JEE Main 2019 — 12 Apr Shift 1 (Previous Year Paper)

Which of the following combinations has the dimension of electrical resistance ($\epsilon_0$ is the permittivity of vacuum and $\mu_0$ is the permeability of vacuum)?

1. A.$\frac{\mu_0}{\epsilon_0}$
2. B.$\frac{\epsilon_0}{\mu_0}$
3. C.$\sqrt{\frac{\mu_0}{\epsilon_0}}$✓
4. D.$\sqrt{\frac{\epsilon_0}{\mu_0}}$

Correct answer: C

The trajectory of a projectile near the surface of the earth is given as $y=2x-9x^2$. If it were launched at an angle $\theta_0$ with speed $v_0$ then ($g=10\ \text{ms}^{-2}$):

1. A.$\theta_0=\sin^{-1}\left(\frac{1}{\sqrt5}\right)$ and $v_0=\frac{5}{3}\ \text{ms}^{-1}$
2. B.$\theta_0=\cos^{-1}\left(\frac{1}{\sqrt5}\right)$ and $v_0=\frac{5}{3}\ \text{ms}^{-1}$✓
3. C.$\theta_0=\sin^{-1}\left(\frac{2}{\sqrt5}\right)$ and $v_0=\frac{3}{5}\ \text{ms}^{-1}$
4. D.$\theta_0=\cos^{-1}\left(\frac{2}{\sqrt5}\right)$ and $v_0=\frac{3}{5}\ \text{ms}^{-1}$

Correct answer: B

A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of $0.70\ \text{ms}^{-1}$ with respect to the man. The speed of the man with respect to the surface is:

1. A.0.20 $\text{ms}^{-1}$✓
2. B.0.28 $\text{ms}^{-1}$
3. C.0.47 $\text{ms}^{-1}$
4. D.0.14 $\text{ms}^{-1}$

Correct answer: A

A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude $\theta_0$. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance $l$ $(l<<L)$, is close to:

1. A.$Mgl$
2. B.$Mgl(1-\theta_0^2)$
3. C.$Mgl\left(1+\frac{\theta_0^2}{2}\right)$
4. D.$Mgl(1+\theta_0^2)$✓

Correct answer: D

A circular disc of radius $b$ has a hole of radius $a$ at its centre (see figure). If the mass per unit area of the disc varies as $\left(\frac{\sigma_0}{r}\right)$, then the radius of gyration of the disc about its axis passing through the centre is:

1. A.$\frac{a+b}{2}$
2. B.$\sqrt{\frac{a^2+b^2+ab}{2}}$
3. C.$\frac{a+b}{3}$
4. D.$\sqrt{\frac{a^2+b^2+ab}{3}}$✓

Correct answer: D

A uniform rod of length $l$ is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is $T(x)$ at a distance $x$ from the axis, then which of the following graphs depicts it most closely?

1. A.Graph 1: $T(x)$ constant from $x=0$ to $x=l$
2. B.Graph 2: $T(x)$ decreasing linearly from a maximum at $x=0$ to zero at $x=l$
3. C.Graph 3: $T(x)$ increasing from zero at $x=0$, concave down, to a maximum at $x=l$
4. D.Graph 4: $T(x)$ maximum at $x=0$, decreasing as a downward parabola (concave down) to zero at $x=l$✓

Correct answer: D

A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance R from it. If $t_1$ and $t_2$ are the values of the time taken by it to hit the target in two possible ways, the product $t_1t_2$ is:

1. A.$R/2g$
2. B.$R/g$
3. C.$2R/g$✓
4. D.$R/4g$

Correct answer: C

At 40°C, a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from 40°C to 20°C it regains its original length of 0.2 m. The value of M is close to: (Coefficient of linear expansion and Young's modulus of brass are $10^{-5}$/°C and $10^{11}\ \text{N/m}^2$, respectively; $g=10\ \text{ms}^{-2}$)

