IMU-CET MOCK TEST — SET 1

Mathematics | 50 Questions
Time target: ~45 minutes
Marking: +1 correct, −0.25 incorrect
Difficulty: Moderate → Hard
Do not look for the answer key yet.

Mathematics

Q1. If the roots of$$x^2-(k+2)x+(k^2-k+2)=0$$x2−(k+2)x+(k2−k+2)=0

are real and distinct, then the range of $k$k is:

A) $k<\frac{3-\sqrt{17}}4$k<43−17​​
B) $\frac{3-\sqrt{17}}4<k<\frac{3+\sqrt{17}}4$43−17​​<k<43+17​​
C) $k>\frac{3+\sqrt{17}}4$k>43+17​​
D) $k<\frac{3-\sqrt{17}}4$k<43−17​​ or $k>\frac{3+\sqrt{17}}4$k>43+17​​

---

Q2. Let$$f(x)=\frac{x^2+ax+b}{x^2+1}.$$f(x)=x2+1×2+ax+b​.

If $f(x)$f(x) has its maximum value at $x=1$x=1 and minimum value at $x=-1$x=−1, then $a+b$a+b equals:

A) 0
B) 1
C) 2
D) 3

---

Q3. The number of real solutions of$$|x^2-5x+4|=x+1$$∣x2−5x+4∣=x+1

is:

A) 1
B) 2
C) 3
D) 4

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Q4. If$$z+\frac1z=2\cos\theta,$$z+z1​=2cosθ,

where $z\neq0$z=0, then$$z^n+\frac1{z^n}$$zn+zn1​

is equal to:

A) $2\cos(n\theta)$2cos(nθ)
B) $2\sin(n\theta)$2sin(nθ)
C) $2^n\cos\theta$2ncosθ
D) $\cos(n\theta)$cos(nθ)

---

Q5. If$$\log_2(x-1)+\log_2(x+3)=3,$$log2​(x−1)+log2​(x+3)=3,

then the value of$$x^2+2x$$x2+2x

is:

A) 5
B) 7
C) 8
D) 9

---

Q6. The coefficient of $x^5$x5 in$$(1+x)^8(1-x)^6$$(1+x)8(1−x)6

is:

A) −14
B) −7
C) 7
D) 14

---

Q7. A point $P(x,y)$P(x,y) moves such that its distance from $(2,0)$(2,0) is twice its distance from $(-2,0)$(−2,0). The locus of $P$P is:

A) A circle
B) A parabola
C) An ellipse
D) A hyperbola

---

Q8. The tangent to the curve$$y=x^3-3x^2+2$$y=x3−3×2+2

which is parallel to the line $y=9x-5$y=9x−5 touches the curve at:

A) $x=1$x=1 only
B) $x=2$x=2 only
C) $x=-1$x=−1 and $x=3$x=3
D) $x=0$x=0 and $x=2$x=2

---

Q9. If$$\int_0^1\frac{x^3}{1+x^2}\,dx= a-\frac12\ln2,$$∫01​1+x2x3​dx=a−21​ln2,

then $a$a is:

A) $\frac12$21​
B) $\frac34$43​
C) $\frac14$41​
D) 1

---

Q10. Evaluate:$$\lim_{x\to0}\frac{\tan x-\sin x}{x^3}.$$x→0lim​x3tanx−sinx​.

A) 0
B) $\frac16$61​
C) $\frac12$21​
D) 1

---

Q11. If the vectors$$\vec a=2\hat i-\hat j+\hat k,\qquad \vec b=\hat i+2\hat j-\lambda\hat k$$a=2i^−j^​+k^,b=i^+2j^​−λk^

are perpendicular, then $\lambda$λ is:

A) 0
B) 2
C) 4
D) −4

---

Q12. The distance between the parallel planes$$2x-3y+6z=7$$2x−3y+6z=7

and$$4x-6y+12z=19$$4x−6y+12z=19

is:

A) $\frac1{7}$71​
B) $\frac2{7}$72​
C) $\frac3{7}$73​
D) $\frac4{7}$74​

---

Q13. If$$\begin{vmatrix} 1&1&1\\ a&b&c\\ a^2&b^2&c^2 \end{vmatrix}=0,$$​1aa2​1bb2​1cc2​​=0,

then which statement must be true?

