Explore topic-wise InterviewSolutions in Current Affairs.

If $a,b>0$ and $\underset{0}{\overset{\infty }{\int }}\frac{\ln \left(bx\right)}{x^2+a^2}dx=\frac{\pi }{2a},$ then the value of $ab$ is

Write the following functions in the simplest form :

${\tan }^{-1}\left(\frac{\cos x-\sin x}{\cos x+\sin x}\right),0<x<\pi$

If $z$ is a complex number, then the conjugate of $z+2\overline{z}$ is

Prove that
cot x cot 2x – cot 2x cot 3x –
cot 3x cot x = 1

If coefficients of $5^{\text{th}},6^{\text{th}}$ and $7^{\text{th}}$ terms in the expansion of $(1+x{)}^n$ are in A.P., then the value(s) of $n$ is/are

If $\alpha +\beta ={90}^{\circ }$, show that the maximum value of $cos\alpha cos\beta is\frac{1}{2}$

If $\sqrt{3}\cot x-\text{cosec}x=1$, then $x$ can be

(where $n\in Z$)

The value of $tan\frac{19\pi }{3}$ is

A whistle emitting a sound of frequency $300\text{Hz}$ is tied to a string of $2\text{m}$ length and is rotated with an angular velocity of $15\text{rad/s}$ in the horizontal plane. Find the range of frequencies heard by the observer stationed at a large distance from the whistle.



[Given, velocity of sound in air $=330\text{m/s}$. Assume, medium is stationary and also that the observer and the source are on the same horizontal plane.]

If $\int e^{ax}cos\left(bx\right)dx=\frac{e^{ax}}{K}(acosbx+bsinbx)+C$, then the K here would be equal to -

Let $p,q,r$ are lengths of an acute angled triangle $△PQR$ opposite to sides $QR,PR,PQ$ respectively. The perpendiculars are drawn from the angles $P$, $Q$ and $R$ on opposite sides and produced to meet the circumscribing circle. If these produced parts be ${\theta }_1,{\theta }_2,{\theta }_3$ respectively, then the value of $\frac{\left(p/{\theta }_1\right)+\left(q/{\theta }_2\right)+\left(r/{\theta }_3\right)}{\tan P+\tan Q+\tan R}$ is
(correct answer + 1, wrong answer - 0.25)

The domain of $f\left(x\right)={\sin }^{-1}x+{\cos }^{-1}x+{\tan }^{-1}x+{\cot }^{-1}x$ is



[2 marks]

Solve the
system of the following equations

Profit earned from Product X is shown below. Another Product Y also has the same profit but it started selling 1.5 years after start of sale of Product X. What will be the new set of input values for the Product Y?

The value of integral $\underset{20}{\overset{30}{\int }}\frac{\ln x}{\ln x+\ln (50-x)}dx$ is

Find the value of r, if ${}^5{P}_r=2^6{P}_{r-1}$

If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{1}=\frac{z}{1}$ and intersect, then k =
[IIT Screening 2004]

In a $\Delta ABC$, $\angle A={30}^{\circ },H$ is the orthocentre and $D$ is the mid point of $\overrightarrow{BC}\cdot$ Segment $HD$ is produced to $T$ such that $HD=DT$. Then the ratio $\frac{AT}{BC}$ is equal to

Which of the following are the common zeros of the polynomials $(x^2-4)(x+3)$ and $(x^2-9)(x+2)?$

The solution of the differential equation $ydx-xdy=y^2\tan \left(\frac{x}{y}\right)dx$ is

( $C$ is constant of integration)

Question:

if f(x)=x cos x, find f"(x), or d2ydx2

Physics Calculus Differentiation

Solution:

Using the Product Rule, we have f'(x)=xddx(cos x)+cos xddx(x)=-xsinx+cosx
To find f"(x) we differentiate f'(x):
f"(x)=ddx(-x sin x+cos x)=-xddx(sin x)+sin x ddx(-x)+ddx(cos x)
=-x cos x-sin x-sin x = -x cos x-2 sin x

my problem is :

I didn't understand how to solve this question

Solve the following system of equations in R.

$\frac{4}{x+1}\le 3\le \frac{6}{x+1},x>0$

For the given expression $\frac{\sqrt{2x-1}}{x-2}<1,x\in$ :

Let matrices $A=\left[\begin{array}{ccc}2x+1& 3y& \\ 0& y^2-5y& \end{array}\right],B=\left[\begin{array}{ccc}x+3& y^2+2& \\ 0& -6& \end{array}\right]$ are equal, then which of the following is(are) not correct

The domain of $f\left(x\right)=\frac{1}{\sqrt{|[|x|-1]|-5}}$ (where [.] represents greatest integer less than or equal to $x$) is

If the first and the
n^th term of a G.P. are a ad b,
respectively, and if P is the product of n terms, prove
that P² = (ab)ⁿ.

If $A$ and $B$ are disjoint non-empty sets, then $A–(A–B)$ is

If $S_n=1^2+{2.2}^2+3^2+{2.4}^2+...=\frac{n(n+1{)}^2}{2}$, where n is even, then the value of $\frac{S_{21}}{4851}$ must be___