JEE Main Full Mock Test: Practice Test 11

Question paper with answer key. Selection Pro

Q1. A particle starts from rest and moves with constant acceleration $4\,\text{m/s}^2$. Its displacement in the fifth second is:

$10\,\text{m}$
$18\,\text{m}$
$20\,\text{m}$
$22\,\text{m}$

Answer: (B) $18\,\text{m}$

Distance covered in the $n$th second is $s_n=u+\frac{a}{2}(2n-1)$. For $u=0$, $a=4$ and $n=5$, $s_5=2(9)=18\,\text{m}$.

Q2. A projectile is thrown with speed $20\,\text{m/s}$ at an angle $60^\circ$ with the horizontal. Taking $g=10\,\text{m/s}^2$, its maximum height is:

$10\,\text{m}$
$15\,\text{m}$
$20\,\text{m}$
$30\,\text{m}$

Answer: (B) $15\,\text{m}$

$H=\frac{u^2\sin^2\theta}{2g}=\frac{400\times3/4}{20}=15\,\text{m}$.

Q3. A force $F=6x$ newton acts on a particle along the $x$-axis. The work done in moving the particle from $x=0$ to $x=2\,\text{m}$ is:

$6\,\text{J}$
$12\,\text{J}$
$18\,\text{J}$
$24\,\text{J}$

Answer: (B) $12\,\text{J}$

$W=\int_0^2 6x\,dx=3x^2\big|_0^2=12\,\text{J}$. Therefore the correct option is $12\,\text{J}$.

Q4. A body of mass $2\,\text{kg}$ is moving with velocity $3\,\text{m/s}$. A constant force of $4\,\text{N}$ acts in the direction of motion for $5\,\text{s}$. Its final velocity is:

$8\,\text{m/s}$
$10\,\text{m/s}$
$13\,\text{m/s}$
$15\,\text{m/s}$

Answer: (C) $13\,\text{m/s}$

Acceleration is $a=F/m=4/2=2\,\text{m/s}^2$. Hence $v=u+at=3+2(5)=13\,\text{m/s}$.

Q5. A particle moves in a circular path of radius $2\,\text{m}$ with speed $4\,\text{m/s}$. Its centripetal acceleration is:

$2\,\text{m/s}^2$
$4\,\text{m/s}^2$
$8\,\text{m/s}^2$
$16\,\text{m/s}^2$

Answer: (C) $8\,\text{m/s}^2$

Centripetal acceleration is $a_c=v^2/r=16/2=8\,\text{m/s}^2$.

Q6. A uniform rod of mass $M$ and length $L$ is pivoted about one end. Its moment of inertia about the pivot is:

$\frac{1}{12}ML^2$
$\frac{1}{6}ML^2$
$\frac{1}{3}ML^2$
$ML^2$

Answer: (C) $\frac{1}{3}ML^2$

For a uniform rod about an axis through one end perpendicular to its length, $I=\frac13ML^2$.

Q7. A solid sphere and a hollow sphere have the same mass and radius and roll without slipping with the same speed. Which has greater rotational kinetic energy?

Solid sphere
Hollow sphere
Both equal
Cannot be determined

Answer: (B) Hollow sphere

For rolling, $K_{rot}=\frac12I\omega^2$. A hollow sphere has $I=\frac23MR^2$, whereas a solid sphere has $I=\frac25MR^2$, so the hollow sphere has greater rotational kinetic energy.

Q8. The escape velocity from the surface of a planet is $v_e$. If the radius of the planet is doubled while its mass remains unchanged, the new escape velocity is:

$v_e$
$v_e/\sqrt2$
$\sqrt2v_e$
$2v_e$

Answer: (B) $v_e/\sqrt2$

$v_e=\sqrt{2GM/R}$. On replacing $R$ by $2R$, $v'_e=v_e/\sqrt2$.

Q9. Two point charges $q$ and $4q$ are separated by distance $r$. The electric field is zero at a point between them. Its distance from charge $q$ is:

$r/3$
$r/2$
$2r/3$
$3r/4$

Answer: (A) $r/3$

Let the point be at distance $x$ from $q$. Equating field magnitudes, $kq/x^2=4kq/(r-x)^2$. Thus $r-x=2x$, giving $x=r/3$.