1. A.9 kg✓
2. B.1.5 kg
3. C.0.9 kg
4. D.0.5 kg

Correct answer: A

When $M_1$ gram of ice at −10°C (specific heat $=0.5\ \text{cal g}^{-1}\text{°C}^{-1}$) is added to $M_2$ gram of water at 50°C, finally no ice is left and the water is at 0°C. The value of latent heat of ice, in cal $\text{g}^{-1}$ is:

1. A.$\frac{5M_1}{M_2}-50$
2. B.$\frac{50M_2}{M_1}$
3. C.$\frac{5M_2}{M_1}-5$
4. D.$\frac{50M_2}{M_1}-5$✓

Correct answer: D

A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is −180 J. The gas absorbs 250 J of heat along the path ab and 60 J along the path bc. The work done by the gas along the path abc is:

1. A.100 J
2. B.120 J
3. C.130 J✓
4. D.140 J

Correct answer: C

Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume? ($R=8.3$ J/mol K)

1. A.15.7 J/mol K
2. B.17.4 J/mol K✓
3. C.19.7 J/mol K
4. D.21.6 J/mol K

Correct answer: B

A progressive wave travelling along the positive $x$-direction is represented by $y(x,t)=A\sin(kx-\omega t+\phi)$. Its snapshot at $t=0$ is given in the figure. For this wave, the phase $\phi$ is:

1. A.0
2. B.$-\frac{\pi}{2}$
3. C.$\frac{\pi}{2}$
4. D.$\pi$✓

Correct answer: D

A submarine (A) travelling at 18 km/hr is being chased along the line of its velocity by another submarine (B) travelling at 27 km/hr. B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of frequency $\nu$. The value of $\nu$ is close to: (Speed of sound in water $=1500\ \text{ms}^{-1}$)

1. A.502 Hz✓
2. B.499 Hz
3. C.504 Hz
4. D.507 Hz

Correct answer: A

A point dipole $\vec{p}=-p_0\hat{x}$ is kept at the origin. The potential and electric field due to this dipole on the $y$-axis at a distance $d$ are, respectively: (Take V = 0 at infinity)

1. A.$0$, $\frac{\vec{p}}{4\pi\epsilon_0d^3}$
2. B.$\frac{|\vec{p}|}{4\pi\epsilon_0d^2}$, $\frac{-\vec{p}}{4\pi\epsilon_0d^3}$
3. C.$0$, $\frac{-\vec{p}}{4\pi\epsilon_0d^3}$✓
4. D.$\frac{|\vec{p}|}{4\pi\epsilon_0d^2}$, $\frac{\vec{p}}{4\pi\epsilon_0d^3}$

Correct answer: C

Shown in the figure is a shell made of a conductor. It has inner radius $a$ and outer radius $b$, and carries charge Q. At its centre is a dipole $\vec{p}$ as shown. In this case:

1. A.surface charge density on the inner surface of the shell is zero everywhere
2. B.surface charge density on the outer surface depends on $|\vec{p}|$
3. C.surface charge density on the inner surface is uniform and equal to $\frac{(Q/2)}{4\pi a^2}$
4. D.electric field outside the shell is the same as that of a point charge at the centre of the shell✓

Correct answer: D

Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants $K_1$, $K_2$ and $K_3$. The first capacitor is filled as shown in fig. I, and the second one is filled as shown in fig II. If these two modified capacitors are charged by the same potential V, the ratio of the energy stored in the two, would be ($E_1$ refers to capacitor (I) and $E_2$ to capacitor (II)):

1. A.$\frac{E_1}{E_2}=\frac{9K_1K_2K_3}{(K_1+K_2+K_3)(K_2K_3+K_3K_1+K_1K_2)}$✓
2. B.$\frac{E_1}{E_2}=\frac{(K_1+K_2+K_3)(K_2K_3+K_3K_1+K_1K_2)}{9K_1K_2K_3}$
3. C.$\frac{E_1}{E_2}=\frac{K_1K_2K_3}{(K_1+K_2+K_3)(K_2K_3+K_3K_1+K_1K_2)}$
4. D.$\frac{E_1}{E_2}=\frac{(K_1+K_2+K_3)(K_2K_3+K_3K_1+K_1K_2)}{K_1K_2K_3}$

