x\right)-f\left(y\right)|\le 2|x-y{|}^{3/2}$, for all $x,y\in R$. If $f\left(0\right)=1$, then $\underset{0}{\overset{1}{\int }}{f}^2\left(x\right)dx$ is equal to :

A computer producing factory has only two plants $T_1$ and $T_2$. Plant $T_1$ produces 20% and plant $T_2$ produces 80% of the total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that P(computer turns out to be defective, given that it is produced in plant $T_1)$ = 10P (computer turns out to be defective, given that it is produced in plant $T_2$), where P(E) denotes the probability of an event E. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then, the probability that it is produced in plant $T_2$, is ?

If $\frac{z-1}{z+1}$ is purely imaginary number $(z\ne -1)$, find the value of |z|.

If $\frac{1}{{\alpha }_k+i}({\alpha }_k\in R)$ are $8$ vertices of a regular octagon for $k=1,2,3,\dots ,8$, where $i=\sqrt{-1}$, then the area of the octagon is

If $A=\{x:-2\le x<2,x\in Z\}$, then the number of proper subsets of $A$ is

Suppose $y=f\left(x\right)$ and $y=g\left(x\right)$ are two functions whose graphs intersect at the three points $(0,4),(2,2)$ and $(4,0)$. And also $f\left(x\right)>g\left(x\right)$ for $x\in (0,2),f\left(x\right)<g\left(x\right)$ for $x\in (2,4)$. If $\underset{0}{\overset{4}{\int }}\left(f\right(x)-g(x\left)\right)dx=10$ and $\underset{2}{\overset{4}{\int }}\left(g\right(x)-f(x\left)\right)dx=5$, then the area between the two curves for $x\in (0,2)$ is

If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the form $7^m+7^n$ is divisible by 5 equals.

Let two fair six-faced dice A and B be thrown simulatneously. If $E_1$ is the event that die A shows up four, $E_2$ is the event that die B shows up two and $E_3$ is the event that the sum of numbers on both dice is odd, then which of the following statements is/are true ?

If $f\left(x\right)=x^3-7x^2+15,$then the approximate value of f(5.001) is