Q10. A capacitor of capacitance $C$ is charged to potential $V$. If its capacitance is doubled while it remains connected to the same battery, the stored energy becomes:

$U/2$
$U$
$2U$
$4U$

Answer: (C) $2U$

For constant voltage, $U=\frac12CV^2$. Doubling $C$ doubles the stored energy.

Q11. A wire of resistance $R$ is stretched uniformly to twice its original length without change in volume. Its new resistance is:

$R/4$
$R/2$
$2R$
$4R$

Answer: (D) $4R$

Since volume is constant, doubling length makes area half. As $R=\rho L/A$, the resistance becomes $2R/(1/2)=4R$.

Q12. A charged particle enters a uniform magnetic field parallel to the field lines. Its path is:

Circular
Helical
Straight line
Parabolic

Answer: (C) Straight line

Magnetic force is $qvB\sin\theta$. For motion parallel to the field, $\theta=0$, so the force is zero and the particle continues in a straight line.

Q13. A circular coil of $N$ turns carries current $I$. If both $N$ and $I$ are doubled, the magnetic moment becomes:

2 times
4 times
6 times
8 times

Answer: (B) 4 times

Magnetic moment is $M=NIA$. Doubling both $N$ and $I$ makes it four times.

Q14. An ideal transformer has $500$ turns in the primary and $100$ turns in the secondary. If the primary voltage is $220\,\text{V}$, the secondary voltage is:

$22\,\text{V}$
$44\,\text{V}$
$110\,\text{V}$
$440\,\text{V}$

Answer: (B) $44\,\text{V}$

For an ideal transformer, $V_s/V_p=N_s/N_p=100/500=1/5$. Hence $V_s=44\,\text{V}$.

Q15. In an electromagnetic wave, the electric and magnetic fields are:

Parallel to each other
Perpendicular to each other and to the direction of propagation
Only parallel to propagation
Randomly oriented

Answer: (B) Perpendicular to each other and to the direction of propagation

Electromagnetic waves are transverse. The electric field, magnetic field and direction of propagation are mutually perpendicular.

Q16. A convex lens forms a real image of an object placed $30\,\text{cm}$ from it. If the focal length is $10\,\text{cm}$, the image distance is:

$10\,\text{cm}$
$15\,\text{cm}$
$20\,\text{cm}$
$30\,\text{cm}$

Answer: (B) $15\,\text{cm}$

Using the lens formula $1/f=1/v-1/u$, with $f=10\,\text{cm}$ and $u=-30\,\text{cm}$, we get $1/v=1/10-1/30=1/15$. Thus $v=15\,\text{cm}$.

Q17. In Young's double-slit experiment, if the slit separation is doubled while wavelength and screen distance remain unchanged, the fringe width becomes:

$\beta/2$
$\beta$
$2\beta$
$4\beta$

Answer: (A) $\beta/2$

Fringe width is $\beta=\lambda D/d$. Doubling $d$ makes the fringe width half.

Q18. The threshold frequency of a metal is $5\times10^{14}\,\text{Hz}$. If incident light has frequency $8\times10^{14}\,\text{Hz}$, the maximum kinetic energy is proportional to:

$3\times10^{14}h$
$5\times10^{14}h$
$8\times10^{14}h$
$13\times10^{14}h$

Answer: (A) $3\times10^{14}h$

Einstein's equation gives $K_{max}=h(\nu-\nu_0)=h(8-5)\times10^{14}=3\times10^{14}h$.

Q19. A radioactive nucleus has a decay constant $\lambda$. Its mean life is:

$\lambda$
$1/\lambda$
$\lambda^2$
$1/\lambda^2$

Answer: (B) $1/\lambda$

The mean life of a radioactive nucleus is $\tau=1/\lambda$.

Q20. The energy of an electron in the ground state of hydrogen atom is approximately:

$-3.4\,\text{eV}$
$-6.8\,\text{eV}$
$-13.6\,\text{eV}$
$+13.6\,\text{eV}$

Answer: (C) $-13.6\,\text{eV}$

For hydrogen, energy of the $n$th orbit is $E_n=-13.6/n^2\,\text{eV}$. For $n=1$, $E=-13.6\,\text{eV}$.

