Under an adiabatic process, the volume of an ideal gas gets doubled.
Question: Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from $\tau_{1}$ to $\tau_{2}$. If $\frac{C_{p}}{C_{v}}=\gamma$ for this gas then a good estimate for $\frac{\tau_{2}}{\tau_{1}}$ is given by:(1) (2) ${ }^{\frac{1+\gamma}{2}}$(2) $\frac{1}{2}$(3) $\left(\frac{1}{2}\right)^{\gamma}$(4) $\left(\frac{1}{2}\right)^{\frac{\gamma+1}{2}}$Correct Option: 1 Solution: (1) We know that Relaxation time, $T \pro...
Read More →The number of
Question: The number of $s p^{2}$ hybridised carbons present in "Aspartame" is _______________________ Solution: (9.00) Structure of aspartame is shown above. It is a methyl ester of dipeptide formed from aspartic acid and phenylalanine. $s p^{2}$ hybridised carbon atoms are shown by the star mark in the structure....
Read More →The length of a rectangle is twice its breadth and its area is 288 cm2
Question: The length of a rectangle is twice its breadth and its area is 288 cm2. Find the dimensions of the rectangle. Solution: Let the length and breadth of the rectangle be $2 x \mathrm{~m}$ and $x \mathrm{~m}$, respectively. According to the question: $2 x \times x=288$ $\Rightarrow 2 x^{2}=288$ $\Rightarrow x^{2}=144$ $\Rightarrow x=12$ or $x=-12$ $\Rightarrow x=12 \quad(\because x$ cannot be negative $)$ $\therefore$ Length $=2 \times 12=24 \mathrm{~m}$ Breadth $=12 \mathrm{~m}$...
Read More →If one end of a focal chord
Question: If one end of a focal chord $\mathrm{AB}$ of the parabola $y^{2}=8 x$ is at A $\left(\frac{1}{2},-2\right)$, then the equation of the tangent to it at B is:(1) $2 x+y-24=0$(2) $x-2 y+8=0$(3) $x+2 y+8=0$(4) $2 x-y-24=0$Correct Option: , 2 Solution: Let parabola $y^{2}=8 x$ at point $\left(\frac{1}{2},-2\right)$ is $\left(2 t^{2}, 4 t\right)$ $\Rightarrow \quad t=\frac{-1}{2}$ Parameter of other end of focal chord is 2 So, coordinates of $B$ is $(8,8)$ $\Rightarrow$ Equation of tangent a...
Read More →The number of chiral carbons in chloramphenicol is
Question: The number of chiral carbons in chloramphenicol is _________. Solution: (2.00)...
Read More →Two moles of an ideal gas
Question: Two moles of an ideal gas with $\frac{C_{p}}{C_{V}}=\frac{5}{3}$ are mixed with 3 moles of another ideal gas with $\frac{C_{p}}{C_{V}}=\frac{4}{3}$. The value of $\frac{C_{p}}{C_{V}}$ for the mixture is:(1) $1.45$(2) $1.50$(3) $1.47$(4) $1.42$Correct Option: , 4 Solution: (4) Using, $\gamma_{\text {mixture }}=\frac{n_{1} C_{p_{1}}+n_{2} C_{p_{2}}}{n_{1} C_{v_{1}}+n_{2} C_{v_{2}}}$ $\Rightarrow \frac{n_{1}}{\gamma_{1}-1}+\frac{n_{2}}{\gamma_{2}-1}=\frac{n_{1}+n_{2}}{\gamma_{m}-1}$ $\Rig...
Read More →The dipole moments of
Question: The dipole moments of $\mathrm{CCl}_{4}, \mathrm{CHCl}_{3}$ and $\mathrm{CH}_{4}$ are in the order:$\mathrm{CHCl}_{3}\mathrm{CH}_{4}=\mathrm{CCl}_{4}$$\mathrm{CCl}_{4}\mathrm{CH}_{4}\mathrm{CHCl}_{3}$$\mathrm{CH}_{4}\mathrm{CCl}_{4}\mathrm{CHCl}_{3}$$\mathrm{CH}_{4}=\mathrm{CCl}_{4}\mathrm{CHCl}_{3}$Correct Option: , 4 Solution:...
Read More →Two water taps together can fill a tank in 6 hours. The tap of larger diameter takes 9 hours less than the smaller one to fill the tank separately.
Question: Two water taps together can fill a tank in 6 hours. The tap of larger diameter takes 9 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank. Solution: Let the tap of smaller diameter fill the tank inxhours. Time taken by the tap of larger diameter to fill the tank = (x 9) hSuppose the volume of the tank beV.Volume of the tank filled by the tap of smaller diameter inxhours =V $\therefore$ Volume of the tank filled by t...