A) $a=b=c$a=b=c
B) At least two of $a,b,c$a,b,c are equal
C) $abc=0$abc=0
D) $a+b+c=0$a+b+c=0

---

Q14. A fair die is thrown repeatedly until either 6 occurs or two consecutive throws give the same number. The probability that 6 occurs first is:

A) $\frac{6}{11}$116​
B) $\frac{5}{11}$115​
C) $\frac12$21​
D) $\frac{3}{7}$73​

---

Q15. Two events $A$A and $B$B satisfy$$P(A)=\frac12,\quad P(B)=\frac35,\quad P(A\cup B)=\frac45.$$P(A)=21​,P(B)=53​,P(A∪B)=54​.

Then $P(A\mid B)$P(A∣B) equals:

A) $\frac13$31​
B) $\frac12$21​
C) $\frac23$32​
D) $\frac34$43​

---

Q16. The equation$$\sin^{-1}x+\sin^{-1}(2x)=\frac{\pi}{2}$$sin−1x+sin−1(2x)=2π​

has a solution $x$x equal to:

A) $\frac15$51​
B) $\frac1{\sqrt5}$5​1​
C) $\frac12$21​
D) $\frac{\sqrt3}{2}$23​​

---

Q17. If$$\tan^{-1}x+\tan^{-1}(2x)=\frac{\pi}{4},$$tan−1x+tan−1(2x)=4π​,

then $x$x is:

A) $\frac{\sqrt5-1}{4}$45​−1​
B) $\frac{\sqrt5+1}{4}$45​+1​
C) $\frac12$21​
D) 1

---

Q18. The minimum value of$$x^2+\frac{16}{x^2+1}$$x2+x2+116​

for real $x$x is:

A) 2
B) 4
C) 5
D) 8

---

Q19. If $a,b,c>0$a,b,c>0 and $abc=1$abc=1, the minimum value of$$\frac1{1+a}+\frac1{1+b}+\frac1{1+c}$$1+a1​+1+b1​+1+c1​

is:

A) $\frac12$21​
B) 1
C) $\frac32$23​
D) 2

---

Q20. The number of solutions of$$2^x+2^{-x}=3$$2x+2−x=3

is:

A) 0
B) 1
C) 2
D) 3

---

Q21. If the arithmetic progression $a, a+d,a+2d,\ldots$a,a+d,a+2d,… has$$S_{10}=150,\qquad S_{20}=500,$$S10​=150,S20​=500,

then its 15th term is:

A) 30
B) 35
C) 40
D) 45

---

Q22. Three numbers are in GP. Their sum is 14 and their product is 64. The middle number is:

A) 2
B) 4
C) 6
D) 8

---

Q23. The equation of the circle passing through $(1,2)$(1,2), $(3,4)$(3,4), and $(-1,4)$(−1,4) has radius:

A) $\sqrt5$5​
B) $\sqrt{10}$10​
C) $3$3
D) $2\sqrt2$22​

---

Q24. The eccentricity of the ellipse$$9x^2+16y^2=144$$9×2+16y2=144

is:

A) $\frac34$43​
B) $\frac{\sqrt7}{4}$47​​
C) $\frac{\sqrt7}{3}$37​​
D) $\frac{\sqrt{15}}4$415​​

---

Q25. A line through $(1,2)$(1,2) cuts the coordinate axes at $A$A and $B$B. The minimum possible area of triangle $OAB$OAB is:

A) 2
B) 4
C) 6
D) 8

---

Q26. If$$\frac{dy}{dx}+y\tan x=\sin x$$dxdy​+ytanx=sinx

and $y(0)=1$y(0)=1, then $y(\pi/4)$y(π/4) is:

A) $\frac12$21​
B) $\frac1{\sqrt2}$2​1​
C) $\sqrt2-1$2​−1
D) 1

---

Q27. If$$f(x)=x^x,\quad x>0,$$f(x)=xx,x>0,

then $f'(1)$f′(1) equals:

A) 0
B) 1
C) $e$e
D) $2$2

---

Q28. The area enclosed between$$y=x^2$$y=x2

and$$y=2x$$y=2x

is:

A) $\frac23$32​
B) $\frac43$34​
C) 2
D) $\frac83$38​

---

Q29. If$$\int_0^{\pi/2}\ln(\sin x)\,dx=-\frac{\pi}{2}\ln2,$$∫0π/2​ln(sinx)dx=−2π​ln2,

then$$\int_0^{\pi/2}\ln(\cos x)\,dx$$∫0π/2​ln(cosx)dx

equals:

A) 0
B) $-\frac{\pi}{2}\ln2$−2π​ln2
C) $-\pi\ln2$−πln2
D) $\frac{\pi}{2}\ln2$2π​ln2

---

Q30. The determinant$$\begin{vmatrix} 1&2&3\\ 2&3&4\\ 3&4&k \end{vmatrix}$$​123​234​34k​​

is zero when:

A) $k=4$k=4
B) $k=5$k=5
C) $k=6$k=6
D) $k=7$k=7

---

Q31. If the roots of$$x^3-6x^2+11x-6=0$$x3−6×2+11x−6=0

are $\alpha,\beta,\gamma$α,β,γ, then$$\frac1{\alpha}+\frac1{\beta}+\frac1{\gamma}$$α1​+β1​+γ1​

is:

A) 1
B) $\frac{11}{6}$611​
C) $\frac52$25​
D) 6

---

Q32. The number of onto functions from a set containing 4 elements to a set containing 3 elements is:

A) 24
B) 30
C) 36
D) 81

---

Q33. A box contains 5 red and 4 blue balls. Two balls are drawn without replacement. Given that at least one is red, the probability that both are red is:

A) $\frac5{17}$175​
B) $\frac5{13}$135​
C) $\frac5{12}$125​
D) $\frac{10}{17}$1710​

---

Q34. If$$\vec a\times\vec b=\vec a\times\vec c$$a×b=a×c

and $\vec a\neq\vec0$a=0, then:

A) $\vec b=\vec c$b=c necessarily
B) $\vec b-\vec c$b−c is parallel to $\vec a$a
C) $\vec b+\vec c$b+c is parallel to $\vec a$a
D) $\vec b\cdot\vec c=0$b⋅c=0

---

Q35. The angle between the planes$$x+2y+2z=5$$x+2y+2z=5

and$$2x-y+2z=7$$2x−y+2z=7

is:

A) $30^\circ$30∘
B) $45^\circ$45∘
C) $60^\circ$60∘
D) $90^\circ$90∘

---

Q36. If$$\sin x+\sin 2x+\sin3x=0,$$sinx+sin2x+sin3x=0,

then which of the following can be a solution?

A) $x=\frac{\pi}{6}$x=6π​
B) $x=\frac{\pi}{4}$x=4π​
C) $x=\frac{\pi}{3}$x=3π​
D) $x=\frac{\pi}{2}$x=2π​

---

Q37. The maximum value of$$\sin x+\cos x+\sin x\cos x$$sinx+cosx+sinxcosx

is:

A) 1
B) $\frac32$23​
C) $1+\frac{\sqrt2}{2}$1+22​​
D) 2

---

Q38. If $x,y>0$x,y>0 and$$x+y=10,$$x+y=10,

the maximum value of$$x^2y^2$$x2y2

is:

A) 100
B) 400
C) 625
D) 2500

---

Q39. If$$\left| \begin{matrix} x&1\\1&x\end{matrix}\right|=0,$$​x1​1x​​=0,

then the values of $x$x are:

A) 0, 1
B) 1 only
C) $1,-1$1,−1
D) $-1$−1 only

---

Q40. The number of distinct arrangements of the letters of MARINE in which the vowels are not together is:

A) 240
B) 360
C) 480
D) 540

---

Q41. If$$(1+x)^n$$(1+x)n

has its 3rd, 4th and 5th coefficients in AP, then $n$n is:

A) 5
B) 6
C) 7
D) 8

---

Q42. The solution set of$$\frac{x-1}{x+2}>2$$x+2x−1​>2

is:

A) $x<-5$x<−5
B) $-5<x<-2$−5<x<−2
C) $x>-2$x>−2
D) $x<-2$x<−2 or $x>1$x>1

---

Q43. If$$\alpha,\beta$$α,β

are roots of$$x^2-4x+1=0,$$x2−4x+1=0,

then$$\alpha^3+\beta^3$$α3+β3

equals:

A) 28
B) 40
C) 52
D) 56

---

Q44. A particle moves along the $x$x-axis with velocity$$v(t)=t^2-4t+3.$$v(t)=t2−4t+3.

The particle changes its direction during $0\le t\le4$0≤t≤4:

A) once
B) twice
C) three times
D) never

---

Q45. The function$$f(x)=x^3-3x$$f(x)=x3−3x

is increasing in:

A) $(-1,1)$(−1,1) only
B) $(-\infty,-1)\cup(1,\infty)$(−∞,−1)∪(1,∞)
C) $(-\infty,1)$(−∞,1)
D) all real numbers

---

Q46. If$$\sum_{r=0}^{n}\binom nr 2^r=729,$$r=0∑n​(rn​)2r=729,

then $n$n is:

A) 5
B) 6
C) 7
D) 8

---

Q47. The coefficient of $x^0$x0 in$$\left(x^2+\frac1x\right)^6$$(x2+x1​)6

is:

A) 15
B) 20
C) 30
D) 60

---

Q48. If the lines$$3x+4y=7$$3x+4y=7

and$$6x+ky=9$$6x+ky=9

are perpendicular, then $k$k is:

A) $-\frac92$−29​
B) $-\frac83$−38​
C) $\frac83$38​
D) $\frac92$29​

---

Q49. A random variable $X$X takes values $0,1,2$0,1,2 with probabilities $p,2p,1-3p$p,2p,1−3p, respectively. If $E(X)=1.2$E(X)=1.2, then $P(X=2)$P(X=2) is:

A) 0.2
B) 0.3
C) 0.4
D) 0.5

---

Q50. Let$$I=\int_0^1\frac{1}{1+x^2}\,dx.$$I=∫01​1+x21​dx.

Which of the following is equal to $I$I?

A) $\ln2$ln2
B) $\frac{\pi}{4}$4π​
C) $\frac12\ln2$21​ln2
D) $\frac{\pi}{2}$2π​

SECTION B — PHYSICS

Q51–Q100 | 50 Questions

Q51. A particle is projected with speed $u$u at an angle $\theta$θ to the horizontal. If its maximum height equals one-fourth of its horizontal range, then $\tan\theta$tanθ is:

A) $1/2$1/2
B) 1
C) 2
D) 4

Q52. A body is projected vertically upward from the ground with speed $30\,m/s$30m/s. Taking $g=10\,m/s^2$g=10m/s2, the ratio of distances travelled during the 3rd and 5th seconds is:

A) 1:1
B) 3:1
C) 1:3
D) 5:3

Q53. A car moves around a circular track of radius $50\,m$50m at $10\,m/s$10m/s. If its speed is increasing at $2\,m/s^2$2m/s2, the magnitude of its total acceleration is:

A) $2\,m/s^2$2m/s2
B) $2\sqrt2\,m/s^2$22​m/s2
C) $2.4\,m/s^2$2.4m/s2
D) $4\,m/s^2$4m/s2

Q54. A block of mass $m$m rests on a rough inclined plane of angle $\theta$θ. The coefficient of static friction is $\mu$μ. The block is just about to slide downward. Then:

A) $\mu=\sin\theta$μ=sinθ
B) $\mu=\cos\theta$μ=cosθ
C) $\mu=\tan\theta$μ=tanθ
D) $\mu=\cot\theta$μ=cotθ

Q55. Two blocks of masses $2\,kg$2kg and $3\,kg$3kg are connected by a light string over a frictionless pulley. The acceleration of the system is:

A) $g/5$g/5
B) $g/3$g/3
C) $2g/5$2g/5
D) $3g/5$3g/5

Q56. A particle moves under a force $F=(3x^2+2x)\,N$F=(3×2+2x)N. The work done in moving it from $x=0$x=0 to $x=2\,m$x=2m is:

A) 8 J
B) 10 J
C) 12 J
D) 16 J

Q57. A body of mass $m$m moving with speed $v$v collides perfectly inelastically with another body of mass $2m$2m initially at rest. The fraction of initial kinetic energy lost is:

A) $1/3$1/3
B) $2/3$2/3
C) $1/2$1/2
D) $3/4$3/4

Q58. A satellite revolves around Earth in a circular orbit. If its orbital radius is increased by a factor of 4, its orbital speed becomes:

A) $4v$4v
B) $2v$2v
C) $v/2$v/2
D) $v/4$v/4

Q59. A planet has the same radius as Earth but twice Earth’s mass. Its escape velocity is:

A) $v_e/2$ve​/2
B) $v_e/\sqrt2$ve​/2​
C) $\sqrt2v_e$2​ve​
D) $2v_e$2ve​

Q60. A uniform rod of length $L$L and mass $M$M is pivoted at one end. Its moment of inertia about the pivot is:

A) $ML^2/2$ML2/2
B) $ML^2/3$ML2/3
C) $ML^2/6$ML2/6
D) $ML^2/12$ML2/12

Q61. A disc and a ring of equal mass and radius roll down an inclined plane without slipping. Which reaches the bottom first?

A) Ring
B) Disc
C) Both simultaneously
D) Depends only on their masses

Q62. A simple pendulum has time period $T$T on Earth. At a height equal to Earth’s radius above the surface, its time period becomes:

A) $T/\sqrt2$T/2​
B) $\sqrt2T$2​T
C) $2T$2T
D) $4T$4T

Q63. In SHM, when displacement is $A/2$A/2, the ratio of kinetic energy to potential energy is:

A) 1:1
B) 1:3
C) 3:1
D) 4:1

Q64. Two SHMs of equal amplitude and frequency have a phase difference of $120^\circ$120∘. Their resultant amplitude is:

A) $A$A
B) $\sqrt2A$2​A
C) $\sqrt3A$3​A
D) $2A$2A

Q65. A wave is represented by$$y=0.02\sin(100\pi t-4\pi x).$$y=0.02sin(100πt−4πx).

Its velocity is:

A) 12.5 m/s
B) 25 m/s
C) 50 m/s
D) 100 m/s

Q66. A source of sound of frequency 500 Hz moves toward a stationary observer with speed $20\,m/s$20m/s. Taking speed of sound as $340\,m/s$340m/s, observed frequency is approximately:

A) 471 Hz
B) 500 Hz
C) 531 Hz
D) 560 Hz

Q67. One mole of an ideal gas expands isothermally from volume $V$V to $2V$2V. The work done is:

A) $RT$RT
B) $RT\ln2$RTln2
C) $2RT$2RT
D) $RT/2$RT/2

Q68. An ideal gas undergoes an adiabatic expansion. During the process:

A) Temperature remains constant
B) Heat is absorbed
C) Work is done at the expense of internal energy
D) Internal energy remains constant

Q69. Two moles of a monoatomic ideal gas are heated at constant volume through $50\,K$50K. The increase in internal energy is:

A) $100R$100R
B) $150R$150R
C) $200R$200R
D) $250R$250R

Q70. A Carnot engine operates between $500\,K$500K and $300\,K$300K. Its efficiency is:

A) 20%
B) 30%
C) 40%
D) 60%

Q71. Two charges $+q$+q and $-q$−q are separated by distance $2a$2a. At the midpoint, the electric potential is:

A) $kq/a$kq/a
B) $-kq/a$−kq/a
C) $2kq/a$2kq/a
D) 0

Q72. A charge $q$q is placed at the centre of a cube. The electric flux through one face is:

A) $q/\epsilon_0$q/ϵ0​
B) $q/(2\epsilon_0)$q/(2ϵ0​)
C) $q/(4\epsilon_0)$q/(4ϵ0​)
D) $q/(6\epsilon_0)$q/(6ϵ0​)

Q73. A capacitor is charged to potential $V$V and disconnected from the battery. If its plate separation is doubled, its stored energy becomes:

A) $U/2$U/2
B) $U$U
C) $2U$2U
D) $4U$4U

Q74. Three capacitors $2\mu F,3\mu F,6\mu F$2μF,3μF,6μF are connected in parallel. Equivalent capacitance is:

A) $1\mu F$1μF
B) $6\mu F$6μF
C) $9\mu F$9μF
D) $11\mu F$11μF

Q75. A wire has resistance $R$R. It is stretched uniformly to twice its original length without changing volume. Its new resistance is:

A) $R/2$R/2
B) $R$R
C) $2R$2R
D) $4R$4R

Q76. A battery of emf $12V$12V and internal resistance $1\Omega$1Ω supplies a current of $2A$2A. The terminal voltage is:

A) 8 V
B) 10 V
C) 12 V
D) 14 V

Q77. A current-carrying wire is placed perpendicular to a magnetic field. If current is doubled and magnetic field is halved, magnetic force becomes:

A) Half
B) Same
C) Double
D) Four times

Q78. An electron enters a uniform magnetic field perpendicular to the field. Its path is:

A) Straight line
B) Parabola
C) Circle
D) Ellipse

Q79. A charged particle enters a magnetic field with velocity having both parallel and perpendicular components. Its trajectory is:

A) Circular
B) Helical
C) Parabolic
D) Straight

Q80. A coil of 100 turns experiences a change in magnetic flux from $5\times10^{-3}\,Wb$5×10−3Wb to zero in $0.1s$0.1s. Average induced emf is:

A) 0.5 V
B) 2 V
C) 5 V
D) 10 V

Q81. In an AC circuit, $V_{rms}=220V$Vrms​=220V. The peak voltage is approximately:

A) 110 V
B) 220 V
C) 311 V
D) 440 V

Q82. In a pure inductive AC circuit, current:

A) Leads voltage by $90^\circ$90∘
B) Lags voltage by $90^\circ$90∘
C) Is in phase with voltage
D) Lags by $180^\circ$180∘

Q83. An ideal transformer has 1000 turns in primary and 200 turns in secondary. If primary voltage is 220 V, secondary voltage is:

A) 11 V
B) 44 V
C) 110 V
D) 440 V

Q84. In Young’s double-slit experiment, fringe width is $\beta$β. If wavelength is doubled and slit separation is halved, the new fringe width is:

A) $\beta/4$β/4
B) $\beta/2$β/2
C) $2\beta$2β
D) $4\beta$4β

Q85. In a double-slit experiment, the intensity at the central maximum is $I_0$I0​. If one slit is closed, intensity becomes:

A) $I_0/4$I0​/4
B) $I_0/2$I0​/2
C) $I_0$I0​
D) $2I_0$2I0​

Q86. The critical angle for glass-air interface is $30^\circ$30∘. Refractive index of glass is:

A) $1/2$1/2
B) $\sqrt2$2​
C) 2
D) $1/\sqrt2$1/2​

Q87. A convex lens of focal length 20 cm forms a real image twice the size of the object. The object distance is:

A) 10 cm
B) 20 cm
C) 30 cm
D) 40 cm

Q88. A concave mirror forms a real image equal in size to the object. The object is placed:

A) At focus
B) Between focus and centre
C) At centre of curvature
D) Beyond centre

Q89. The de Broglie wavelength of an electron accelerated through potential $V$V is proportional to:

A) $V$V
B) $1/V$1/V
C) $\sqrt V$V​
D) $1/\sqrt V$1/V​

Q90. In the photoelectric effect, increasing the intensity of incident light while keeping frequency fixed above threshold primarily increases:

A) Maximum kinetic energy
B) Stopping potential
C) Photoelectric current
D) Work function

Q91. The half-life of a radioactive substance is 10 days. The fraction remaining after 30 days is:

A) $1/2$1/2
B) $1/4$1/4
C) $1/8$1/8
D) $1/16$1/16

Q92. In Bohr’s model, the radius of the $n$n-th orbit is proportional to:

A) $n$n
B) $n^2$n2
C) $1/n$1/n
D) $1/n^2$1/n2

Q93. A nucleus has mass defect $0.01u$0.01u. Its binding energy is approximately:

A) 0.931 MeV
B) 9.31 MeV
C) 93.1 MeV
D) 931 MeV

Q94. A semiconductor diode is forward biased when:

A) P-side is connected to negative terminal
B) N-side is connected to positive terminal
C) P-side is connected to positive terminal
D) Both terminals are grounded

Q95. In a transistor, if emitter current is $10mA$10mA and collector current is $9.5mA$9.5mA, the base current is:

A) 0.05 mA
B) 0.5 mA
C) 1.5 mA
D) 19.5 mA

Q96. An ideal logic gate gives output 0 only when both inputs are 1. The gate is:

A) OR
B) AND
C) NAND
D) NOR

Q97. A body of mass $2kg$2kg is attached to a spring of spring constant $200N/m$200N/m. Its angular frequency is:

A) 5 rad/s
B) 10 rad/s
C) 20 rad/s
D) 100 rad/s

Q98. A projectile has maximum range $R$R. If its initial velocity is doubled, the maximum range becomes:

A) $2R$2R
B) $3R$3R
C) $4R$4R
D) $R/2$R/2

Q99. A body is moving in a circular path with constant speed. Which quantity is necessarily changing?

A) Speed
B) Kinetic energy
C) Velocity
D) Mass

Q100. A 4 kg block is pulled by a horizontal force of 20 N on a frictionless surface. Starting from rest, its kinetic energy after 5 s is:

A) 250 J
B) 500 J
C) 625 J
D) 1000 J

---

SECTION C — CHEMISTRY

Q101–Q120 | 20 Questions

Q101. For a reaction, doubling the concentration of reactant doubles the rate, while doubling the concentration of another reactant makes the rate four times. The overall order is:

A) 1
B) 2
C) 3
D) 4

Q102. For a first-order reaction, the half-life is independent of:

A) Temperature
B) Rate constant
C) Initial concentration
D) Activation energy

Q103. The pH of $10^{-3}M$10−3M HCl is approximately:

A) 1
B) 2
C) 3
D) 11

Q104. A buffer solution resists change in:

A) Temperature
B) Pressure
C) pH
D) Volume

Q105. Which has the highest boiling point?

A) CH₄
B) NH₃
C) H₂O
D) HF

Q106. The hybridisation of carbon in $CO_2$CO2​ is:

A) sp
B) sp²
C) sp³
D) dsp²

Q107. Which molecule has zero dipole moment?

A) H₂O
B) NH₃
C) CO₂
D) SO₂

Q108. The oxidation state of chromium in $K_2Cr_2O_7$K2​Cr2​O7​ is:

A) +3
B) +4
C) +6
D) +7

Q109. Which species is paramagnetic?

A) $N_2$N2​
B) $O_2$O2​
C) $CO_2$CO2​
D) $CH_4$CH4​

Q110. The strongest reducing agent among alkali metals in aqueous solution is generally:

A) Li
B) Na
C) K
D) Cs

Q111. The IUPAC name of $CH_3CH(CH_3)CH_2OH$CH3​CH(CH3​)CH2​OH is:

A) 2-methylpropan-1-ol
B) 2-methylpropan-2-ol
C) butan-2-ol
D) 3-methylpropan-1-ol

Q112. Benzene primarily undergoes:

A) Addition reactions
B) Electrophilic substitution
C) Nucleophilic substitution
D) Elimination

Q113. Which reagent distinguishes aldehydes from ketones?