Q21. A gas expands adiabatically. Which quantity remains zero?

Work done
Change in internal energy
Heat exchanged
Pressure

Answer: (C) Heat exchanged

In an adiabatic process, there is no heat exchange, so $Q=0$.

Q22. For an ideal gas, if the absolute temperature is quadrupled, the rms speed of its molecules becomes:

Half
Unchanged
Twice
Four times

Answer: (C) Twice

RMS speed varies as $v_{rms}\propto\sqrt T$. Thus when $T$ becomes $4T$, speed becomes $2v_{rms}$.

Q23. The ratio of specific heats $\gamma=C_P/C_V$ for a monoatomic ideal gas is:

$4/3$
$5/3$
$7/5$
$3/2$

Answer: (B) $5/3$

For a monoatomic ideal gas, $C_V=3R/2$ and $C_P=5R/2$, hence $\gamma=5/3$.

Q24. A liquid drop is divided into 8 identical smaller drops. If the original radius is $R$, the radius of each smaller drop is:

$R/2$
$R/4$
$R/8$
$2R$

Answer: (A) $R/2$

Volume is conserved: $\frac43\pi R^3=8\times\frac43\pi r^3$. Thus $r^3=R^3/8$ and $r=R/2$.

Q25. The time period of a simple pendulum is $2\,\text{s}$ on Earth. On a planet where gravitational acceleration is $g/4$, its time period becomes:

$1\,\text{s}$
$2\,\text{s}$
$4\,\text{s}$
$8\,\text{s}$

Answer: (C) $4\,\text{s}$

Since $T\propto1/\sqrt g$, reducing $g$ to $g/4$ makes the period twice as large. Hence $T'=4\,\text{s}$.

Q26. The number of molecules present in $18\,\text{g}$ of water is approximately:

$3.011\times10^{23}$
$6.022\times10^{23}$
$1.204\times10^{24}$
$9.033\times10^{23}$

Answer: (B) $6.022\times10^{23}$

$18\,\text{g}$ of water is one mole. Therefore it contains Avogadro's number, $6.022\times10^{23}$ molecules.

Q27. The de Broglie wavelength of a particle is inversely proportional to its:

Mass only
Momentum
Kinetic energy only
Charge

Answer: (B) Momentum

According to de Broglie's relation, $\lambda=h/p$, so wavelength is inversely proportional to momentum.

Q28. For a spontaneous process at constant temperature and pressure, Gibbs free energy change must be:

$\Delta G>0$
$\Delta G=0$ always
$\Delta G<0$
$\Delta G=\Delta H$ always

Answer: (C) $\Delta G<0$

A spontaneous process at constant $T$ and $P$ has $\Delta G<0$.

Q29. For a reaction, if $K_c>1$, the equilibrium mixture generally contains:

Mostly reactants
Mostly products
Only reactants
No products

Answer: (B) Mostly products

A large equilibrium constant indicates that products are favoured at equilibrium.

Q30. The pH of a $10^{-4}\,\text{M}$ strong monoprotic acid at ordinary concentration approximation is:

$2$
$3$
$4$
$10$

Answer: (C) $4$

For a strong acid, $[H^+]=10^{-4}\,\text{M}$, so pH $=4$.

Q31. The oxidation state of chromium in $K_2Cr_2O_7$ is:

$+3$
$+4$
$+6$
$+7$

Answer: (C) $+6$

$2(+1)+2x+7(-2)=0$, giving $2x=12$ and $x=+6$.

Q32. Which element has the highest first ionisation enthalpy among the following?

Answer: (D) C

First ionisation enthalpy generally increases across the period. Among Li, Be, B and C, carbon has the highest value.

Q33. Which molecule has a linear geometry?

$NH_3$
$H_2O$
$CO_2$
$CH_4$

Answer: (C) $CO_2$

$CO_2$ has two electron domains around carbon and no lone pair on the central atom, giving a linear geometry with bond angle $180^\circ$.

Q34. Which of the following has the highest lattice energy, considering comparable ionic charges and crystal type?

