Examples

Q. $\int \{1+2\tan x(\tan x+\sec x){\}}^{\frac{1}{2}}dx$ is equal to

1. $ln|\sec x(\sec x-\tan x)|+c$
2. $ln|cosecx(\sec x+\tan x)|+c$
3. $ln|\sec x(\sec x+\tan x)|+c$
4. $ln|(\sec x+\tan x)|+c$

Q. The momentum $p$ of a particle changes with time according to the relation: $\frac{dp}{dt}=(10+2t)N$. If the momentum is zero at $t=0s$. What will the momentum in $Ns$ at $t=10s$

Q. If $v=(4t^2+5t+1)m/s$ is the expression according to which the velocity of a particle varies, then the expression for instantaneous displacement at any time $t$ will be (Assume $s=0$ at $t=0$)

1. $\frac{4}{3}{t}^3+\frac{5}{2}{t}^2+t$
2. $4t^3+t+1$
3. $\frac{4}{3}{t}^3+\frac{5}{2}{t}^2+t+1$
4. $3t^3+5t^2+t$

Q.

Consider the following two statements

1.Linear momentum of a system of particles is zero

2.Kinetic energy of a system of particles is zero

Then

1. 1 implies 2 and 2 implies 1

2. 1 does not imply 2 and 2 does not imply 1

3. 1 implies 2 but 2 does not imply 1

4. 1 does not imply 2 but 2 implies 1

Q.

The charge flown through a circuit in the time interval between t and t+dt is given by $dq=e^{-t/\tau }dt$, where $\tau$ is a constant. Find the toatal charge flown through the circuit t = 0 to t = $\tau$

1. $\tau (\frac{1}{e}-1)$

2. $\tau (1-\frac{1}{e})$

3. $\tau (1+\frac{1}{e})$

4. None of these

Q. $\int {\sin }^{2}x\cos xdx=?$

1. $\frac{1}{2}{\cos }^{2}x+c$
2. $\frac{1}{3}{\cos }^{3}x+c$
3. $\frac{1}{2}{\sin }^{2}x+c$
4. $\frac{1}{3}{\sin }^{3}x+c$

Q. $\int {\sin }^{2}x\cos xdx=?$

1. $\frac{1}{2}{\cos }^{2}x+c$
2. $\frac{1}{2}{\sin }^{2}x+c$
3. $\frac{1}{3}{\cos }^{3}x+c$
4. $\frac{1}{3}{\sin }^{3}x+c$

Q. Find the integral of $\int \frac{1}{(x+2)(x+3)}dx$

1. ${\log }_e\frac{(x+2)}{(x+3)}+C$
2. ${\log }_e(x+2)+{\log }_e(x+3)+C$
3. ${\log }_e\frac{(x+3)}{(x+2)}+C$
4. None of these

Q. $\int \{1+2\tan x(\tan x+\sec x){\}}^{\frac{1}{2}}dx$ is equal to

1. $ln|\sec x(\sec x-\tan x)|+c$
2. $ln|cosecx(\sec x+\tan x)|+c$
3. $ln|\sec x(\sec x+\tan x)|+c$
4. $ln|(\sec x+\tan x)|+c$