JEE Main Full Mock Test: Practice Test 10

Question paper with answer key. Selection Pro

Q1. A particle starts from rest and moves with constant acceleration $4\,\text{m/s}^2$. Its speed after $5\,\text{s}$ is:

$10\,\text{m/s}$
$15\,\text{m/s}$
$20\,\text{m/s}$
$25\,\text{m/s}$

Answer: (C) $20\,\text{m/s}$

Using $v=u+at$, with $u=0$, $a=4\,\text{m/s}^2$ and $t=5\,\text{s}$, we get $v=20\,\text{m/s}$.

Q2. A projectile is thrown with speed $20\,\text{m/s}$ at an angle of $45^\circ$ with the horizontal. Taking $g=10\,\text{m/s}^2$, its maximum height is:

$5\,\text{m}$
$10\,\text{m}$
$15\,\text{m}$
$20\,\text{m}$

Answer: (B) $10\,\text{m}$

$H=\frac{u^2\sin^2\theta}{2g}=\frac{400(1/2)}{20}=10\,\text{m}$.

Q3. A force of $10\,\text{N}$ acts on a body of mass $2\,\text{kg}$. The acceleration produced is:

$2\,\text{m/s}^2$
$5\,\text{m/s}^2$
$10\,\text{m/s}^2$
$20\,\text{m/s}^2$

Answer: (B) $5\,\text{m/s}^2$

From Newton's second law, $F=ma$. Hence $a=F/m=10/2=5\,\text{m/s}^2$.

Q4. A block of mass $5\,\text{kg}$ is pulled horizontally by a force of $20\,\text{N}$ on a frictionless surface. Its acceleration is:

$2\,\text{m/s}^2$
$4\,\text{m/s}^2$
$5\,\text{m/s}^2$
$10\,\text{m/s}^2$

Answer: (B) $4\,\text{m/s}^2$

Since the surface is frictionless, net force is $20\,\text{N}$. Thus $a=F/m=20/5=4\,\text{m/s}^2$.

Q5. A body of mass $2\,\text{kg}$ is moving with speed $3\,\text{m/s}$. Its kinetic energy is:

$3\,\text{J}$
$6\,\text{J}$
$9\,\text{J}$
$18\,\text{J}$

Answer: (C) $9\,\text{J}$

$K=\frac12mv^2=\frac12(2)(3^2)=9\,\text{J}$.

Q6. A force of $10\,\text{N}$ acts on a body through a displacement of $5\,\text{m}$ in the direction of force. Work done is:

$2\,\text{J}$
$15\,\text{J}$
$50\,\text{J}$
$100\,\text{J}$

Answer: (C) $50\,\text{J}$

$W=Fs\cos0^\circ=10\times5=50\,\text{J}$.

Q7. A spring of force constant $100\,\text{N/m}$ is compressed by $0.2\,\text{m}$. The elastic potential energy stored is:

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

Answer: (B) $2\,\text{J}$

$U=\frac12kx^2=\frac12(100)(0.2)^2=2\,\text{J}$.

Q8. A body of mass $2\,\text{kg}$ moves in a circle of radius $1\,\text{m}$ with speed $4\,\text{m/s}$. The centripetal force is:

$8\,\text{N}$
$16\,\text{N}$
$32\,\text{N}$
$64\,\text{N}$

Answer: (C) $32\,\text{N}$

$F_c=mv^2/r=2(16)/1=32\,\text{N}$.

Q9. The escape velocity from the surface of Earth is approximately:

$5.6\,\text{km/s}$
$7.9\,\text{km/s}$
$11.2\,\text{km/s}$
$15.0\,\text{km/s}$

Answer: (C) $11.2\,\text{km/s}$

The escape velocity from Earth is $v_e=\sqrt{2GM/R}$, approximately $11.2\,\text{km/s}$.

Q10. Two masses $m$ and $m$ are separated by distance $r$. Their gravitational force is $F$. If the distance is doubled, the force becomes:

$F/2$
$F/4$
$2F$
$4F$

Answer: (B) $F/4$

Since $F\propto1/r^2$, doubling $r$ makes the force $F/4$.