Correct answer: A

To verify Ohm's law, a student connects the voltmeter across the battery as, shown in the figure. The measured voltage is plotted as a function of the current, and the following graph is obtained. If $V_0$ is almost zero, identify the correct statement:

1. A.The value of the resistance R is 1.5 $\Omega$
2. B.The emf of the battery is 1.5 V and its internal resistance is 1.5 $\Omega$✓
3. C.The potential difference across the battery is 1.5 V when it sends a current of 1000 mA
4. D.The emf of the battery is 1.5 V and the value of R is 1.5 $\Omega$

Correct answer: B

The resistive network shown below is connected to a D.C. source of 16 V. The power consumed by the network is 4 Watt. The value of R is:

1. A.6 $\Omega$
2. B.8 $\Omega$✓
3. C.1 $\Omega$
4. D.16 $\Omega$

Correct answer: B

A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of $40\pi\ \text{rad s}^{-1}$ about its axis, perpendicular to its plane. If the magnetic field at its centre is $3.8\times10^{-9}$ T, then the charge carried by the ring is close to ($\mu_0=4\pi\times10^{-7}\ \text{N/A}^2$).

1. A.$4\times10^{-5}$ C
2. B.$2\times10^{-6}$ C
3. C.$7\times10^{-6}$ C
4. D.$3\times10^{-5}$ C✓

Correct answer: D

A galvanometer of resistance 100 $\Omega$ has 50 divisions on its scale and has sensitivity of 20 $\mu$A/division. It is to be converted to a voltmeter with three ranges, of 0-2V, 0-10 V and 0-20 V. The appropriate circuit to do so is:

1. A.Galvanometer G in series with $R_1$, $R_2$, $R_3$, tapped after each resistor for 2 V, 10 V, 20 V, with $R_1=1900\ \Omega$, $R_2=9900\ \Omega$, $R_3=19900\ \Omega$
2. B.Same arrangement with taps labelled 20 V, 10 V, 2 V and $R_1=19900\ \Omega$, $R_2=9900\ \Omega$, $R_3=1900\ \Omega$
3. C.Same arrangement with taps 2 V, 10 V, 20 V and $R_1=1900\ \Omega$, $R_2=8000\ \Omega$, $R_3=10000\ \Omega$✓
4. D.Same arrangement with taps 2 V, 10 V, 20 V and $R_1=2000\ \Omega$, $R_2=8000\ \Omega$, $R_3=10000\ \Omega$

Correct answer: C

A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45°, and 40 times per minute where the dip is 30°. If $B_1$ and $B_2$ are respectively the total magnetic field due to the earth at the two places, then the ratio $B_1/B_2$ is best given by:

1. A.0.7✓
2. B.1.8
3. C.2.2
4. D.3.6

Correct answer: A

An electromagnetic wave is represented by the electric field $\vec{E}=E_0\hat{n}\sin[\omega t+(6y-8z)]$. Taking unit vectors in $x$, $y$ and $z$ directions to be $\hat{i}$, $\hat{j}$, $\hat{k}$, the direction of propagation $\hat{s}$, is:

1. A.$\hat{s}=\frac{3\hat{i}-4\hat{j}}{5}$
2. B.$\hat{s}=\left(\frac{-3\hat{j}+4\hat{k}}{5}\right)$✓
3. C.$\hat{s}=\frac{-4\hat{k}+3\hat{j}}{5}$
4. D.$\hat{s}=\frac{4\hat{j}-3\hat{k}}{5}$

Correct answer: B

A concave mirror has radius of curvature of 40 cm. It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance $d$ from the surface of water. The value of $d$ is close to: (Refractive index of water = 1.33)

1. A.11.7 cm
2. B.8.8 cm✓
3. C.6.7 cm
4. D.13.4 cm

Correct answer: B

In a double slit experiment, when a thin film of thickness $t$ having refractive index $\mu$ is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of $t$ is ($\lambda$ is the wavelength of the light used):

