Start streak

JEE Main Full Mock Test: Practice Test 08

Question paper with answer key. Selection Pro

Q1. A block of mass m is attached to a spring of force constant k and placed on a smooth horizontal surface. The spring is compressed by x and released. At the instant its speed is half its maximum speed, the displacement is:
  1. $x/2$
  2. $\sqrt{3}x/2$
  3. $x/\sqrt{2}$
  4. $x/4$

Answer: (B) $\sqrt{3}x/2$

For SHM, $v^2=\omega^2(A^2-y^2)$. With $v= v_{max}/2=\omega A/2$, we get $y^2=3A^2/4$, hence $y=\sqrt3A/2$.

Q2. A charged particle enters a uniform magnetic field perpendicular to its velocity. If its kinetic energy is quadrupled, the radius of its circular path becomes:
  1. $2r$
  2. $4r$
  3. $r/2$
  4. $r$

Answer: (A) $2r$

Since $r=\sqrt{2mK}/qB$, radius is proportional to $\sqrt K$. Quadrupling kinetic energy doubles the radius.

Q3. A capacitor is charged to potential V and then disconnected from the battery. Its plate separation is doubled. The electrostatic energy stored becomes:
  1. $U/2$
  2. $2U$
  3. $U$
  4. $4U$

Answer: (B) $2U$

After disconnection charge remains constant. Since $C\propto1/d$, doubling separation halves capacitance. As $U=Q^2/(2C)$, energy doubles.

Q4. A projectile is projected with speed $u$. If its maximum height is one-third of its horizontal range, the angle of projection is:
  1. $30^\circ$
  2. $45^\circ$
  3. $\tan^{-1}(4/3)$
  4. $60^\circ$

Answer: (C) $\tan^{-1}(4/3)$

For a projectile, $H=\frac{u^2\sin^2\theta}{2g}$ and $R=\frac{u^2\sin2\theta}{g}$. Hence $\frac{H}{R}=\frac{\tan\theta}{4}$. Given $H=R/3$, $\tan\theta/4=1/3$, so $\tan\theta=4/3$.

Q5. Two resistors R and 2R are connected in parallel across an ideal battery. The ratio of power dissipated in R to that in 2R is:
  1. $1:2$
  2. $2:1$
  3. $1:4$
  4. $4:1$

Answer: (B) $2:1$

In parallel, voltage is same and $P=V^2/R$. Therefore $P_R:P_{2R}=1/R:1/(2R)=2:1$.

Q6. A uniform rod of length L is pivoted at one end and released from the horizontal position. Its angular speed when it reaches the vertical position is:
  1. $\sqrt{3g/L}$
  2. $\sqrt{g/L}$
  3. $\sqrt{6g/L}$
  4. $\sqrt{2g/L}$

Answer: (A) $\sqrt{3g/L}$

The centre of mass falls through $L/2$, so loss of gravitational potential energy is $mgL/2$. At the vertical position, $\frac12 I\omega^2=mgL/2$, with $I=\frac13mL^2$. Thus $\frac16mL^2\omega^2=\frac12mgL$, giving $\omega=\sqrt{3g/L}$.

Q7. A particle executes SHM with amplitude A. The ratio of its kinetic energy to potential energy when displacement is A/2 is:
  1. $1:3$
  2. $3:1$
  3. $1:1$
  4. $4:1$

Answer: (B) $3:1$

Potential energy fraction is $x^2/A^2=1/4$, so kinetic energy is $3/4$. Hence K:U=3:1.

Q8. A gas undergoes a complete cycle on a P-V diagram. If the cycle is clockwise, the net work done by the gas is:
  1. Negative
  2. Zero
  3. Positive
  4. Always equal to heat rejected

Answer: (C) Positive

For a clockwise cycle, the area enclosed in the P-V diagram is positive work done by the gas.

Q9. A satellite is moved from a circular orbit of radius R to another circular orbit of radius 4R around Earth. The ratio of its orbital speeds is:
  1. $1:2$
  2. $2:1$
  3. $1:4$
  4. $4:1$

Answer: (B) $2:1$

Orbital speed $v=\sqrt{GM/r}$. Thus $v_R/v_{4R}=2$.