NaCl
KCl
MgO
CaO

Answer: (C) MgO

MgO contains $Mg^{2+}$ and $O^{2-}$ ions, giving much stronger electrostatic attraction than the singly charged ions in NaCl and KCl.

Q35. The rate constant of a first-order reaction has the unit:

$\text{mol L}^{-1}\text{s}^{-1}$
$\text{s}^{-1}$
$\text{L mol}^{-1}\text{s}^{-1}$
$\text{mol}^{-1}\text{s}^{-1}$

Answer: (B) $\text{s}^{-1}$

For a first-order reaction, rate $=k[A]$, so $k$ has unit time$^{-1}$, i.e. $\text{s}^{-1}$.

Q36. If the half-life of a first-order reaction is $10$ min, its rate constant is approximately:

$0.0693\,\text{min}^{-1}$
$0.693\,\text{min}^{-1}$
$6.93\,\text{min}^{-1}$
$0.00693\,\text{min}^{-1}$

Answer: (A) $0.0693\,\text{min}^{-1}$

For a first-order reaction, $k=0.693/t_{1/2}=0.693/10=0.0693\,\text{min}^{-1}$.

Q37. The cell reaction is spontaneous under standard conditions when the standard cell potential is:

Negative
Zero
Positive
Always one

Answer: (C) Positive

$\Delta G^\circ=-nFE^\circ_{cell}$. For spontaneity, $\Delta G^\circ<0$, requiring $E^\circ_{cell}>0$.

Q38. During electrolysis of molten NaCl, sodium is produced at the:

Anode
Cathode
Salt bridge
Both electrodes

Answer: (B) Cathode

At the cathode, reduction occurs: $Na^+ + e^-\rightarrow Na$.

Q39. The major product of addition of $HBr$ to propene in the presence of peroxide is:

1-bromopropane
2-bromopropane
1,2-dibromopropane
Propanol

Answer: (A) 1-bromopropane

In the presence of peroxide, HBr adds through a radical mechanism following anti-Markovnikov orientation, giving 1-bromopropane.

Q40. Which reagent is commonly used to distinguish aldehydes from ketones?

Tollens' reagent
NaCl
HCl
Conc. H2SO4

Answer: (A) Tollens' reagent

Aldehydes generally reduce Tollens' reagent to metallic silver, while ordinary ketones do not.

Q41. Which compound gives a positive Fehling's test?

Acetone
Benzaldehyde
Ethanal
Benzophenone

Answer: (C) Ethanal

Aliphatic aldehydes such as ethanal reduce Fehling's solution to give a brick-red precipitate of $Cu_2O$.

Q42. The major product of dehydration of 2-methyl-2-propanol is:

Ethene
Propene
2-methylpropene
2-methylpropane

Answer: (C) 2-methylpropene

Acid-catalysed dehydration of tert-butanol gives 2-methylpropene as the alkene product.

Q43. The geometry of $[PtCl_4]^{2-}$ is:

Tetrahedral
Square planar
Octahedral
Linear

Answer: (B) Square planar

$Pt^{2+}$ is a $d^8$ ion and commonly forms square-planar complexes such as $[PtCl_4]^{2-}$.

Q44. The coordination number of chromium in $K_4[Cr(CN)_6]$ is:

Answer: (C) 6

Six cyanide ligands are directly coordinated to chromium, so the coordination number is $6$.

Q45. Which of the following is an example of an addition polymer?

Nylon-6,6
Terylene
PVC
Bakelite

Answer: (C) PVC

PVC is formed by addition polymerisation of vinyl chloride molecules.

Q46. The monomer of Teflon is:

Ethene
Vinyl chloride
Tetrafluoroethene
Styrene

Answer: (C) Tetrafluoroethene

Teflon (PTFE) is obtained by polymerisation of tetrafluoroethene, $CF_2=CF_2$.

Q47. Which compound is most acidic among the following?

Ethanol
Phenol
Water
Acetic acid

Answer: (D) Acetic acid

Acetic acid has a resonance-stabilised carboxylate conjugate base and is substantially more acidic than phenol, water and ethanol.