Q11. A simple pendulum has length $1\,\text{m}$. Taking $g=\pi^2\,\text{m/s}^2$, its time period is:

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

Answer: (B) $2\,\text{s}$

$T=2\pi\sqrt{L/g}=2\pi\sqrt{1/\pi^2}=2\,\text{s}$.

Q12. A wave has frequency $500\,\text{Hz}$ and wavelength $0.6\,\text{m}$. Its speed is:

$100\,\text{m/s}$
$200\,\text{m/s}$
$300\,\text{m/s}$
$500\,\text{m/s}$

Answer: (C) $300\,\text{m/s}$

Wave speed is $v=f\lambda=500\times0.6=300\,\text{m/s}$.

Q13. The electric field due to a point charge $q$ at distance $r$ is proportional to:

$r$
$1/r$
$1/r^2$
$r^2$

Answer: (C) $1/r^2$

From Coulomb's law, $E=\frac{1}{4\pi\varepsilon_0}\frac{q}{r^2}$, so $E\propto1/r^2$.

Q14. A capacitor of capacitance $5\,\mu\text{F}$ is connected to a $10\,\text{V}$ battery. The charge stored is:

$5\,\mu\text{C}$
$25\,\mu\text{C}$
$50\,\mu\text{C}$
$100\,\mu\text{C}$

Answer: (C) $50\,\mu\text{C}$

$Q=CV=5\,\mu\text{F}\times10\,\text{V}=50\,\mu\text{C}$.

Q15. A $10\,\Omega$ resistor is connected across a $20\,\text{V}$ battery. The current through it is:

$0.5\,\text{A}$
$1\,\text{A}$
$2\,\text{A}$
$4\,\text{A}$

Answer: (C) $2\,\text{A}$

Using Ohm's law, $I=V/R=20/10=2\,\text{A}$.

Q16. Two resistors $6\,\Omega$ and $3\,\Omega$ are connected in parallel. Their equivalent resistance is:

$1\,\Omega$
$2\,\Omega$
$3\,\Omega$
$9\,\Omega$

Answer: (B) $2\,\Omega$

$\frac1R=\frac16+\frac13=\frac12$, hence $R=2\,\Omega$.

Q17. A charged particle enters a uniform magnetic field perpendicular to the field. Its path is:

Straight line
Circular
Parabolic
Elliptical

Answer: (B) Circular

The magnetic force is always perpendicular to velocity and acts as centripetal force, producing circular motion.

Q18. The magnetic field at the centre of a circular coil of radius $R$ carrying current $I$ and having $N$ turns is:

$\frac{\mu_0I}{2R}$
$\frac{\mu_0NI}{2R}$
$\frac{\mu_0NI}{R}$
$\frac{\mu_0I}{NR}$

Answer: (B) $\frac{\mu_0NI}{2R}$

For an $N$-turn circular coil, $B=\frac{\mu_0NI}{2R}$ at the centre.

Q19. A coil has $100$ turns and area $0.01\,\text{m}^2$. It is placed in a magnetic field of $0.5\,\text{T}$. If the field changes uniformly to zero in $0.1\,\text{s}$, the average induced emf is:

$0.5\,\text{V}$
$5\,\text{V}$
$50\,\text{V}$
$100\,\text{V}$

Answer: (B) $5\,\text{V}$

Average emf $=N\Delta\Phi/\Delta t=N A\Delta B/\Delta t=100(0.01)(0.5)/0.1=5\,\text{V}$.

Q20. In a photoelectric experiment, the stopping potential is increased when:

Intensity is decreased
Frequency of incident light is increased
Work function is increased only
Area of metal is increased

Answer: (B) Frequency of incident light is increased

$K_{\max}=h\nu-\phi=eV_s$. Therefore, increasing frequency increases the stopping potential.

Q21. The number of moles present in $18\,\text{g}$ of water is:

$0.5$
$1$
$2$
$18$

Answer: (B) $1$

Molar mass of water is $18\,\text{g/mol}$. Thus moles $=18/18=1$.

Q22. The atomic number of an element represents the number of:

Neutrons
Protons
Nucleons
Neutrons + electrons

Answer: (B) Protons

Atomic number $Z$ is defined as the number of protons in the nucleus.