Q10. In Young's double-slit experiment, the wavelength is doubled while slit separation remains unchanged. The fringe width becomes:
  1. Half
  2. Double
  3. Four times
  4. Unchanged

Answer: (B) Double

Fringe width $\beta=\lambda D/d$, so doubling wavelength doubles fringe width.

Q11. An electron and a proton are accelerated through the same potential difference. The ratio of their de Broglie wavelengths $\lambda_e/\lambda_p$ is approximately:
  1. $\sqrt{m_p/m_e}$
  2. $\sqrt{m_e/m_p}$
  3. $m_p/m_e$
  4. $1$

Answer: (A) $\sqrt{m_p/m_e}$

For the same accelerating potential, $\lambda=h/\sqrt{2mqV}\propto1/\sqrt m$. Hence $\lambda_e/\lambda_p=\sqrt{m_p/m_e}$.

Q12. A wire of resistance R is cut into n equal parts and all parts are connected in parallel. Equivalent resistance is:
  1. $R/n$
  2. $R/n^2$
  3. $nR$
  4. $R$

Answer: (B) $R/n^2$

Each part has resistance R/n. n identical pieces in parallel give $(R/n)/n=R/n^2$.

Q13. A particle of charge q moves with velocity v in electric and magnetic fields E and B. For zero net force when the fields are perpendicular, the required speed is:
  1. $E/B$
  2. $B/E$
  3. $EB$
  4. $E+B$

Answer: (A) $E/B$

For crossed fields and perpendicular velocity, $qE=qvB$, hence $v=E/B$.

Q14. A thin lens of focal length 20 cm is combined with another lens of focal length -30 cm in contact. The equivalent focal length is:
  1. 60 cm
  2. -60 cm
  3. 12 cm
  4. -12 cm

Answer: (A) 60 cm

$1/F=1/20-1/30=1/60$, hence F=60 cm.

Q15. The rms speed of gas molecules at temperature T is proportional to:
  1. T
  2. $\sqrt T$
  3. $1/T$
  4. $T^2$

Answer: (B) $\sqrt T$

From kinetic theory, $v_{rms}=\sqrt{3RT/M}$, so it is proportional to $\sqrt T$.

Q16. A current loop has magnetic moment M in a uniform magnetic field B. Its maximum torque is:
  1. $MB$
  2. $M/B$
  3. $B/M$
  4. $0$

Answer: (A) $MB$

Torque is $\tau=MB\sin\theta$, maximum at $90^\circ$.

Q17. A radioactive sample has half-life 10 days. The fraction remaining after 30 days is:
  1. $1/2$
  2. $1/4$
  3. $1/8$
  4. $1/16$

Answer: (C) $1/8$

30 days corresponds to three half-lives, so remaining fraction is $(1/2)^3=1/8$.

Q18. A metal has work function 2 eV. Light of photon energy 5 eV falls on it. Maximum kinetic energy of emitted electrons is:
  1. 2 eV
  2. 3 eV
  3. 5 eV
  4. 7 eV

Answer: (B) 3 eV

Einstein's equation gives $K_{max}=E_\gamma-\phi=5-2=3$ eV.

Q19. A capacitor and an inductor are connected in an LC circuit. If capacitance is increased four times, the angular frequency becomes:
  1. $2\omega$
  2. $\omega/2$
  3. $4\omega$
  4. $\omega/4$

Answer: (B) $\omega/2$

$\omega=1/\sqrt{LC}$. Increasing C fourfold reduces angular frequency by factor 2.

Q20. A body of mass m moving with speed v collides elastically head-on with an identical body initially at rest. The velocity of the first body after collision is:
  1. v
  2. v/2
  3. 0
  4. -v

Answer: (C) 0

In a perfectly elastic head-on collision between identical masses, velocities are exchanged. The first body comes to rest.

Q21. The electric field inside a uniformly charged thin spherical shell is:
  1. Zero everywhere
  2. Constant non-zero
  3. Inversely proportional to r
  4. Maximum at center

Answer: (A) Zero everywhere

By Gauss's law, a Gaussian surface inside the shell encloses zero charge, so electric field is zero.