Q48. The number of $\sigma$ and $\pi$ bonds in benzene, $C_6H_6$, respectively, is:

$6,3$
$12,3$
$12,6$
$6,6$

Answer: (B) $12,3$

Benzene contains six C-C sigma bonds and six C-H sigma bonds, giving 12 sigma bonds. It has three pi bonds in its Kekule representation.

Q49. Which species has the highest bond order according to molecular orbital theory?

$O_2$
$O_2^+$
$O_2^-$
$O_2^{2-}$

Answer: (B) $O_2^+$

Removing one electron from antibonding $\pi^*$ orbitals increases the bond order. Thus $O_2^+$ has bond order $2.5$, greater than $O_2$ ($2$), $O_2^-$ ($1.5$) and $O_2^{2-}$ ($1$).

Q50. Which of the following is a strong reducing agent?

$F_2$
$Cl_2$
$Li$
$O_2$

Answer: (C) $Li$

Lithium readily loses its valence electron and has a very negative standard reduction potential, making it a strong reducing agent.

Q51. If $z=1-i$, then $z^4$ is:

$-4$
$4$
$-4i$
$4i$

Answer: (A) $-4$

$(1-i)^2=-2i$, so $(1-i)^4=(-2i)^2=-4$.

Q52. The coefficient of $x^4$ in $(1+x)^9$ is:

$84$
$126$
$144$
$210$

Answer: (B) $126$

The coefficient is ${}^{9}C_4=\frac{9\times8\times7\times6}{24}=126$.

Q53. If the roots of $x^2-7x+k=0$ differ by $1$, then $k$ is:

$10$
$12$
$13$
$14$

Answer: (B) $12$

Let roots be $\alpha,\beta$. Then $(\alpha-\beta)^2=(\alpha+\beta)^2-4\alpha\beta$. Thus $1=49-4k$, giving $k=12$. Therefore the correct option is $12$.

Q54. The sum of the first $20$ terms of the arithmetic progression $3,7,11,\ldots$ is:

$760$
$820$
$820$
$840$

Answer: (B) $820$

Here $a=3$, $d=4$, $n=20$. $S_n=\frac n2[2a+(n-1)d]=10[6+76]=820$.

Q55. If $A$ is a $2\times2$ matrix with $|A|=3$, then $|5A|$ is:

$15$
$25$
$50$
$75$

Answer: (D) $75$

For a $2\times2$ matrix, $|kA|=k^2|A|$. Hence $|5A|=25\times3=75$. Therefore the correct option is $75$.

Q56. If $\vec a=2\hat i+\hat j$ and $\vec b=\hat i-2\hat j$, then $\vec a\cdot\vec b$ is:

$-4$
$0$
$2$
$4$

Answer: (B) $0$

$\vec a\cdot\vec b=(2)(1)+(1)(-2)=0$.

Q57. The slope of the tangent to $y=x^3-3x$ at $x=1$ is:

$-3$
$0$
$3$
$6$

Answer: (B) $0$

$dy/dx=3x^2-3$. At $x=1$, slope $=3-3=0$.

Q58. The maximum value of $x^2(4-x)$ for $0\le x\le4$ is:

$\frac{64}{27}$
$\frac{128}{27}$
$\frac{256}{27}$
$8$

Answer: (C) $\frac{256}{27}$

Let $f(x)=4x^2-x^3$. Then $f'(x)=8x-3x^2=x(8-3x)=0 \implies x=8/3$. Maximum value $f(8/3)=(8/3)^2(4-8/3)=\frac{256}{27}$.

Q59. The value of $\int_0^{\pi/2}\sin x\,dx$ is:

$0$
$1$
$2$
$\pi/2$

Answer: (B) $1$

$\int_0^{\pi/2}\sin x\,dx=[-\cos x]_0^{\pi/2}=1$.

Q60. The derivative of $\ln(x^2+1)$ is:

$\frac{1}{x^2+1}$
$\frac{2x}{x^2+1}$
$\frac{x}{x^2+1}$
$2x\ln(x^2+1)$

Answer: (B) $\frac{2x}{x^2+1}$

Using the chain rule, $\frac{d}{dx}\ln(x^2+1)=\frac{2x}{x^2+1}$.

Q61. The limit $\lim_{x\to0}\frac{\sin 3x}{x}$ is:

Answer: (C) $3$

$\frac{\sin3x}{x}=3\frac{\sin3x}{3x}\to3$.