Q23. Which orbital has the highest penetration among the following?

$3s$
$3p$
$3d$
$4s$

Answer: (A) $3s$

For the same principal shell, penetration follows $s>p>d>f$. Hence $3s$ has greater penetration than $3p$ and $3d$.

Q24. The most electronegative element is:

Oxygen
Nitrogen
Fluorine
Chlorine

Answer: (C) Fluorine

Fluorine has the highest electronegativity on the Pauling scale.

Q25. 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 is linear with bond angle $180^\circ$.

Q26. The bond order of $O_2$ according to molecular orbital theory is:

$1$
$1.5$
$2$
$3$

Answer: (C) $2$

The bond order of oxygen molecule is $2$, corresponding to a double bond.

Q27. For an exothermic reaction, the value of $\Delta H$ is:

Positive
Negative
Zero
Always infinite

Answer: (B) Negative

An exothermic reaction releases heat, so its enthalpy change is negative: $\Delta H<0$.

Q28. If the equilibrium constant $K_c$ for a reaction is very large, the equilibrium mixture contains predominantly:

Reactants
Products
Equal reactants and products
Only catalyst

Answer: (B) Products

A large $K_c$ indicates that products are strongly favoured at equilibrium.

Q29. The pH of a neutral solution at $25^\circ\text{C}$ is:

$0$
$5$
$7$
$14$

Answer: (C) $7$

At $25^\circ\text{C}$, neutral water has $[H^+]=10^{-7}\,\text{M}$, so pH is $7$.

Q30. The oxidation number 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 $x=+6$.

Q31. The standard electrode potential of the standard hydrogen electrode is:

$0\,\text{V}$
$1\,\text{V}$
$-1\,\text{V}$
$0.76\,\text{V}$

Answer: (A) $0\,\text{V}$

The standard hydrogen electrode is assigned a standard reduction potential of exactly $0\,\text{V}$.

Q32. During electrolysis, oxidation occurs at the:

Cathode
Anode
Salt bridge
Electrolyte only

Answer: (B) Anode

Oxidation always occurs at the anode, while reduction occurs at the cathode.

Q33. For a first-order reaction, the unit of rate constant is:

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

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

For a first-order reaction, rate $=k[A]$, so the unit of $k$ is $\text{s}^{-1}$.

Q34. The half-life of a first-order reaction is independent of:

Rate constant
Initial concentration
Temperature
Activation energy

Answer: (B) Initial concentration

For a first-order reaction, $t_{1/2}=\frac{0.693}{k}$, so it is independent of initial concentration.

Q35. Which of the following is an ideal colligative property?

Viscosity
Osmotic pressure
Surface tension
Refractive index

Answer: (B) Osmotic pressure

Osmotic pressure depends on the number of solute particles and is a colligative property.

Q36. The oxidation state of oxygen in $H_2O_2$ is:

$-2$
$-1$
$0$
$+1$

Answer: (B) $-1$

In peroxides, oxygen has oxidation state $-1$.

Q37. Which of the following is an amphoteric oxide?

$Na_2O$
$CO_2$
$Al_2O_3$
$SO_2$

Answer: (C) $Al_2O_3$

$Al_2O_3$ reacts with both acids and bases, so it is amphoteric.

Q38. Which halogen is the strongest oxidising agent?

$F_2$
$Cl_2$
$Br_2$
$I_2$

Answer: (A) $F_2$

Fluorine has the highest standard reduction potential among halogens and is therefore the strongest oxidising agent.

Q39. The IUPAC name of $CH_3CH_2OH$ is:

Methanol
Ethanol
Propanol
Ethanal

Answer: (B) Ethanol

$CH_3CH_2OH$ contains two carbon atoms and an alcohol group, so its IUPAC name is ethanol.

Q40. The major product of addition of $HBr$ to propene in the absence of peroxide is:

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

Answer: (B) 2-bromopropane

In the absence of peroxide, HBr follows Markovnikov addition and gives 2-bromopropane as the major product.

Q41. Which reagent is commonly used to oxidise a primary alcohol to an aldehyde under controlled conditions?