Q22. A transformer has 1000 turns in primary and 200 turns in secondary. If primary voltage is 220 V, secondary voltage is:
  1. 44 V
  2. 110 V
  3. 440 V
  4. 22 V

Answer: (A) 44 V

$V_s/V_p=N_s/N_p=200/1000$, so $V_s=44$ V.

Q23. A body is projected vertically upward. At a height equal to one-fourth of its maximum height, its speed is:
  1. $u/2$
  2. $u\sqrt3/2$
  3. $u/\sqrt2$
  4. $u\sqrt{3}/4$

Answer: (B) $u\sqrt3/2$

Using $v^2=u^2-2gh$ and $H=u^2/(2g)$, at $h=H/4$, $v^2=u^2(1-1/4)=3u^2/4$.

Q24. The energy stored in a stretched spring is U. If its extension is doubled, the stored energy becomes:
  1. U
  2. 2U
  3. 4U
  4. U/2

Answer: (C) 4U

Spring energy $U=\frac12kx^2$, so doubling extension makes energy four times.

Q25. A conducting sphere is given charge Q. If its radius is doubled while charge remains unchanged, its potential becomes:
  1. 2V
  2. V/2
  3. 4V
  4. V

Answer: (B) V/2

Potential of isolated sphere is $V=kQ/R$. Doubling radius halves potential.

Q26. For a first-order reaction, the time required for 90% completion is approximately how many half-lives?
  1. 2.32
  2. 3.32
  3. 4.32
  4. 1.32

Answer: (B) 3.32

For 90% completion, 10% remains. Number of half-lives $n=\log_2 10\approx3.32$.

Q27. Which species has the largest bond order among the following?
  1. $O_2$
  2. $O_2^+$
  3. $O_2^-$
  4. $O_2^{2-}$

Answer: (B) $O_2^+$

Removing an electron from antibonding $\pi^*$ increases bond order. Thus $O_2^+$ has bond order 2.5.

Q28. The pH of a $10^{-3}$ M HCl solution is approximately:
  1. 2
  2. 3
  3. 11
  4. 1

Answer: (B) 3

Strong acid completely dissociates, so $[H^+]=10^{-3}$ M and pH=3.

Q29. Which complex is expected to be diamagnetic?
  1. $[Fe(CN)_6]^{3-}$
  2. $[Fe(CN)_6]^{4-}$
  3. $[FeF_6]^{3-}$
  4. $[CoF_6]^{3-}$

Answer: (B) $[Fe(CN)_6]^{4-}$

$Fe^{2+}$ is d6 and CN− is strong field, giving low-spin $t_{2g}^6$, which is diamagnetic.

Q30. Which compound undergoes SN1 reaction most readily?
  1. Methyl chloride
  2. Ethyl chloride
  3. tert-Butyl chloride
  4. Vinyl chloride

Answer: (C) tert-Butyl chloride

SN1 depends on carbocation stability. The tert-butyl carbocation is highly stabilized by hyperconjugation and inductive effects.

Q31. The major product of dehydration of 2-methyl-2-butanol is:
  1. 2-methyl-1-butene
  2. 2-methyl-2-butene
  3. 1-butene
  4. 2-butene

Answer: (B) 2-methyl-2-butene

Acid-catalyzed dehydration follows Zaitsev's rule, giving the more substituted 2-methyl-2-butene as major product.

Q32. Which element has the highest first ionization enthalpy among the following?
  1. B
  2. C
  3. N
  4. O

Answer: (C) N

Nitrogen has a stable half-filled 2p3 configuration, giving higher first ionization enthalpy than oxygen.

Q33. For an ideal gas, the compressibility factor Z is:
  1. 0
  2. 1
  3. Greater than 1 always
  4. Less than 1 always

Answer: (B) 1

An ideal gas obeys PV=nRT exactly, so $Z=PV/nRT=1$.