Read More →Let a line y=m x(m>0) intersect the parabola
Question: Let a line $y=m x(m0)$ intersect the parabola, $y^{2}=x$ at a point $P$, other than the origin. Let the tangent to it at $P$ meet the $x$-axis at the point $Q$, If area $(\Delta O P Q)=4$ sq. units, then $m$ is equal to________. Solution: Let the coordinates of $P=P\left(t^{2}, t\right)$ Tangent at $P\left(t^{2}, t\right)$ is $t y=\frac{x+t^{2}}{2}$ $\Rightarrow \quad 2 t y=x+t^{2}$ $Q\left(-t^{2}, 0\right), O(0,0)$ $\therefore \quad$ Area of $\Delta O P Q=\frac{1}{2}\left|\begin{array...
Read More →The IUPAC name of the following compound is:
Question: The IUPAC name of the following compound is: 2-nitro-4-hydroxymethyl-5-amino benzaldehyde3-amino-4-hydroxymethyl-5-nitrobenzaldehyde5 -amino-4-hydroxymethyl-2-nitrobenzaldehyde4-amino-2-formyl-5-hydroxymethyl nitrobenzeneCorrect Option: , 3 Solution: 5 -Amino-4-hydroxymethyl-2-nitrobenzaldehyde...
Read More →A litre of dry air at STP expands adiabatically to a volume of 3 litres.
Question: A litre of dry air at STP expands adiabatically to a volume of 3 litres. If $\gamma=1.40$, the work done by air is: $\left(3^{1.4}=4.6555\right)$ [Take air to be an ideal gas](1) $60.7 \mathrm{~J}$(2) $90.5 \mathrm{~J}$(3) $100.8 \mathrm{~J}$(4) $48 \mathrm{~J}$Correct Option: , 2 Solution: (2) Given, $V_{1}=1$ litre, $P_{1}=1 \mathrm{~atm}$ $V_{2}=3$ litre, $\gamma=1.40$ Using, $P V^{r}=$ constant $\Rightarrow P_{1} V_{1}^{\gamma}=P_{2} V_{2}^{\gamma}$ $\Rightarrow P_{2}=P_{1} \times\...
Read More →The locus of a point which divides the line segment
Question: The locus of a point which divides the line segment joining the point $(0,-1)$ and a point on the parabola, $x^{2}=4 y$, internally in the ratio $1: 2$, is:(1) $9 x^{2}-12 y=8$(2) $9 x^{2}-3 y=2$(3) $x^{2}-3 y=2$(4) $4 x^{2}-3 y=2$Correct Option: 1 Solution: Let point $P$ be $\left(2 t, t^{2}\right)$ and $Q$ be $(h, k)$ Using section formula, $h=\frac{2 t}{3}, k=\frac{-2+t^{2}}{3}$ Hence, locus is $3 k+2=\left(\frac{3 h}{2}\right)^{2}$ $\Rightarrow \quad 9 x^{2}=12 y+8$...
Read More →In a dilute gas at pressure P and temperature T,
Question: In a dilute gas at pressure $P$ and temperature $T$, the mean time between successive collisions of a molecule varies with $T$ is :(1) $T$(2) $\frac{1}{\sqrt{T}}$(3) $\frac{1}{T}$(4) $\sqrt{T}$Correct Option: , 2 Solution: (2) Mean free path, $\lambda=\frac{1}{\sqrt{2} \pi n d^{2}}$ where, $d=$ diameter of the molecule $n=$ number of molecules per unit volume But, mean time of collision, $\tau=\frac{\lambda}{v_{\mathrm{rms}}}$ But $v_{\mathrm{rms}}=\sqrt{\frac{3 k T}{R}}$ $\therefore \...
Read More →Which of the following compounds shows geometrical isomerism?
Question: Which of the following compounds shows geometrical isomerism?2-methylpent-2-ene4-methylpent-2-ene4-methylpent-1-ene2 -methylpent-1-eneCorrect Option: , 2 Solution:...
Read More →Two pipes running together can fill a tank in
Question: Two pipes running together can fill a tank in $11 \frac{1}{0}$ minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately. Solution: Let the time taken by one pipe to fill the tank bexminutes. Time taken by the other pipe to fill the tank = (x+ 5) minSuppose the volume of the tank beV.Volume of the tank filled by one pipe inxminutes =V $\therefore$ Volume of the tank filled by one pipe in 1 minut...
Read More →Among the following compounds, geometrical isomerism is exhibited by:
Question: Among the following compounds, geometrical isomerism is exhibited by:Both (b) and (c)Correct Option: , 4 Solution:...
Read More →Molecules of an ideal gas are known to have three translational degrees
Question: Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of $T$. The total internal energy, U of a mole of this gas, and the value of $\gamma\left(=\frac{C_{p}}{C_{v}}\right)$ are given, respectively, by:(1) $\mathrm{U}=\frac{5}{2} \mathrm{RT}$ and $\gamma=\frac{6}{5}$(2) $\mathrm{U}=5 \mathrm{RT}$ and $\gamma=\frac{7}{5}$(3) $\mathrm{U}=\frac{5}{2} \mathrm{RT}$ and $\gamma=\frac{7}{...
