Explore topic-wise InterviewSolutions in Current Affairs.

If $f\left(x\right)=\left(h_1\right(x)-h_1(-x\left)\right)\left(h_2\right(x)-h_2(-x\left)\right)\cdots \left(h_{2n+1}\right(x)-h_{2n+1}(-x\left)\right),$ where $h_1\left(x\right),h_2\left(x\right),\cdots \cdots h_n\left(x\right)$ are defined everywhere and $f\left(200\right)=0$, then $f\left(x\right)$ is

Given below are four jumbled sentences. Select the option that gives their correct order.

$A:$ I should have charged double the amount, but it didn't occur to me then.

$B:$ Now, after all the expenses and the gardener's salary, I made a profit of only five hundred rupees.

$C:$ The jasmine plants flowered twice and I sold $250$ grams of buds just for ten rupees.

$D:$ Had I charged at least twenty rupees, I would have made a good profit.

If $15{\sin }^4\alpha +10{\cos }^4\alpha =6,$ for some $\alpha \in R,$ then the value of $27{\sec }^6\alpha +8{\text{cosec}}^6\alpha$ is equal to

Find the derivative of $sin\left(x^2\right)+(sinx{)}^2+si{n}^2(x^2)$

The integral of a certain graph is given by $A=(1+3x{)}^{\frac{1}{2}}-1$; $x\ge 0$. The average value of $A$ w.r.t. $x$ as $x$ increases from $1$ to $8$ is

विद्यार्थी संघ के मंत्री अविनाश बाबू के झंडा गाड़ने पर क्या प्रतिक्रिया हुई?

The value of x in $(0,\pi )$ which satisfy the equation

$8^{-+|cosx|+co{s}^{2}x+|co{s}^{3}x|+\cdots to\infty }=4^3$ is

Letbe
fixed real numbers and define a function

What
isf(x)?
For some

computef(x).

N characters of information are held on magnetic tape, in batches of x character each; the batch processing time is $\alpha +\beta x^2$ seconds, $\alpha ,\beta$ are constants. The optimum value of x for fast processing is

The equation of the plane passing through the point $(4,5,1),(0,-1,-1)$ and $(-4,4,4),$ is

The maximum integral value of $a$ for which the equation $a\sin x+\cos 2x=2a-7$ has a solution is :

The value of $(\cos \theta +\sin \theta +1)(\cos \theta +\sin \theta -1)-2\sin \theta \cos \theta$ is

If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is

If a, b, c are
in A.P,; b, c, d are in G.P and
are
in A.P. prove that a, c, e are in G.P.

The domain of the function $f\left(x\right)=\frac{1}{1-\left\{x\right\}}$ is

(where $\{.\}$ denotes the fractional part of $x$)

If P(n) : $49n+16n+\lambda$ is divisible by 64 for $nϵN$ is true. then the least negative integral value of $\lambda$ is

A guard of 12 men is formed from a group of n soldiers in all possible ways. If the number of times two particular soldiers A and B are together on guardis thrice the number of times there particular soldiers C,D,E are together on gurard, then n =

Let $f:R\to R$ be defined as

$f\left(x\right)=\{\begin{array}{cc}\frac{\lambda |x^2-5x+6|}{\mu (5x-x^2-6)},& x<2\\ & \\ e^{\frac{\tan (x-2)}{x-\left[x\right]}},& x>2\\ \mu ,& x=2\end{array}$

where $\left[x\right]$ is the greatest integer less than or equal to $x$. If $f$ is continuous at $x=2,$ then $\lambda +\mu$ is equal to

A die is rolled and two events A and B are defined as follows.

A: An odd number turns up

B: A prime Number turns up

Find the value of 36 P$(A\cup B)$.

The length of the curve $y=\frac{2}{3}{x}^{3/2}$ between $x=0$ and $x=1$ is

Question 2 (ii)

For which value of k will the following pair of linear equations have no solution?

3x + y = 1

(2k -1)x + (k -1)y = 2k + 1

If $3A={\left[\begin{array}{ccc}-1& -2& -2\\ 2& 1& -2\\ x& -2& y\end{array}\right]}^T$ such that $A{A}^T=I$, then which of the following is/are correct

If $PQ$ is a double ordinate of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ such that $OPQ$ is an equilateral triangle, $O$ being the centre of the hyperbola, then the eccentricity $e$ of the hyperbola satisfies

Let $f\left(x\right)=x^2-2x+1,$ then the value of $c$ that satisfy the $LMVT$ for the function on the interval $[0,1]$ is

If f(x) and g(x) are two functions of x, then the integration of product of f(x) and g(x) is:

If $2(1+\tan \alpha +{\tan }^2\alpha +\cdots \infty )=\sqrt{3}+1,$ where $0<\alpha <\frac{\pi }{4},$ then the sum of the solutions of the equation $\sin \theta =\sin \alpha$ in $[0,4\pi ]$ is equal to

If the greatest value of the term independent of $x$ in the expansion of ${(x\sin \alpha +a\frac{\cos \alpha }{x})}^{10}$ is $\frac{10!}{(5!{)}^2},$ then the value of $a$ is equal to

A line passing througjh the point of intersection of $x+y=4$ and $x-y=2$ makes an angle of ${\tan }^{-1}\frac{3}{4}$ with the $x$ axis. It intersects the parabola $y^2=4(x-3)$ at point $(x_1,y_1)$ and $(x_2,y_2)$ respectively. Then $|x_1-x_2|$ is equal to;

${\log }_{25}36=$ ?

Using Binomial Theorem, evaluate (96)³

${lim}_{x\to 4}\frac{x^3-64}{x^2-16}$