Q34. Which of the following is an example of a disproportionation reaction?
  1. $Zn+Cu^{2+}\to Zn^{2+}+Cu$
  2. $Cl_2+2OH^-\to Cl^-+ClO^-+H_2O$
  3. $NaCl\to Na^++Cl^-$
  4. $HCl+NaOH\to NaCl+H_2O$

Answer: (B) $Cl_2+2OH^-\to Cl^-+ClO^-+H_2O$

Chlorine is simultaneously reduced to Cl− and oxidized to ClO−, so it is disproportionation.

Q35. The number of sigma and pi bonds in benzene are respectively:
  1. 6 and 6
  2. 12 and 3
  3. 12 and 6
  4. 6 and 3

Answer: (B) 12 and 3

Benzene has 6 C-C sigma, 6 C-H sigma and 3 pi bonds: 12 sigma and 3 pi.

Q36. Which colligative property is most suitable for determining molar mass of proteins?
  1. Elevation in boiling point
  2. Depression in freezing point
  3. Osmotic pressure
  4. Relative lowering of vapour pressure

Answer: (C) Osmotic pressure

Proteins are high-molar-mass substances; osmotic pressure can be measured at room temperature using dilute solutions and is highly sensitive.

Q37. For a spontaneous process at constant temperature and pressure, Gibbs free energy change is:
  1. Positive
  2. Zero only
  3. Negative
  4. Always equal to enthalpy change

Answer: (C) Negative

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

Q38. Which reagent converts an aldehyde into a primary alcohol?
  1. PCC
  2. $NaBH_4$
  3. $KMnO_4$
  4. $HNO_3$

Answer: (B) $NaBH_4$

Sodium borohydride reduces aldehydes to primary alcohols.

Q39. The hybridization of carbon in CO2 is:
  1. sp
  2. sp2
  3. sp3
  4. dsp2

Answer: (A) sp

CO2 is linear with two electron domains around carbon, so carbon is sp hybridized.

Q40. Which oxide is amphoteric?
  1. $Na_2O$
  2. $MgO$
  3. $Al_2O_3$
  4. $SO_3$

Answer: (C) $Al_2O_3$

Al2O3 reacts with both acids and bases, hence it is amphoteric.

Q41. The oxidation state of chromium in $K_2Cr_2O_7$ is:
  1. +3
  2. +4
  3. +6
  4. +7

Answer: (C) +6

$2(+1)+2x+7(-2)=0$ gives x=+6.

Q42. Which has the highest lattice enthalpy among the following alkali metal halides?
  1. LiF
  2. LiCl
  3. NaF
  4. KF

Answer: (A) LiF

Lattice enthalpy increases as ionic sizes decrease. Li+ and F− are the smallest pair here.

Q43. The major product when propene reacts with HBr in the presence of peroxide is:
  1. 2-bromopropane
  2. 1-bromopropane
  3. Propane
  4. 1,2-dibromopropane

Answer: (B) 1-bromopropane

Peroxide effect causes anti-Markovnikov addition of HBr, giving 1-bromopropane.

Q44. Which molecule has the highest dipole moment?
  1. CO2
  2. BF3
  3. NH3
  4. CCl4

Answer: (C) NH3

CO2, BF3 and CCl4 are symmetrical and have zero net dipole moment. NH3 is polar.

Q45. For a weak acid HA, increasing its concentration generally causes its degree of ionization to:
  1. Increase
  2. Decrease
  3. Remain unchanged
  4. Become zero

Answer: (B) Decrease

For a weak electrolyte, degree of ionization decreases as concentration increases, approximately following Ostwald's dilution law.

Q46. Which polymer is a condensation polymer?
  1. Polythene
  2. PVC
  3. Nylon-6,6
  4. Teflon

Answer: (C) Nylon-6,6

Nylon-6,6 is formed by condensation of hexamethylenediamine and adipic acid with elimination of water.

Q47. The strongest acid among the following is:
  1. Phenol
  2. Ethanol
  3. p-Nitrophenol
  4. p-Cresol

Answer: (C) p-Nitrophenol

The electron-withdrawing nitro group stabilizes the phenoxide ion, increasing acidity.

Q48. Which quantum number determines the orientation of an orbital in space?
  1. Principal quantum number
  2. Azimuthal quantum number
  3. Magnetic quantum number
  4. Spin quantum number

Answer: (C) Magnetic quantum number

The magnetic quantum number m_l determines orbital orientation in space.