Read More →If y=m x+4 is a tangent to both the parabolas
Question: If $y=m x+4$ is a tangent to both the parabolas, $y^{2}=4 x$ and $x^{2}=2 b y$, then $b$ is equal to:(1) $-32$(2) $-64$(3) $-128$(4) 128Correct Option: 3, Solution: $y=m x+4$...(i) Tangent of $y^{2}=4 x$ is $\Rightarrow \quad y=m x+\frac{1}{m}$...(ii) $\left[\because\right.$ Equation of tangent of $y^{2}=4 a x$ is $\left.y=m x+\frac{a}{m}\right]$ From (i) and (ii) $4=\frac{1}{m} \Rightarrow m=\frac{1}{4}$ So, line $y=\frac{1}{4} x+4$ is also tangent to parabola $x^{2}=2 b y$, so solve ...
Read More →The increasing order of basicity of the following compounds is:
Question: The increasing order of basicity of the following compounds is: $(A)(B)(C)(D)(2)$$(B)(A)(D)(C)$$(\mathrm{D})(\mathrm{A})(\mathrm{B})(\mathrm{C})$$(B)(A)(C)(D)$Correct Option: , 2 Solution:...
Read More →Two taps running together can fill a tank in
Question: Two taps running together can fill a tank in $3 \frac{1}{13}$ hours. If one tap takes 3 hours more than the other to fill the tank then how much time will each tap take to fill the tank? Solution: Let one tap fills the tank in $x$ hours. Therefore, the other tap will fill the tank in $(x+3)$ hours. Time taken by both taps, running together, to fill the tank $=3 \frac{1}{13}$ hours $=\frac{40}{13}$ hours Part filled by one tap in 1 hour $=\frac{1}{x}$ Part filled by the other tap in 1 h...
Read More →The increasing order of basicity of the following compounds is:
Question: The increasing order of basicity of the following compounds is: $(A)(B)(C)(D)(2)$$(B)(A)(D)(C)$$(\mathrm{D})(\mathrm{A})(\mathrm{B})(\mathrm{C})$$(B)(A)(C)(D)$Correct Option: Solution:...
Read More →Nitrogen gas is at
Question: Nitrogen gas is at $300^{\circ} \mathrm{C}$ temperature. The temperature (in $\mathrm{K}$ ) at which the $\mathrm{rms}$ speed of a $\mathrm{H}_{2}$ molecule would be equal to the rms speed of a nitrogen molecule, is_______ (Molar mass of $\mathrm{N}_{2}$ gas $28 \mathrm{~g}$ ); Solution: (41) Room mean square speed is given by $v_{r m s}=\sqrt{\frac{3 R T}{M}}$ $T=$ temperature of the gas molecule We have given $v_{\mathrm{N}_{2}}=v_{\mathrm{H}_{2}}$ $\therefore \sqrt{\frac{3 R T_{\mat...
Read More →The centre of the circle passing through the point
Question: The centre of the circle passing through the point $(0,1)$ and touching the parabola $y=x^{2}$ at the point $(2,4)$ is:(1) $\left(\frac{-53}{10}, \frac{16}{5}\right)$(2) $\left(\frac{6}{5}, \frac{53}{10}\right)$(3) $\left(\frac{3}{10}, \frac{16}{5}\right)$(4) $\left(\frac{-16}{5}, \frac{53}{10}\right)$Correct Option: , 4 Solution: (d) Circle passes through $A(0,1)$ and $B(2,4)$. So its centre is the point of intersection of perpendicular bisector of $A B$ and normal to the parabola at ...
Read More →Number of molecules in a volume
Question: Number of molecules in a volume of $4 \mathrm{~cm}^{3}$ of a perfect monoatomic gas at some temperature $T$ and at a pressure of $2 \mathrm{~cm}$ of mercury is close to? (Given, mean kinetic energy of a molecule (at $T$ ) is $4 \times 10^{-14} \mathrm{erg}, g=980 \mathrm{~cm} /$ $\mathrm{s}^{2}$, density of mercury $=13.6 \mathrm{~g} / \mathrm{cm}^{3}$ )(1) $4.0 \times 10^{18}$(2) $4.0 \times 10^{16}$(3) $5.8 \times 10^{16}$(4) $5.8 \times 10^{18}$Correct Option: , 3 Solution: (3) Give...
Read More →The increasing order of the acidity of the
Question: The increasing order of the acidity of the $\alpha$-hydrogen of the following compounds is : $(\mathrm{D})(\mathrm{C})(\mathrm{A})(\mathrm{B})$$(B)(C)(A)(D)$$(\mathrm{A})(\mathrm{C})(\mathrm{D})(\mathrm{B})$$(C)(A)(B)(D)$Correct Option: 1 Solution: (a) Acidity $\propto$ stability of conjugate base Thus increasing order of acidity is $\mathrm{D}\mathrm{C}\mathrm{A}\mathrm{B}$....
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