1. A.$\frac{\lambda}{2(\mu-1)}$
2. B.$\frac{2\lambda}{(\mu-1)}$
3. C.$\frac{\lambda}{(\mu-1)}$✓
4. D.$\frac{\lambda}{(2\mu-1)}$

Correct answer: C

The value of numerical aperature of the objective lens of a microscope is 1.25. If light of wavelength 5000 Å is used, the minimum separation between two points, to be seen as distinct, will be:

1. A.0.48 $\mu$m
2. B.0.12 $\mu$m
3. C.0.38 $\mu$m
4. D.0.24 $\mu$m✓

Correct answer: D

The stopping potential $V_0$ (in volt) as a function of frequency ($\nu$) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be: (Given: Planck's constant $h=6.63\times10^{-34}$ Js, electron charge $e=1.6\times10^{-19}$ C)

1. A.1.66 eV✓
2. B.1.82 eV
3. C.1.95 eV
4. D.2.12 eV

Correct answer: A

An excited $He^+$ ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm, in making a transition to ground state. The quantum number $n$, corresponding to its initial excited state is (for photon of wavelength $\lambda$, energy $E=\frac{1240\ \text{eV}}{\lambda\ (\text{in nm})}$):

1. A.n = 7
2. B.n = 6
3. C.n = 5✓
4. D.n = 4

Correct answer: C

The truth table for the circuit given in the fig. is:

1. A.A B Y: 0 0 1; 0 1 1; 1 0 0; 1 1 0✓
2. B.A B Y: 0 0 0; 0 1 0; 1 0 1; 1 1 1
3. C.A B Y: 0 0 1; 0 1 0; 1 0 0; 1 1 0
4. D.A B Y: 0 0 1; 0 1 1; 1 0 1; 1 1 1

Correct answer: A

The transfer characteristic curve of a transistor, having input and output resistance 100 $\Omega$ and 100 k$\Omega$ respectively, is shown in the figure. The Voltage and Power gain, are respectively:

1. A.$5\times10^4$, $5\times10^6$
2. B.$5\times10^4$, $2.5\times10^6$✓
3. C.$5\times10^4$, $5\times10^5$
4. D.$2.5\times10^4$, $2.5\times10^6$

Correct answer: B

Which of the following statements is not true about RNA?

1. A.It is present in the nucleus of the cell
2. B.It has always double stranded $\alpha$-helix structure✓
3. C.It controls the synthesis of protein
4. D.It usually does not replicate

Correct answer: B

The increasing order of the $pK_b$ of the following compound is: (A) 1-(4-fluorophenyl)-3-phenylthiourea (B) 1-(4-methoxyphenyl)-3-phenylthiourea (C) 1-(4-nitrophenyl)-3-phenylthiourea (D) 1-(4-methylphenyl)-3-phenylthiourea

1. A.(A) < (C) < (D) < (B)
2. B.(B) < (D) < (C) < (A)
3. C.(B) < (D) < (A) < (C)✓
4. D.(C) < (A) < (D) < (B)

Correct answer: C

The major product of the following reaction is: 3-(3-hydroxyphenyl)propan-1-ol (benzene ring bearing $-CH_2CH_2CH_2OH$ and, meta to it, $-OH$) $\xrightarrow{\text{(1) }CrO_3\text{; (2) }SOCl_2/\Delta\text{; (3) }\Delta}$

1. A.Indan-1-one with the ring OH para to the carbonyl-bearing ring carbon (5-hydroxy-1-indanone)✓
2. B.Indan-1-one with the ring OH ortho to the carbonyl-bearing ring carbon (7-hydroxy-1-indanone)
3. C.Indan-1-one with a ring Cl ortho to the carbonyl-bearing ring carbon (7-chloro-1-indanone)
4. D.Indan-1-one with a ring Cl para to the carbonyl-bearing ring carbon (5-chloro-1-indanone)

Correct answer: A

Glucose and Galactose are having identical configuration in all the positions except position.