$PCC$
$NaBH_4$
$LiAlH_4$
$H_2/Ni$

Answer: (A) $PCC$

PCC (pyridinium chlorochromate) can oxidise a primary alcohol to an aldehyde without generally proceeding to the carboxylic acid.

Q42. Which compound gives a positive Tollens' test?

Ethane
Propanone
Ethanal
Benzene

Answer: (C) Ethanal

Aldehydes such as ethanal reduce Tollens' reagent and produce the characteristic silver mirror.

Q43. The functional group present in carboxylic acids is:

$-OH$
$-CHO$
$-COOH$
$-CO-$

Answer: (C) $-COOH$

Carboxylic acids contain the carboxyl functional group $-COOH$.

Q44. The coordination number of the central metal ion in $[Co(NH_3)_6]^{3+}$ is:

Answer: (C) $6$

Six $NH_3$ ligands are directly coordinated to cobalt, so the coordination number is $6$.

Q45. Which ligand is a strong-field ligand?

$Cl^-$
$F^-$
$CN^-$
$Br^-$

Answer: (C) $CN^-$

$CN^-$ is a strong-field ligand and produces large crystal-field splitting.

Q46. If $z=1+i$, then $|z|$ is:

$1$
$\sqrt{2}$
$2$
$3$

Answer: (B) $\sqrt{2}$

$|z|=\sqrt{1^2+1^2}=\sqrt2$.

Q47. The coefficient of $x^2$ in $(1+x)^6$ is:

$6$
$12$
$15$
$20$

Answer: (C) $15$

The coefficient is ${}^{6}C_2=15$.

Q48. If the roots of $x^2-8x+k=0$ are equal, then $k$ is:

$8$
$12$
$16$
$32$

Answer: (C) $16$

Equal roots require $b^2-4ac=0$. Thus $64-4k=0$, giving $k=16$.

Q49. The sum of the first $20$ natural numbers is:

$190$
$200$
$210$
$220$

Answer: (C) $210$

$S=\frac{n(n+1)}2=\frac{20\times21}{2}=210$.

Q50. The determinant $\begin{vmatrix}3&2\\1&4\end{vmatrix}$ is:

$8$
$10$
$12$
$14$

Answer: (B) $10$

Determinant $=3(4)-2(1)=12-2=10$.

Q51. If $\vec a\cdot\vec b=|\vec a||\vec b|$, the angle between the two non-zero vectors is:

$0^\circ$
$45^\circ$
$90^\circ$
$180^\circ$

Answer: (A) $0^\circ$

Since $\vec a\cdot\vec b=|a||b|\cos\theta$, we have $\cos\theta=1$, giving $\theta=0^\circ$.

Q52. The slope of the line joining $(2,3)$ and $(6,11)$ is:

Answer: (B) $2$

$m=\frac{11-3}{6-2}=\frac84=2$.

Q53. The equation of the line passing through $(1,2)$ with slope $3$ is:

$y=3x+1$
$y=3x-1$
$y=x+3$
$y=2x+3$

Answer: (B) $y=3x-1$

Using point-slope form, $y-2=3(x-1)$, hence $y=3x-1$.

Q54. The derivative of $\sin x$ is:

$\cos x$
$-\cos x$
$\sin x$
$-\sin x$

Answer: (A) $\cos x$

$\frac{d}{dx}(\sin x)=\cos x$.

Q55. The maximum value of $4x-x^2$ for real $x$ is:

Answer: (B) $4$

$4x-x^2=4-(x-2)^2$. Therefore the maximum value is $4$.

Q56. The value of $\int_0^\pi \sin x\,dx$ is:

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

Answer: (C) $2$

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

Q57. The limit $\lim_{x\to0}\frac{\sin x}{x}$ is:

$0$
$1$
$\infty$
$-1$

Answer: (B) $1$

The standard trigonometric limit is $\lim_{x\to0}\frac{\sin x}{x}=1$.

Q58. The distance between $(0,0)$ and $(3,4)$ is:

Answer: (C) $5$

$d=\sqrt{3^2+4^2}=5$.

Q59. The equation of the circle with centre $(0,0)$ and radius $5$ is:

$x^2+y^2=5$
$x^2+y^2=10$
$x^2+y^2=25$
$x^2+y^2=50$

Answer: (C) $x^2+y^2=25$

For centre $(0,0)$ and radius $r$, the equation is $x^2+y^2=r^2$. Hence $x^2+y^2=25$.