Q49. A buffer solution contains equal concentrations of a weak acid and its salt. Its pH is:
  1. Equal to pKa
  2. Equal to 7 always
  3. Equal to pKb
  4. Always zero

Answer: (A) Equal to pKa

Henderson-Hasselbalch equation gives pH=pKa+log([salt]/[acid]); equal concentrations make the logarithmic term zero.

Q50. Which metal is extracted by electrolytic reduction of its molten salt?
  1. Copper
  2. Sodium
  3. Iron
  4. Zinc

Answer: (B) Sodium

Highly reactive sodium cannot be reduced from aqueous solution and is obtained by electrolysis of molten NaCl.

Q51. If the roots of x^2-6x+k=0 are in the ratio 1:2, then k is:
  1. 6
  2. 8
  3. 9
  4. 12

Answer: (A) 6

Let the roots be $a$ and $2a$. Their sum is $3a=6$, so $a=2$. Their product is $k=a(2a)=4$. Hence $k=4$.

Q52. The maximum value of $x(1-x)$ for real x is:
  1. 1
  2. 1/2
  3. 1/4
  4. 2

Answer: (C) 1/4

$x(1-x)=1/4-(x-1/2)^2$, so maximum is 1/4.

Q53. If $|z-1|=|z+1|$, then z lies on:
  1. Real axis
  2. Imaginary axis
  3. Unit circle
  4. Line y=x

Answer: (B) Imaginary axis

Equal distances from 1 and -1 imply the perpendicular bisector of the segment joining them, i.e. the imaginary axis.

Q54. The value of $\lim_{x\to0}(1+x)^{1/x}$ is:
  1. 0
  2. 1
  3. e
  4. Infinity

Answer: (C) e

This is the standard exponential limit, equal to e.

Q55. The area enclosed between y=x and y=x^2 is:
  1. 1/3
  2. 1/6
  3. 1/2
  4. 2/3

Answer: (B) 1/6

Intersections are 0 and 1. Area is $\int_0^1(x-x^2)dx=1/2-1/3=1/6$.

Q56. If vectors a and b are perpendicular and |a|=3, |b|=4, then |a+b| is:
  1. 1
  2. 5
  3. 7
  4. 12

Answer: (B) 5

For perpendicular vectors, $|a+b|=\sqrt{a^2+b^2}=5$.

Q57. The distance between the planes 2x-3y+6z-5=0 and 2x-3y+6z+10=0 is:
  1. 5/7
  2. 15/7
  3. 3
  4. 15

Answer: (B) 15/7

Distance is $|10-(-5)|/\sqrt{4+9+36}=15/7$.

Q58. The eccentricity of a hyperbola is always:
  1. Less than 1
  2. Equal to 1
  3. Greater than 1
  4. Zero

Answer: (C) Greater than 1

For a hyperbola, $e>1$.

Q59. The number of real solutions of $e^x=x+2$ is:
  1. 0
  2. 1
  3. 2
  4. 3

Answer: (C) 2

The convex function e^x intersects the line x+2 twice: one root near -1.84 and another near 1.15.

Q60. If A is a 3x3 matrix and |A|=2, then |3A| is:
  1. 6
  2. 18
  3. 54
  4. 9

Answer: (C) 54

For a $3\times3$ matrix, $|kA|=k^3|A|$. Therefore $|3A|=3^3\times2=54$.

Q61. The coefficient of x^3 in $(1+x)^5(1-x)^3$ is:
  1. $-6$
  2. $-2$
  3. $2$
  4. $10$

Answer: (A) $-6$

$(1+x)^5(1-x)^3=(1+x)^2(1-x^2)^3$. Up to the $x^3$ term, $(1+2x+x^2)(1-3x^2+\cdots)$ gives the $x^3$ coefficient $2(-3)=-6$.

Q62. The general solution of $dy/dx=3x^2$ is:
  1. $y=x^3+C$
  2. $y=3x+C$
  3. $y=x^2+C$
  4. $y=3x^3+C$

Answer: (A) $y=x^3+C$

Integrating $3x^2$ gives $y=x^3+C$.