1. A.C − 2
2. B.C − 3
3. C.C − 4✓
4. D.C − 5

Correct answer: C

The major product of the following addition reaction is $H_3C-CH=CH_2 \xrightarrow{Cl_2/H_2O}$

1. A.$CH_3-CH(Cl)-CH_2(OH)$
2. B.$H_3C-CH(OH)-CH_2Cl$✓
3. C.$H_3C$–(epoxide) (methyloxirane, propylene oxide)
4. D.$H_3C-CO-CH_3$ (acetone)

Correct answer: B

The major products of the following reaction are: 4-Chlorophenol $\xrightarrow{\text{(1) }CHCl_3/\text{aq. NaOH; (2) HCHO, NaOH (conc.); (3) }H_3O^+}$

1. A.5-Chloro-2-hydroxybenzoic acid (OH, and ortho COOH, Cl para to OH) and methanol
2. B.4-Chloro-2-(hydroxymethyl)phenol (OH, ortho $CH_2OH$, Cl para to OH) and formic acid✓
3. C.2,5-Dihydroxybenzoic acid (OH, ortho COOH, OH para) and methanol
4. D.2-(Hydroxymethyl)benzene-1,4-diol (OH, ortho $CH_2OH$, OH para) and formic acid

Correct answer: B

Which of the following is a thermosetting polymer?

1. A.PVC
2. B.Bakelite✓
3. C.Nylon 6
4. D.Buna-N

Correct answer: B

But-2-ene on reaction with alkaline $KMnO_4$ at elevated temperature followed by acidification will give:

1. A.$CH_3-CH(OH)-CH(OH)-CH_3$
2. B.2 molecules of $CH_3CHO$
3. C.one molecule of $CH_3CHO$ and one molecule of $CH_3COOH$
4. D.2 molecules of $CH_3COOH$✓

Correct answer: D

The major product(s) obtained in the following reaction is/are: 4-Bromocyclohexene $\xrightarrow{\text{(i) }KO^tBu\text{; (ii) }O_3/Me_2S}$

1. A.$OHC-CH_2-CH_2-CHO$ and $OHC-CHO$✓
2. B.$OHC-CH_2-CH_2-CH=CH-CHO$
3. C.$OHC-CH_2-CHO$
4. D.$OHC-CH_2-CH(O^tBu)-CH_2-CH_2-CHO$

Correct answer: A

An organic compound 'A' is oxidized with $Na_2O_2$ followed by boiling with $HNO_3$. The resultant solution is then treated with ammonium molybdate to yield a yellow precipitate. Based on above observation, the element present in the given compound is:

1. A.Sulphur
2. B.Nitrogen
3. C.Fluorine
4. D.Phosphorus✓

Correct answer: D

The group number, number of valence electrons, and valency of an element with atomic number 15, respectively, are:

1. A.15, 6 and 2
2. B.16, 6 and 3
3. C.15, 5 and 3✓
4. D.16, 5 and 2

Correct answer: C

The idea of froth floatation method came from a person X and this method is related to the process Y of ores. X and Y, respectively, are:

1. A.washer man and reduction
2. B.washer woman and concentration✓
3. C.fisher woman and concentration
4. D.fisher man and reduction

Correct answer: B

The metal that gives hydrogen gas upon treatment with both acid as well as base is:

1. A.magnesium
2. B.iron
3. C.zinc✓
4. D.mercury

Correct answer: C

The correct sequence of thermal stability of the following carbonates is:

1. A.$MgCO_3<CaCO_3<SrCO_3<BaCO_3$✓
2. B.$MgCO_3<SrCO_3<CaCO_3<BaCO_3$
3. C.$BaCO_3<CaCO_3<SrCO_3<MgCO_3$
4. D.$BaCO_3<SrCO_3<CaCO_3<MgCO_3$

Correct answer: A

The correct statement among the following is:

1. A.Ni(CO)$_4$ is diamagnetic and [NiCl$_4$]$^{2-}$ and [Ni(CN)$_4$]$^{2-}$ are paramagnetic.
2. B.Ni(CO)$_4$ and [NiCl$_4$]$^{2-}$ are diamagnetic and [Ni(CN)$_4$]$^{2-}$ is paramagnetic.
3. C.[Ni(CN)$_4$]$^{2-}$ and [NiCl$_4$]$^{2-}$ are diamagnetic and Ni(CO)$_4$ is paramagnetic.
4. D.Ni(CO)$_4$ and [Ni(CN)$_4$]$^{2-}$ are diamagnetic and [NiCl$_4$]$^{2-}$ is paramagnetic.✓

Correct answer: D

The basic structural unit of feldspar, zeolites, mica, and asbestos is:

1. A.$SiO_2$
2. B.$-(Si(R)_2-O)_n-$ (R = Me)
3. C.$(SiO_3)^{2-}$
4. D.$(SiO_4)^{4-}$✓

Correct answer: D

An example of a disproportionation reaction is:

1. A.$2MnO_4^-+10I^-+16H^+\to2Mn^{2+}+5I_2+8H_2O$
2. B.$2KMnO_4\to K_2MnO_4+MnO_2+O_2$
3. C.$2CuBr\to CuBr_2+Cu$✓
4. D.$2NaBr+Cl_2\to2NaCl+Br_2$

Correct answer: C

The complex ion that will lose its crystal field stabilization energy upon oxidation of its metal to +3 state is: (Phen = 1,10-phenanthroline, and ignore pairing energy)

1. A.$[Co(phen)_3]^{2+}$
2. B.$[Ni(phen)_3]^{2+}$
3. C.$[Fe(phen)_3]^{2+}$✓
4. D.$[Zn(phen)_3]^{2+}$

Correct answer: C

Complete removal of both the axial ligands (along the $z$-axis) from an octahedral complex leads to which of the following splitting patterns? (relative orbital energies not on scale).

1. A.Energy increasing: $d_{xz},d_{yz}$ < $d_{xy}$ < $d_{z^2}$ < $d_{x^2-y^2}$
2. B.Energy increasing: $d_{xy}$ < $d_{xz},d_{yz}$ < $d_{x^2-y^2}$ < $d_{z^2}$
3. C.Energy increasing: $d_{xz},d_{yz}$ < $d_{z^2}$ < $d_{xy}$ < $d_{x^2-y^2}$✓
4. D.Energy increasing: $d_{xy}$ < $d_{yz},d_{xz}$ < $d_{z^2}$ < $d_{x^2-y^2}$

Correct answer: C

The correct set of species responsible for the photochemical smog is:

1. A.$N_2$, $O_2$, $O_3$ and hydrocarbons
2. B.$N_2$, $NO_2$ and hydrocarbons
3. C.NO, $NO_2$, $O_3$ and hydrocarbons✓
4. D.$CO_2$, $NO_2$, $SO_2$ and hydrocarbons

Correct answer: C

5 moles of $AB_2$ weigh $125\times10^{-3}$ kg and 10 moles of $A_2B_2$ weigh $300\times10^{-3}$ kg. The molar mass of A ($M_A$) and molar mass of B ($M_B$) in kg mol$^{-1}$ are:

1. A.$M_A=5\times10^{-3}$ and $M_B=10\times10^{-3}$✓
2. B.$M_A=10\times10^{-3}$ and $M_B=5\times10^{-3}$
3. C.$M_A=25\times10^{-3}$ and $M_B=50\times10^{-3}$
4. D.$M_A=50\times10^{-3}$ and $M_B=25\times10^{-3}$

Correct answer: A

An element has a face-centred cubic (fcc) structure with a cell edge of $a$. The distance between the centres of two nearest tetrahedral voids in the lattice is:

1. A.$a$
2. B.$\frac{3}{2}a$
3. C.$\frac{a}{2}$✓
4. D.$\sqrt2a$

Correct answer: C

The electrons are more likely to be found:

1. A.only in the region a
2. B.in the region a and b
3. C.only in the region c
4. D.in the region a and c✓

Correct answer: D

Enthalpy of sublimation of iodine is 24 cal $\text{g}^{-1}$ at 200 °C. If specific heat of $I_2(s)$ and $I_2$(vap) are 0.055 and 0.031 cal $\text{g}^{-1}\text{K}^{-1}$ respectively, then enthalpy of sublimation of iodine at 250 °C in cal $\text{g}^{-1}$ is:

1. A.22.8✓
2. B.11.4
3. C.5.7
4. D.2.85

Correct answer: A

An ideal gas is allowed to expand from 1 L to 10 L against a constant external pressure of 1 bar. The work done in kJ is:

1. A.−0.9✓
2. B.−2.0
3. C.+10.0
4. D.−9.0

Correct answer: A

The mole fraction of a solvent in aqueous solution of a solute is 0.8. The molality (in mol $\text{kg}^{-1}$) of the aqueous solution is:

1. A.13.88✓
2. B.$13.88\times10^{-1}$
3. C.$13.88\times10^{-2}$
4. D.$13.88\times10^{-3}$

Correct answer: A

What is the molar solubility of $Al(OH)_3$ in 0.2 M NaOH solution? Given that, solubility product of $Al(OH)_3=2.4\times10^{-24}$:

1. A.$3\times10^{-22}$✓
2. B.$3\times10^{-19}$
3. C.$12\times10^{-23}$
4. D.$12\times10^{-21}$

Correct answer: A

Given: $Co^{3+}+e^-\to Co^{2+}$; $E°=+1.81$ V $Pb^{4+}+2e^-\to Pb^{2+}$; $E°=+1.67$ V $Ce^{4+}+e^-\to Ce^{3+}$; $E°=+1.61$ V $Bi^{3+}+3e^-\to Bi$; $E°=+0.20$ V Oxidizing power of the species will increase in the order:

1. A.$Co^{3+}<Ce^{4+}<Bi^{3+}<Pb^{4+}$
2. B.$Co^{3+}<Pb^{4+}<Ce^{4+}<Bi^{3+}$
3. C.$Bi^{3+}<Ce^{4+}<Pb^{4+}<Co^{3+}$✓
4. D.$Ce^{4+}<Pb^{4+}<Bi^{3+}<Co^{3+}$

Correct answer: C

In the following reaction; $xA\to yB$ $\log_{10}\left[-\frac{d[A]}{dt}\right]=\log_{10}\left[\frac{d[B]}{dt}\right]+0.3010$ 'A' and 'B' respectively can be:

1. A.$C_2H_2$ and $C_6H_6$
2. B.n-Butane and Iso-butane
3. C.$C_2H_4$ and $C_4H_8$✓
4. D.$N_2O_4$ and $NO_2$

Correct answer: C

Peptization is a:

1. A.process of converting a colloidal solution into precipitate
2. B.process of converting precipitate into colloidal solution✓
3. C.process of converting soluble particles to form colloidal solution
4. D.process of bringing colloidal molecule into solution

Correct answer: B

For $x\in\left(0,\frac{3}{2}\right)$, let $f(x)=\sqrt{x}$, $g(x)=\tan x$ and $h(x)=\frac{1-x^2}{1+x^2}$. If $\phi(x)=((h\circ f)\circ g)(x)$, then $\phi\left(\frac{\pi}{3}\right)$ is equal to:

1. A.$\tan\frac{\pi}{12}$
2. B.$\tan\frac{5\pi}{12}$
3. C.$\tan\frac{7\pi}{12}$
4. D.$\tan\frac{11\pi}{12}$✓

Correct answer: D

If $\alpha$ and $\beta$ are the roots of the equation $375x^2-25x-2=0$, then $\lim_{n\to\infty}\sum_{r=1}^{n}\alpha^r+\lim_{n\to\infty}\sum_{r=1}^{n}\beta^r$ is equal to:

1. A.$\frac{7}{116}$
2. B.$\frac{1}{12}$✓
3. C.$\frac{29}{358}$
4. D.$\frac{21}{346}$

Correct answer: B

The equation $|z-i|=|z-1|$, $i=\sqrt{-1}$, represents:

1. A.a circle of radius 1.
2. B.a circle of radius $\frac{1}{2}$.
3. C.the line through the origin with slope −1.
4. D.the line through the origin with slope 1.✓

Correct answer: D

If $B=\begin{bmatrix}5 & 2\alpha & 1\\ 0 & 2 & 1\\ \alpha & 3 & -1\end{bmatrix}$ is the inverse of a $3\times3$ matrix A, then the sum of all values of $\alpha$ for which $\det(A)+1=0$, is:

1. A.2
2. B.1✓
3. C.0
4. D.−1

Correct answer: B

If A is a symmetric matrix and B is a skew-symmetric matrix such that $A+B=\begin{bmatrix}2 & 3\\ 5 & -1\end{bmatrix}$, then AB is equal to:

1. A.$\begin{bmatrix}-4 & 2\\ 1 & 4\end{bmatrix}$
2. B.$\begin{bmatrix}4 & -2\\ 1 & -4\end{bmatrix}$
3. C.$\begin{bmatrix}4 & -2\\ -1 & -4\end{bmatrix}$✓
4. D.$\begin{bmatrix}-4 & -2\\ -1 & 4\end{bmatrix}$

Correct answer: C

The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is:

1. A.$2^{20}-1$
2. B.$2^{20}$✓
3. C.$2^{20}+1$
4. D.$2^{21}$

Correct answer: B

The coefficient of $x^{18}$ in the product $(1+x)(1-x)^{10}(1+x+x^2)^9$ is:

1. A.84✓
2. B.126
3. C.−126
4. D.−84

Correct answer: A

Let $S_n$ denote the sum of the first $n$ terms of an A.P.. If $S_4=16$ and $S_6=-48$, then $S_{10}$ is equal to:

1. A.−260
2. B.−320✓
3. C.−380
4. D.−410

Correct answer: B

For $x\in\mathbf{R}$, let $[x]$ denote the greatest integer $\le x$, then the sum of the series $\left[-\frac{1}{3}\right]+\left[-\frac{1}{3}-\frac{1}{100}\right]+\left[-\frac{1}{3}-\frac{2}{100}\right]+\ldots+\left[-\frac{1}{3}-\frac{99}{100}\right]$ is:

1. A.−135
2. B.−153
3. C.−131
4. D.−133✓

Correct answer: D

Let $f:\mathbf{R}\to\mathbf{R}$ be a continuously differentiable function such that $f(2)=6$ and $f'(2)=\frac{1}{48}$. If $\int_6^{f(x)}4t^3dt=(x-2)g(x)$, then $\lim_{x\to2}g(x)$ is equal to:

1. A.12
2. B.18✓
3. C.24
4. D.36

Correct answer: B

If $e^y+xy=e$, the ordered pair $\left(\frac{dy}{dx},\frac{d^2y}{dx^2}\right)$ at $x=0$ is equal to:

1. A.$\left(-\frac{1}{e},\frac{1}{e^2}\right)$✓
2. B.$\left(\frac{1}{e},-\frac{1}{e^2}\right)$
3. C.$\left(\frac{1}{e},\frac{1}{e^2}\right)$
4. D.$\left(-\frac{1}{e},-\frac{1}{e^2}\right)$

Correct answer: A

A 2 m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate 25 cm/sec., then the rate (in cm/sec.) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is 1 m above the ground is:

1. A.$\frac{25}{3}$
2. B.$\frac{25}{\sqrt3}$✓
3. C.25
4. D.$25\sqrt3$

Correct answer: B

If $m$ is the minimum value of $k$ for which the function $f(x)=x\sqrt{kx-x^2}$ is increasing in the interval $[0,3]$ and M is the maximum value of $f$ in $[0,3]$ when $k=m$, then the ordered pair $(m,M)$ is equal to: