MCQ 11 Mark
Find the value of $12.9g - 7.05g.$
- A
$5.84g$
- ✓
$5.8g$
- C
$5.86g$
- D
$5.9g$
AnswerCorrect option: B. $5.8g$
View full question & answer→MCQ 21 Mark
Obtain the dimensional equation for universal gas constant.
- ✓
$[\text{ML}^2\text{T}^{-2}]\text{ mol }^{-1}\text{K}^{-1}$
- B
$[\text{M}^2\text{LT}^{-1}\text{mol }^{-2}\text{K}^{-2}]$
- C
$[\text{ML}^{2}\text{L}\text{T}^{-1}\text{ mol}^{-1}\text{K}^{-1}]$
- D
$[\text{ML}^{3}\text{L}\text{T}^{-1}\text{ mol}^{-1}\text{K}^{-2}]$
AnswerCorrect option: A. $[\text{ML}^2\text{T}^{-2}]\text{ mol }^{-1}\text{K}^{-1}$
According to ideal gas equation for universal gas constant.
i.e., $\text{pV = nR}T,$ where $n$ is the number of moles of gases.
$\text{R}=\frac{(\text{p})(\text{V})}{(\text{n})(\text{T})}=\frac{[\text{ML}^{-1}\text{T}^2][\text{L}^3]}{{[\text{mol}][\text{K}]}}$
$=[\text{ML}^2\text{T}^{-2}\text{mol}^{-1}\text{K}^{-1}]$
View full question & answer→MCQ 31 Mark
Which one of the following is not a unit of British system of units?
MCQ 41 Mark
The quantity having the same unit in all system of unit is:
AnswerTime is the quantity which has the same unit in all systems of unit, i.e. second. Other three quantities, i.e. mass, length and temperature have different units in different systems.
View full question & answer→MCQ 51 Mark
Age of the universe is about $10^{10}$ year, whereas the mankind has existed for $10^6$ year. For how many seconds would the man have existed if age of universe were $1$ day?
- A
$9.2s$
- B
$10.2s$
- ✓
$8.6s$
- D
$10.5s$
AnswerCorrect option: C. $8.6s$
View full question & answer→MCQ 61 Mark
Which of the following has neither units nor dimensions?
MCQ 71 Mark
Dimension formula of $\text{AQ}$, heat supplied to the system is:
- ✓
$\ce{[ML^2T^{-2}]}$
- B
$\ce{[MLT^{-2}]}$
- C
$\ce{[ML^2T^{-1}]}$
- D
$\ce{[MLT^1]}$
AnswerCorrect option: A. $\ce{[ML^2T^{-2}]}$
View full question & answer→MCQ 81 Mark
The dimensions of entropy are:
- A
$[\text{M}^0\text{L}^{-1}\text{T}^0\text{K}]$
- B
$[\text{M}^0\text{L}^{-2}\text{T}^{0}\text{k}^2]$
- C
$[\text{MLT}^{-2}\text{K}]$
- ✓
$[\text{ML}^2\text{T}^{-2}\text{k}^{-1}]$
AnswerCorrect option: D. $[\text{ML}^2\text{T}^{-2}\text{k}^{-1}]$
View full question & answer→MCQ 91 Mark
The length and breadth of a metal sheet are $3.124m$ and $3.002m$ respectively. The area of this sheet up to four correct significant figures is:
- A
$9.37m^2$
- ✓
$9.378m^2$
- C
$9.3782m^2$
- D
$9.378248m^2$
AnswerCorrect option: B. $9.378m^2$
As area $=$ length $\times$ breadth, therefore, as per rules numerical value of area has four significant digits.
View full question & answer→MCQ 101 Mark
Which of the following systems of units is not based on units of mass, length and time alone?
- ✓
$\text{S.I.}$
- B
$\text{MKS}.$
- C
$\text{FPS.}$
- D
$\text{CGS.}$
AnswerCorrect option: A. $\text{S.I.}$
International system $\text{(SI)}$ is not based on units of mass, length and time alone.