Q63. If tan A=1/2 and tan B=1/3, where A+B is acute, then tan(A+B) is:
  1. 1
  2. 5/6
  3. 6/5
  4. 1/5

Answer: (A) 1

$\tan(A+B)=(1/2+1/3)/(1-1/6)=1$.

Q64. The probability that a randomly selected integer from 1 to 100 is divisible by 2 or 3 is:
  1. 1/2
  2. 2/3
  3. 67/100
  4. 5/6

Answer: (C) 67/100

Multiples of 2:50, of 3:33, of 6:16. Union=50+33-16=67.

Q65. The determinant of the matrix [[1,1,1],[1,2,3],[1,4,9]] is:
  1. 2
  2. 4
  3. 6
  4. 8

Answer: (A) 2

Expanding the determinant gives $1(18-12)-1(9-3)+1(4-2)=6-6+2=2$. Hence the determinant is $2$.

Q66. The radius of the circle x^2+y^2-6x+8y=0 is:
  1. 3
  2. 4
  3. 5
  4. 6

Answer: (C) 5

Completing squares gives $(x-3)^2+(y+4)^2=25$, so radius is 5.

Q67. The derivative of x^x for x>0 is:
  1. $x^{x-1}$
  2. $x^x$
  3. $x^x(1+\ln x)$
  4. $x^{x}(\ln x-1)$

Answer: (C) $x^x(1+\ln x)$

Taking logs, ln y=x ln x. Hence y'/y=ln x+1, giving $y'=x^x(1+\ln x)$.

Q68. If the arithmetic mean of two positive numbers is 10 and their geometric mean is 8, their numbers are:
  1. 4 and 16
  2. 5 and 15
  3. 8 and 12
  4. 6 and 14

Answer: (A) 4 and 16

Sum=20 and product=64. The roots of t^2-20t+64=0 are 4 and 16.

Q69. The number of solutions of sin x = x/2 in [0, 2π] is:
  1. 1
  2. 2
  3. 3
  4. 4

Answer: (B) 2

x=0 is one solution and there is one positive nonzero intersection in (0,2), while no solution occurs beyond 2 because x/2>1.

Q70. The minimum value of x^2+4x+7 is:
  1. 1
  2. 2
  3. 3
  4. 7

Answer: (C) 3

Complete square: $(x+2)^2+3$, so minimum is 3.

Q71. If a line has direction ratios (2,-1,2), its direction cosines are:
  1. (2,-1,2)
  2. (2/3,-1/3,2/3)
  3. (1,-1,1)
  4. (1/2,-1,2)

Answer: (B) (2/3,-1/3,2/3)

Magnitude of direction-ratio vector is 3, so divide each component by 3.

Q72. The integral $\int_0^1 \frac{dx}{1+x^2}$ equals:
  1. $\pi/2$
  2. $\pi/4$
  3. 1
  4. 2

Answer: (B) $\pi/4$

Antiderivative is tan^{-1}x, giving $\tan^{-1}(1)-\tan^{-1}(0)=\pi/4$.

Q73. If the roots of x^2+px+q=0 are both positive, which condition must hold?
  1. p>0,q<0
  2. p<0,q>0
  3. p>0,q>0
  4. p<0,q<0

Answer: (B) p<0,q>0

Sum of roots=-p>0 implies p<0; product=q>0. Thus p<0 and q>0.

Q74. The variance of the numbers 2,4,6,8,10 is:
  1. 4
  2. 8
  3. 16
  4. 10

Answer: (B) 8

Mean is 6. Squared deviations are 16,4,0,4,16; their average is 40/5=8.

Q75. The tangent to the parabola y^2=4ax at the point (at^2,2at) is:
  1. $ty=x+at^2$
  2. $ty=x+at^2$ with a negative sign
  3. $y=tx+a$
  4. $ty=x-at^2$

Answer: (A) $ty=x+at^2$

For the parabola $y^2=4ax$, the tangent at $(at^2,2at)$ is $ty=x+at^2$. Hence the correct option is $ty=x+at^2$.