Q62. The distance between the parallel lines $3x+4y+5=0$ and $3x+4y-10=0$ is:

Answer: (B) $3$

Distance $=|c_1-c_2|/\sqrt{a^2+b^2}=15/5=3$.

Q63. The equation of the circle having diameter with endpoints $(0,0)$ and $(4,0)$ is:

$x^2+y^2-4x=0$
$x^2+y^2+4x=0$
$x^2+y^2-2x=0$
$x^2+y^2+2x=0$

Answer: (A) $x^2+y^2-4x=0$

The centre is $(2,0)$ and radius is $2$. Thus $(x-2)^2+y^2=4$, giving $x^2+y^2-4x=0$.

Q64. The length of the latus rectum of the parabola $y^2=8x$ is:

$2$
$4$
$8$
$16$

Answer: (C) $8$

For $y^2=4ax$, $4a=8$, so $a=2$. Latus rectum length is $4a=8$.

Q65. For the hyperbola $x^2/9-y^2/16=1$, its eccentricity is:

$4/3$
$5/3$
$3/5$
$5/4$

Answer: (B) $5/3$

Here $a^2=9$ and $b^2=16$. Thus $c^2=a^2+b^2=25$, so $e=c/a=5/3$.

Q66. If $\sin\theta=3/5$ and $\theta$ is acute, then $\cos\theta$ is:

$3/5$
$4/5$
$5/3$
$1/5$

Answer: (B) $4/5$

For an acute angle, $\cos\theta=\sqrt{1-\sin^2\theta}=\sqrt{1-9/25}=4/5$.

Q67. The principal value of $\sin^{-1}(-1/2)$ is:

$\pi/6$
$-\pi/6$
$5\pi/6$
$-5\pi/6$

Answer: (B) $-\pi/6$

The principal range of $\sin^{-1}x$ is $[-\pi/2,\pi/2]$. Therefore $\sin^{-1}(-1/2)=-\pi/6$.

Q68. A fair die is thrown twice. The probability that the sum is $9$ is:

$1/18$
$1/9$
$1/12$
$5/36$

Answer: (B) $1/9$

Favourable outcomes are $(3,6),(4,5),(5,4),(6,3)$, four outcomes out of $36$. Probability $=4/36=1/9$.

Q69. The variance of the data $2,4,6,8$ is:

Answer: (B) $5$

Mean $=5$. Squared deviations are $9,1,1,9$, whose sum is $20$. Population variance $=20/4=5$.

Q70. If $A$ is a $3\times3$ matrix and $|A|=5$, then $|A^{-1}|$ is:

$5$
$-5$
$1/5$
$25$

Answer: (C) $1/5$

For a nonsingular matrix, $|A^{-1}|=1/|A|$. Hence $|A^{-1}|=1/5$.

Q71. The general solution of $dy/dx=2y$ is:

$y=2x+C$
$y=Ce^{2x}$
$y=Ce^x$
$y=x^2+C$

Answer: (B) $y=Ce^{2x}$

Separating variables, $dy/y=2dx$. Integrating gives $\ln y=2x+C$, hence $y=Ce^{2x}$.

Q72. The area under the curve $y=x^2$ from $x=0$ to $x=2$ is:

$4/3$
$8/3$
$3$
$4$

Answer: (B) $8/3$

$\int_0^2x^2dx=[x^3/3]_0^2=8/3$.

Q73. If $\alpha$ and $\beta$ are roots of $x^2-4x+1=0$, then $1/\alpha+1/\beta$ equals:

Answer: (C) $4$

$\frac1\alpha+\frac1\beta=\frac{\alpha+\beta}{\alpha\beta}=4/1=4$.

Q74. The number of ways of arranging $5$ distinct books on a shelf is:

$25$
$60$
$100$
$120$

Answer: (D) $120$

The number of arrangements of $5$ distinct objects is $5!=120$.

Q75. The number of ways of choosing $2$ objects from $7$ distinct objects is:

$14$
$21$
$28$
$35$

Answer: (B) $21$

Number of selections is ${}^{7}C_2=7\times6/2=21$.