Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{\sin ^{2} x}{(1+\cos x)} d x=?$ A. $x+\sin x+C$ B. $x-\sin x+C$ C. $\sin x-x+C$ D. $-\sin x-x+C$ Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\sec ^{2} x}{\operatorname{cosec}^{2} x} d x=?$ A. $\tan x+x+C$ B. $\tan x-x+C$ C. $-\tan x+x+C$ D. $-\tan x-x+C$ Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \sec x(\sec x+\tan x) d x=?$ A. $\tan x-\sec x+C$ B. $-\tan x+\sec x+C$ C. $\tan x+\sec x+C$ D. $-\tan x-\sec x+C$ Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \cot ^{2} x d x=?$ A. $-\cot x-x+C$ B. $\cot \mathrm{x}-\mathrm{x}+\mathrm{C}$ C. $-\cot x+x+C$ D. $\cot x+x+C$ Solution: Given: $\int \cot ^{2} x d x=\int\left((\csc x)^{2}-1\right) d x$ $=-\cot x-x+c$...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{(1-\sin x)}{\cos ^{2} x} d x=?$ A. $\tan x+\sec x+C$ B. $\tan x-\sec x+C$ C. $-\tan x+\sec x+C$ D. $-\tan x-\sec x+C$ Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\sin 2 x}{\sin x} d x=?$ A. $2 \sin x+C$ B. $\frac{1}{2} \sin x+C$ C. $2 \cos x+C$ D. $\frac{1}{2} \cos x+C$ Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{d x}{(1-\cos 2 x)}=?$ A. $\frac{1}{2} \cot \mathrm{x}+\mathrm{C}$ B. $2 \cot x+C$ C. $-\frac{1}{2} \cot x+C$ D. $-2 \cot x+C$ Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\cos 2 x}{\sin ^{2} x \cos ^{2} x} d x=?$ A. $\cot x+\tan x+C$ B. $-\cot x+\tan x+C$ C. $\cot x-\tan x+C$ D. $-\cot x-\tan x+C$ Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \sqrt{1+\sin 2 x} d x=?$ A. $\sin x+\cos x+C$ B. $-\sin x+\cos x+C$ C. $\sin x-\cos x+C$ D. $-\sin x-\cos x+C$ Solution:...
Read More →A charged capacitor of capacitance C is discharged through a resistance R.
Question: A charged capacitor of capacitance $\mathrm{C}$ is discharged through a resistance $\mathrm{R}$. A radioactive sample decays with an averagelife. Find the value of $\mathrm{R}$ for which the ratio of electrostatic field energy stored in the capacitor to the activity of the radioactive sample remains constant in time. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \sqrt{1+\cos 2 x} d x=?$ A. $\sqrt{2} \cos x+C$ B. $\sqrt{2} \sin \mathrm{x}+\mathrm{C}$ C. $-\sqrt{2} \cos x+C$ D. $-\sqrt{2} \sin x+C$ Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{(\cos 2 x-\cos 2 \alpha)}{(\cos x-\cos \alpha)} d x=?$ A. $2 \sin x+2 x \cos \alpha+C$ B. $2 \sin x-2 x \cos \alpha+C$ C. $-2 \sin x+2 x \cos \alpha+C$ D. $-2 \sin x-2 x \cos \alpha+C$ Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\cos 2 x}{\cos ^{2} x \sin ^{2} x} d x=?$ A. $-\cot x-\tan x+C$ B. $-\cot x+\tan x+C$ C. $\cot x-\tan x+C$ D. $\cot x+\tan x+C$ Solution:...
Read More →A human body excretes (removes by waste discharge, sweating etc.) certain materials
Question: A human body excretes (removes by waste discharge, sweating etc.) certain materials by a law similar to radioactivity. If technetium is injected in some from in a human body, the body excretes half the amount in 24 hours. A patient is given an injection containing ${ }^{99} \mathrm{Tc}$. This isotope is radioactive with a half-life of 6 hours. The activity from the body just after the injection is $6 \mu \mathrm{Ci}$. How much time will elapse before the activity falls to $3 \mu \mathr...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{1}{\sin ^{2} x \cos ^{2} x} d x=?$ A. $\tan x+\cot x+C$ B. $-\tan x+\cot x+C$ C. $\tan x-\cot x+C$ D. none of these Solution:...