View full question & answer→MCQ 111 Mark
Percentage errors in the measurement of mass and speed are 2% and 3%, respectively. The error in the estimation of kinetic energy obtained by measuring mass and speed will be:
AnswerKinetic energy, $\text{K}=\frac{1}{2}\text{mv}^2$ $\therefore\frac{\Delta\text{K}}{\text{K}}\times100=\frac{\Delta\text{m}}{\text{m}}\times100+\frac{2\Delta\text{v}}{\text{v}}\times100$ $=2\%+2\times3\%=8\%$
View full question & answer→MCQ 121 Mark
The pair$(s)$ of physical quantities that have the same dimensions is $($are$):$
- A
Volumetric strain and coefficient of friction.
- B
Disintegration constant of a radioactive substance and frequency of light wave.
- ✓
Heat capacity and gravitational potential.
- D
Planck's constant and torque.
AnswerCorrect option: C. Heat capacity and gravitational potential.
Volumetric strain $\frac{\Delta\text{V}}{\text{V}}=\frac{\text{L}^3}{\text{L}^3}=1$
Coefficient of friction $\mu=\frac{\text{F}}{\text{R}}=\frac{\text{MLT}^{-2}}{\text{MLT}^{-2}}=1$
$\lambda=\frac{0.693}{\text{T}}=\text{T}^{-1}$
$\text{v}=\frac{1}{\text{T}}=\text{T}^{-1}$
Both have same dimensions.
Heat capacity is measured in $\text{cal/kg}$ and gravitational potential is measured in $\text{joule/ kg.}$ Both have the same dimensions $\ce{[L^2T^{-2}]}$.
View full question & answer→MCQ 131 Mark
If the size of bacteria is $1u$, then the number of bacteria in $1m$ length will be:
View full question & answer→MCQ 141 Mark
Which of the following is a dimensional constant?
MCQ 151 Mark
If $C$ represents capacitance and $R$ represents resistance, then the unit of $\ce{CR^2}$ are:
$A.$ Henry
$B.$ Volt $-$ Second/ Ampere
$C.$ Volt/ ampere
$D.$ Joule/ampere$^2$
- A
$A$ and $B$
- B
$B$ and $D$
- ✓
$A , B$ and $D$
- D
AnswerCorrect option: C. $A , B$ and $D$
We know that $\frac{\text{L}}{\text{R}}=\text{t}$ and $\text{RC}=\text{t}$
$\frac{\text{L}}{\text{R}}=\text{RC}$ or $\text{CR}^2=\text{L}$
Unit of $\ce{CR^2}$ are the same as unit of $L,$ which is henry.
From $\text{e}=\text{L}=\frac{\text{edt}}{\text{dI}}=\frac{\text{Volt sec}}{\text{Ampere}}$
$\text{From}\text{U}=\frac{1}{2}\text{LI}^2,\text{L}=\frac{2\text{U}}{\text{I}^2}=\frac{\text{Joule}}{\text{Ampere}^2}$
View full question & answer→MCQ 161 Mark
Which of the following time measuring devices is most precise?
- A
- B
- C
- ✓
An atomic clock. Give reason for your answer.
AnswerCorrect option: D. An atomic clock. Give reason for your answer.
The least count of a wall clock, stop watch, digital watch and atomic clock are $1 \sec, \frac{1}{10}\text{sec},\frac{1}{100}\text{sec}$ and $\frac{1}{10^{13}}\text{sec}$ respectively.
So atomic clock is most precise.
View full question & answer→MCQ 171 Mark
The velocity of a body moving in viscous medium is given by $\text{v}=\frac{\text{A}}{\text{B}}\Big[1-\text{e}^{\frac{-\text{t}}{\text{B}}}\Big]$
- A
$[\text{M}^0\text{L}^0\text{T}^0]$
- ✓
$[\text{M}^0\text{L}^1\text{T}^0]$
- C
$[\text{M}^0\text{L}^1\text{T}^{-2}]$
- D
$[\text{M}^1\text{L}^1\text{T}^{-1}]$
AnswerCorrect option: B. $[\text{M}^0\text{L}^1\text{T}^0]$
View full question & answer→MCQ 181 Mark
Size of the universe is of the order of:
- A
$10^{40}m$
- ✓
$10^{26}m$
- C
$10^{18}m$
- D
$10^{44}m$
AnswerCorrect option: B. $10^{26}m$
View full question & answer→MCQ 191 Mark
When $1m, 1\ kg$ and $1$ min are taken as the fundamental units, the magnitude of the force is $36$ units. What will be the value of this force in $\text{CGS}$ system?
- A
$10^5$ dyne
- ✓
$10^3$ dyne
- C
$10^8$ dyne
- D
$10^4$ dyne
AnswerCorrect option: B. $10^3$ dyne
As, dimensional formula of force $\ce{= [MLT^{-2}]}$
$n_1 = 36, M_1 = 1\ kg, L_1 = 1m, T_1 = 1\ min = 60s$
$n_2= ?, M_2 = 1g, L_2 = 1\ cm, T_2= 1s$
So, conversion of $36$ units into $\text{CGS}$ system
$\text{n}_2=\text{n}_1\Big[\frac{\text{M}_1}{\text{M}_2}\Big]^{\text{a}}\Big[\frac{\text{L}_1}{\text{L}_2}\Big]^{\text{b}}\Big[\frac{\text{T}_1}{\text{T}_2}\Big]^{\text{c}}$
$\text{n}_2=\text{n}_1\Big[\frac{\text{1Kg}}{\text{1g}}\Big]^{\text{1}}\Big[\frac{\text{1m}}{\text{1cm}}\Big]^{\text{1}}\Big[\frac{\text{1 min}}{\text{1 s}}\Big]^{\text{c}}$
$=36\Big[\frac{1000\text{g}}{1\text{g}}\Big]\Big[\frac{100\text{cm}}{1\text{cm}}\Big]^1\Big[\frac{60\text{s}}{1\text{s}}\Big]^{-2}$
$=10^3\text{ dyne}$
View full question & answer→MCQ 201 Mark
If $P, Q, R$ are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?
- ✓
$\frac{(\text{P}-\text{Q})}{\text{R}}$
- B
$\frac{\text{PQ}}{\text{R}}$
- C
$\frac{(\text{PR}-\text{Q}^2)}{\text{R}}$
- D
$\frac{(\text{R}+\text{Q})}{\text{P}}$
AnswerCorrect option: A. $\frac{(\text{P}-\text{Q})}{\text{R}}$
In option $(a)$ and $(e)$ there is term $(P - Q)$ and $(R + Q)$ as different physical quantities can never be added or subtracted so option $(a)$ and $(e)$ can never be meaningful.
In option $(b)$, the dimension of $PQ$ may be equal to dimension of $R$ so option $(b)$ can be possible. Similarly dimensions of $PR$ and $Q^2$ may be equal and gives the possibility of option $(d)$.
In option $(c)$, there is no addition subtraction gives the possibilities of option $(c)$.
Hence, verifies the right option $(a)$ and $(e)$.
View full question & answer→MCQ 211 Mark
The dimensional formula for latent heat is:
- ✓
$\ce{M^0L^2T^{-1}}$
- B
$\ce{ML^2T^{-1}}$
- C
$\ce{MLT^{-2}}$
- D
$\ce{ML^2T^{-2}}$
AnswerCorrect option: A. $\ce{M^0L^2T^{-1}}$
View full question & answer→MCQ 221 Mark
If $R$ and $L$ represent resistance and self$-$inductance respectively, which of the following combinations has the dimensions of frequency?
- ✓
$\frac{\text{R}}{\text{L}}$
- B
$\frac{\text{L}}{\text{R}}$
- C
$\sqrt{\frac{\text{R}}{\text{L}}}$
- D
$\sqrt{\frac{\text{L}}{\text{R}}}$
AnswerCorrect option: A. $\frac{\text{R}}{\text{L}}$
View full question & answer→MCQ 231 Mark
Which of the following is not a physical quantity?
MCQ 241 Mark
View full question & answer→MCQ 251 Mark
Which one of the following physical quantities is not a fundamental quantity?
- A
- B
Thermodynamic temperature.
- C
- ✓
View full question & answer→MCQ 261 Mark
A device which is used for measurement of length to an accuracy of about $10^{-4}m,$ is:
- A
- B
- C
- ✓
Either $(a)$ or $(b).$
AnswerCorrect option: D. Either $(a)$ or $(b).$
View full question & answer→MCQ 271 Mark
Which of the following are not a unit of time?
AnswerCorrect option: D. $A$ and $C$
Parsec and light year are those practical units which are used to measure large distances.
For example:
The distance between sun and earth or other celestial bodies.
So they are the units of length not time. Here, second and year represent time.
$1$ light year $($distance that light travels in $1$ year with speed $= 3 \times 10^8m/s.) = 9.46 \times 10^{11}m$ And $1$ par see $= 3.08 \times 10^{16}m$
View full question & answer→MCQ 281 Mark
The number of significant figures in $0.06900$ is:
AnswerIn the number $0.06900,$ two zeroes before six are not significant figure and two zero on right side of $9$ are significant figures. Significant figures are underlined, so verifies option $(b).$
View full question & answer→MCQ 291 Mark
Dimensions of gravitational constant are:
- ✓
$\text{M}^{-1}\text{L}^3\text{T}^{-2}$
- B
$\text{M}^{-2}\text{L}^3\text{T}^{-1}$
- C
$\text{M}^{3}\text{L}^{-1}\text{T}^{-2}$
- D
$\text{M}^{-1}\text{L}^2\text{T}^{-3}$
AnswerCorrect option: A. $\text{M}^{-1}\text{L}^3\text{T}^{-2}$
From $\text{F}=\frac{\text{G}\text{m}_1\text{m}_2}{\text{r}^2}$
$\text{G}=\frac{\text{F}\text{r}^2}{\text{m}_1\text{m}_2}=\frac{(\text{MLT}^{-2})\text{L}^2}{\text{M}^2}=[\text{M}^{-1}\text{L}^3\text{T}^{-2}]$
View full question & answer→MCQ 301 Mark
$\text{SI}$ unit of capacitance is:
AnswerCorrect option: C. $\ce{coulomb (volt)^{-1}}$
$\text{SI}$ unit of capacitance is coulomb $\ce{(volt)^{-1}}$. However, $\text{ohm-second}$ is the unit of inductance, $Wb$ is the unit of magnetic flux and $\ce{A-m^2}$ is the unit of magnetic moment.
View full question & answer→MCQ 311 Mark
We measure the period of oscillation of a simple pendulum. In successive measurements, the readings turn out to be $2.63s, 2.56s$ and $2.42s.$ Calculate the mean absolute error.
- ✓
$0.076s$
- B
$0.42s$
- C
$0.92s$
- D
$0.10s$
AnswerCorrect option: A. $0.076s$
View full question & answer→MCQ 321 Mark
Which of the following sets cannot enter into the list of fundamental quantities in any system of units?
- ✓
Length, time and velocity.
- B
Length, mass and velocity.
- C
- D
AnswerCorrect option: A. Length, time and velocity.
Length, time and velocity can be deduced from one another. Therefore, they cannot enter into the list of fundamental quantities in any system.
View full question & answer→MCQ 331 Mark
The numbers $2.745$ and $2.735$ on rounding off to $3$ significant figures will give:
- A
$2.75$ and $2.74.$
- B
$2.74$ and $2.73.$
- C
$2.75$ and $2.73.$
- ✓
$2.74$ and $2.74.$
AnswerCorrect option: D. $2.74$ and $2.74.$
Key concept: While rounding off measurements, we use the following rules by convention:
- If the digit to be dropped is less than $5,$ then the preceding digit is left unchanged.
- If the digit to be dropped is more than $5,$ then the preceding digit is raised by one.
- If the digit to be dropped is $5$ followed by digits other than zero, then the preceding digit is raised by one.
- If digit to be dropped is $5$ or $5$ followed by zeros, then preceding digit is left unchanged, if it is even.
- If digit to be dropped is $5$ or $5$ followed by zeros, then the preceding digit is raised by one, if it is odd.
Units and Measurements,
Let us round off $2.745$ to $3$ significant figures.
Here the digit to be dropped is $5,$ then preceding digit is left unchanged, if it is even.
Hence on rounding off $2.745,$ it would be $2.74.$
Now consider $2.737,$ here also the digit to be dropped is $5,$ then the preceding digit is raised by one, if it is odd. Hence on rounding off $2.735$ to $3$ significant figures, it would be $2.74.$ View full question & answer→MCQ 341 Mark
The surface area of a solid cylinder of radius $2.0\ cm$ and height $A \ cm$ is equal to $1.5 \times 10^4(mm)^2$. Here, $A$ refers to:
- A
$0.9\ cm$
- ✓
$10\ cm$
- C
$30\ cm$
- D
$15\ cm$
AnswerCorrect option: B. $10\ cm$
View full question & answer→MCQ 351 Mark
View full question & answer→MCQ 361 Mark
Which of the following quantities can be written in $\text{SI}$ units in $\ce{kg^2 m^2 A^{-2}S^{-3}}?$
Answer$\text{R}=\text{M}^1\text{L}^2\text{T}^{-3}\text{A}^{-2}\dots$ from
$\text{R}=\frac{\text{V}}{\text{I}}=\frac{\frac{\text{W}}{\text{q}}}{\text{I}}=\frac{\text{ML}^2\text{T}^{-2}}{\text{AT A}}=[\text{M}^1\text{L}^2\text{T}^{-3}\text{A}^{-2}]$
$\text{C}=\frac{\text{q}}{\text{V}}=\frac{\text{q}}{{\frac{\text{W}}{\text{q}}}}=\frac{\text{q}^2}{\text{W}}=\frac{(\text{AT})^2}{\text{ML}^2\text{T}^{-2}}=[\text{M}^{-1}\text{L}^{-2}\text{T}^{4}\text{A}^{2}]$
$\text{I}=\frac{\text{E}}{\frac{\text{dI}}{\text{dt}}}=\frac{\frac{\text{W}}{\text{q}}}{\frac{\text{dI}}{\text{dt}}}=\frac{\text{ML}^2\text{T}^{-2}\text{T}}{\text{AT A}}=[\text{ML}^2\text{T}^{-2}\text{T}^{-2}]$
Now $\text{ RC}=[\text{M}^1\text{L}^2\text{T}^{-3}\text{T}^{-2}][\text{M}^{-1}\text{L}^{-2}\text{T}^{4}\text{T}^2]=\text{T}^{1}$
And $\frac{\text{L}}{\text{R}}=\frac{[\text{ML}^2\text{T}^{-2}\text{A}^{-2}]}{[\text{M}^1\text{L}^2\text{T}^{-3}\text{A}^{-2}]}=\text{T}^1$
View full question & answer→MCQ 371 Mark
Number of degrees present in one radian is:
- A
$58^\circ$
- ✓
$57.3^\circ$
- C
$56.3^\circ$
- D
$56^\circ$
AnswerCorrect option: B. $57.3^\circ$
We know that,
$\pi\text{ radian}=180^{\circ}$
$1\text{ radian}=\frac{180}{\pi}=\frac{180}{22}\times7=57.3^{\circ}$
View full question & answer→MCQ 381 Mark
Calculate the relative errors in measurement of mass $1.02\text{g}\pm0.01\text{g}$ and $9.89\text{g}\pm0.01\text{g}$
- A
$\pm1\%$ and $\pm0.2\%$
- ✓
$\pm1\%$ and $\pm0.1\%$
- C
$\pm2\%$ and $\pm0.3\%$
- D
$\pm3\%$ and $\pm0.4\%$
AnswerCorrect option: B. $\pm1\%$ and $\pm0.1\%$
View full question & answer→MCQ 391 Mark
Force $(F)$ and density $(d)$ are related as $\text{F}=\frac{\alpha}{\beta+\sqrt{\text{d}}}$ Then, the dimensions of a and $B$ are:
- A
$[\text{M}^{\frac{3}{2}}\text{L}^{\frac{-1}{2}}\text{T}^{-2}],[\text{ML}^{-3}\text{T}^0]$
- ✓
$[\text{M}^{\frac{3}{2}}\text{L}^{\frac{-1}{2}}\text{T}^{-2}],[\text{M}^{\frac{1}{2}}\text{L}^{\frac{-3}{2}}\text{T}^0]$
- C
$[\text{M}^2\text{L}^2\text{T}^{-1}],[\text{ML}^{-1}\text{T}^{\frac{-3}{2}}]$
- D
$[\text{M LT}^{-2}],[\text{ML}^{-2}\text{T}^{\frac{-2}{3}}]$
AnswerCorrect option: B. $[\text{M}^{\frac{3}{2}}\text{L}^{\frac{-1}{2}}\text{T}^{-2}],[\text{M}^{\frac{1}{2}}\text{L}^{\frac{-3}{2}}\text{T}^0]$
View full question & answer→MCQ 401 Mark
- A
- B
Ampere$-$second.