Q60. The eccentricity of an ellipse is:

$0
$e=1$
$e>1$
$e=2$

Answer: (A) $0

For an ellipse, eccentricity satisfies $0\le e<1$. For a non-circular ellipse, $0

Q61. If $\tan\theta=\sqrt3$ and $0<\theta<\pi/2$, then $\theta$ is:

$\pi/6$
$\pi/4$
$\pi/3$
$\pi/2$

Answer: (C) $\pi/3$

In the first quadrant, $\tan\theta=\sqrt3$ gives $\theta=\pi/3$.

Q62. The principal value of $\sin^{-1}(1)$ is:

$0$
$\pi/6$
$\pi/4$
$\pi/2$

Answer: (D) $\pi/2$

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

Q63. The probability of getting a six when a fair die is thrown once is:

$1/2$
$1/3$
$1/6$
$1/12$

Answer: (C) $1/6$

There is one favourable outcome out of six equally likely outcomes, so probability is $1/6$.

Q64. The mean of $2,4,6,8,10$ is:

Answer: (C) $6$

Mean $=\frac{2+4+6+8+10}{5}=\frac{30}{5}=6$.

Q65. The variance of a dataset in which every observation is equal to $5$ is:

$0$
$1$
$5$
$25$

Answer: (A) $0$

All observations are equal to their mean, so every deviation is zero. Hence variance is $0$.

Q66. If $A$ is a $2\times2$ matrix and $|A|=3$, then $|2A|$ is:

$6$
$9$
$12$
$24$

Answer: (C) $12$

For a $2\times2$ matrix, $|kA|=k^2|A|$. Thus $|2A|=4(3)=12$.

Q67. The general solution of $\frac{dy}{dx}=2x$ is:

$y=x^2+C$
$y=2x^2+C$
$y=x+C$
$y=2x+C$

Answer: (A) $y=x^2+C$

Integrating, $y=\int2x\,dx=x^2+C$.

Q68. The area under $y=x^2$ from $x=0$ to $x=1$ is:

$1/4$
$1/3$
$1/2$
$1$

Answer: (B) $1/3$

$\int_0^1x^2dx=\left[\frac{x^3}{3}\right]_0^1=\frac13$.

Q69. If $\alpha$ and $\beta$ are roots of $x^2-7x+10=0$, then $\alpha\beta$ is:

$5$
$7$
$10$
$14$

Answer: (C) $10$

For $ax^2+bx+c=0$, product of roots is $\alpha\beta=c/a$. Hence $\alpha\beta=10$.

Q70. The number of ways of selecting $2$ objects from $7$ distinct objects is:

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

Answer: (B) $21$

The number of selections is ${}^{7}C_2=\frac{7\times6}{2}=21$.

Q71. The value of $\log_{10}1000$ is:

$1$
$2$
$3$
$10$

Answer: (C) $3$

Since $10^3=1000$, $\log_{10}1000=3$.

Q72. If $f(x)=x^2+3x$, then $f'(1)$ is:

Answer: (C) $5$

$f'(x)=2x+3$. Therefore $f'(1)=2+3=5$.

Q73. The value of $\int e^x\,dx$ is:

$e^x+C$
$xe^x+C$
$e^{x+1}+C$
$x^2e^x+C$

Answer: (A) $e^x+C$

Since the derivative of $e^x$ is itself, $\int e^x dx=e^x+C$.

Q74. The value of $\lim_{x\to0}\frac{1-\cos x}{x^2}$ is:

$0$
$1/2$
$1$
$2$

Answer: (B) $1/2$

Using the standard limit, $\lim_{x\to0}\frac{1-\cos x}{x^2}=\frac12$.

Q75. If the vectors $\vec a$ and $\vec b$ are parallel and non-zero, then their cross product is:

$|a||b|$
$1$
$0$
$-1$

Answer: (C) $0$

$|\vec a\times\vec b|=|a||b|\sin\theta$. For parallel vectors, $\theta=0^\circ$ or $180^\circ$, so the cross product is zero.