Read More →A sample contains a mixture of
Question: A sample contains a mixture of ${ }^{108} \mathrm{Ag}$ and ${ }^{110} \mathrm{Ag}$ isotopes each having an activity of $8.0 \times 10^{8}$ disintegrations per second. ${ }^{110} \mathrm{Ag}$ is known to have a larger half-life than ${ }^{108} \mathrm{Ag}$. The activity $\mathrm{A}$ is measured as a function of time and the following data are obtained. (a) Plot In $\left(\mathrm{A} / \mathrm{A}_{0}\right)$ versus time. (b) See that for large values of time, the plot is nearly linear. De...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{(1-\cos 2 x)}{(1+\cos 2 x)} d x=?$ A. $\tan x+x+C$ B. $\tan \mathrm{x}-\mathrm{x}+\mathrm{C}$ C. $-\tan \mathrm{x}+\mathrm{x}+\mathrm{C}$ D. $-\tan x-x+C$ Solution:...
Read More →Can disintegrate either by emitting an ????-particle or by emitting a 83212Bi-particle.
Question: Can disintegrate either by emitting an $\alpha$-particle or by emitting a 83212Bi-particle. (a) Write the two equations showing the products of the decays. (b) The probabilities of disintegration by $\alpha$-and $\beta$-decays are in ratio $7 / 13$. The overall half-life of ${ }^{212} \mathrm{Bi}$ is one hour. If $1 \mathrm{~g}$ of pure ${ }^{212} \mathrm{Bi}$ is taken at $12: 00$ noon, what will be the composition of this sample at 1 p.m. the same day? Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\sec x}{(\sec x+\tan x)} d x=?$ A. $\tan x+\sec x+C$ B. $\tan x-\sec x+C$ C. $-\tan x+\sec x+C$ D. $-\tan x-\sec x+C$ Solution:...
Read More →A vessel of volume 125cm3 contains tritium (3H, t1/2=12.3y) at 500 kPa and 300k.
Question: A vessel of volume $125 \mathrm{~cm}^{3}$ contains tritium $\left({ }^{3} \mathrm{H}, \mathrm{t}_{1 / 2}=12.3 \mathrm{y}\right)$ at $500 \mathrm{kPa}$ and $300 \mathrm{k}$. Calculate the activity of the gas. PV=nRT= $\frac{m}{n} R T$ PV=NKT Solution:...
Read More →In an agricultural experiment, a solution containing 1 mole of
Question: In an agricultural experiment, a solution containing 1 mole of a radioactive material ( $\mathrm{t}_{1 / 2}=14.3$ days) was injected into the roots of a plant. The plant was allowed 70 hours to settle down and then activity was measured in its fruit. If the activity measured was $1 \mu \mathrm{Ci}$, what percent of activity is transmitted from the root to the fruit in steady state? Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \operatorname{cosec} x(\operatorname{cosec} x+\cot x) d x=?$ A. $\cot x-\operatorname{cosec} x+C$ B. $-\cot x+\operatorname{cosec} x+C$ C. $\cot x+\operatorname{cosec} x+C$ D. $-\cot x-\operatorname{cosec} x+C$ Solution:...
Read More →Consider the situation of the previous problem.
Question: Consider the situation of the previous problem. Suppose the production of the radioactive isotope starts at $t=0$. Find the number of active nuclei at time $t$. Solution:...
Read More →A radioactive isotope is being produced at a constant rate
Question: A radioactive isotope is being produced at a constant rate $\mathrm{dN} / \mathrm{dt}=\mathrm{R}$ in an experiment. The isotope has a half-life $\mathrm{t}_{1 / 2}$. Show that after a time $tt_{1 / 2}$ the number of active nuclei will become constant. Find the value of this constant. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int 2^{\log x} d x=?$ A. $\frac{2^{\log x+1}}{(\log x+1)}+C$ B. $\frac{\mathrm{x}^{(\log 2+1)}}{(\log 2+1)}+\mathrm{C}$ C. $\frac{2^{\log x}}{\log 2}+C$ 2adc D. $\frac{2^{\log x}}{2}+C$ Solution:...
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