- C
- ✓
$B$ and $C$
AnswerCorrect option: D. $B$ and $C$
Unit of charge $=$ Coulomb $\ce{= Ampere \times Sec.}$
View full question & answer→MCQ 411 Mark
The density of a cube is measured by measuring its mass and the length of its sides. If the maximum errors in the measurement of mass and length are $3\%$ and $2\%$ respectively, then the maximum error in the measurement of density is:
View full question & answer→MCQ 421 Mark
Which of the following measurements is most precise?
- ✓
$5.00\ mm.$
- B
$5.00\ cm.$
- C
$5.00m.$
- D
$5.00\ km.$
AnswerCorrect option: A. $5.00\ mm.$
All the measurements are upto two places of decimal, least unit is $mm.$
so $5.00\ mm$ measurement is most precise.
Hence, verifies answer $(a).$
View full question & answer→MCQ 431 Mark
To determine the number of significant figures, scientific notation is
- A
$a^b$
- ✓
$a \times 10^b$
- C
$a \times 10^2$
- D
$a \times 10^4$
AnswerCorrect option: B. $a \times 10^b$
View full question & answer→MCQ 441 Mark
The mean length of an object is $5\ cm.$ Which of the following measurements is most accurate?
- ✓
$4.9\ cm.$
- B
$4.805\ cm.$
- C
$5.25\ cm.$
- D
$5.4\ cm.$
AnswerCorrect option: A. $4.9\ cm.$
Error or absolute error
$|\Delta\text{a}_1|=|5-4.9|=0.1\text{cm},\ |\Delta\text{a}_2|=|5-4.805|=0.195\text{cm}$
$|\Delta\text{a}_3|=|5-5.25|=0.25\text{cm},\ |\Delta\text{a}_4|=|5-5.4|=0.4\text{cm}$
$|\Delta\text{a}_1|$ is minimum.
Hence verifies option $(a).$
View full question & answer→MCQ 451 Mark
Which physical quantities have same dimension?
MCQ 461 Mark
The dimensions of capacitance are $($where $Q$ is the dimension of charge$):$
AnswerCorrect option: A. $\ce{M^{-1}L^{-2}T^2Q^2}$
View full question & answer→MCQ 471 Mark
If $\ce{P, Q, R}$ are physical quantities, having different dimensions, which of following combinations can never be meaningful quantity?
- ✓
$\Big(\frac{\text{P}-\text{Q}}{\text{R}}\Big)$
- B
$\text{PQ}-\text{R}$
- C
$\frac{\text{PQ}}{\text{R}}$
- D
$\frac{\text{PR}-\text{Q}^2}{\text{R}}$
AnswerCorrect option: A. $\Big(\frac{\text{P}-\text{Q}}{\text{R}}\Big)$
View full question & answer→MCQ 481 Mark
The velocity $v$ of a particle is given in terms of time $t$ is:
- A
$\text{L}^2;\text{TLT}^{-2}$
- B
$\text{LT}^2;\text{LT};\text{L}$
- ✓
$\text{LT}^{-2};\text{L};\text{T}$
- D
$\text{L};\text{LT};\text{T}^2$
AnswerCorrect option: C. $\text{LT}^{-2};\text{L};\text{T}$
As $c$ is added to $t,$ therefore, $c$ has the dimensions of $[T]$
As $,\frac{\text{b}}{\text{t}}=\text{v}$
$\therefore\text{b}=\text{v}\times\text{t}=\text{LT}^{-1}\times\text{T}=[\text{L}]$
From $\text{v}=\text{at},\text{a}=\frac{\text{v}}{\text{t}}=\frac{\text{LT}^{-1}}{\text{T}}=[\text{LT}^{-2}]$
View full question & answer→MCQ 491 Mark
A dimensionless quantity:
AnswerA dimensionless quantity may have a unit. For example, angle has a unit but is dimensionless.
View full question & answer→MCQ 501 Mark
The length and breadth of a rectangular sheet are $16.2\ cm$ and $10.1\ cm,$ respectively. The area of the sheet in appropriate significant figures and error is:
AnswerCorrect option: A. $164\pm3\text{cm}^2$
View full question & answer→