A) NaOH
B) Tollens’ reagent
C) HCl
D) NaCl

Q114. The major product of dehydration of 2-butanol is predominantly:

A) 1-butene
B) cis-2-butene only
C) trans-2-butene predominantly
D) butane

Q115. The monomer used to produce PVC is:

A) Ethene
B) Propene
C) Vinyl chloride
D) Styrene

Q116. The coordination number of Co in $[Co(NH_3)_6]Cl_3$[Co(NH3​)6​]Cl3​ is:

A) 3
B) 4
C) 6
D) 9

Q117. Which has the greatest lattice energy generally?

A) NaCl
B) MgO
C) KCl
D) CaO

Q118. According to Le Chatelier’s principle, increasing pressure favors the side having:

A) More gaseous moles
B) Fewer gaseous moles
C) Equal gaseous moles only
D) Higher temperature

Q119. For an exothermic reaction at equilibrium, increasing temperature generally:

A) Increases $K$K
B) Decreases $K$K
C) Does not affect $K$K
D) Makes $K=1$K=1

Q120. The number of sigma and pi bonds in benzene respectively is:

A) 6, 3
B) 9, 3
C) 12, 3
D) 12, 6

---

SECTION D — ENGLISH

Q121–Q160 | 40 Questions

Q121. Choose the word closest in meaning to “meticulous”:

A) Careless
B) Thorough
C) Rapid
D) Uncertain

Q122. Choose the antonym of “obsolete”:

A) Ancient
B) Outdated
C) Current
D) Useless

Q123. Identify the grammatically correct sentence:

A) Neither of the boys have completed their work.
B) Neither of the boys has completed his work.
C) Neither of the boys have completed his work.
D) Neither boys has completed their work.

Q124. Choose the correctly spelt word:

A) Accomodation
B) Acommodation
C) Accommodation
D) Accommadation

Q125. “To hit the nail on the head” means:

A) To make a mistake
B) To describe something exactly
C) To work carelessly
D) To avoid an issue

Q126. Choose the correct passive form:

“They will have completed the project by Monday.”

A) The project will complete by Monday.
B) The project will be completed by Monday.
C) The project will have been completed by Monday.
D) The project has been completed by Monday.

Q127. Choose the correct indirect speech:

He said, “I am working hard.”

A) He said that I am working hard.
B) He said that he was working hard.
C) He said that he is working hard.
D) He says that he was working hard.

Q128. Fill in the blank:

“Hardly had the ship left the harbour _____ the storm began.”

A) than
B) when
C) then
D) while

Q129. Choose the correct preposition:

“He is proficient _____ mathematics.”

A) at
B) in
C) on
D) with

Q130. Identify the error:

“Each of the candidates have submitted their application.”

A) Each
B) candidates
C) have
D) application

Q131. The word “ambiguous” means:

A) Clear
B) Having more than one possible meaning
C) Incorrect
D) Extremely difficult

Q132. Choose the best replacement:

“He is senior than me.”

A) senior from me
B) senior to me
C) senior with me
D) senior over me

Q133. Choose the correctly punctuated sentence:

A) However we decided to continue.
B) However, we decided to continue.
C) However we, decided to continue.
D) However; we decided, to continue.

Q134. Choose the synonym of “prudent”:

A) Reckless
B) Wise
C) Aggressive
D) Impulsive

Q135. Choose the antonym of “scarce”:

A) Rare
B) Limited
C) Abundant
D) Insufficient

Q136. “The captain called off the operation.” Here “called off” means:

A) Started
B) Cancelled
C) Announced
D) Delayed briefly

Q137. Choose the correct sentence:

A) The news are shocking.
B) The news is shocking.
C) The news were shocking.
D) The news have shocking.

Q138. Complete the sentence:

“If I had known about the problem, I _____ helped you.”

A) will have
B) would
C) would have
D) had

Q139. Choose the correct spelling:

A) Questionnaire
B) Questionaire
C) Questionnair
D) Questionnare

Q140. The phrase “in lieu of” means:

A) In addition to
B) Instead of
C) Because of
D) In spite of

Q141. Choose the word that best completes the sentence:

“The evidence was _____ to prove his innocence.”

A) insufficient
B) sufficient
C) reluctant
D) ambiguous

Q142. Choose the correct form:

“Neither the captain nor the engineers _____ available.”

A) was
B) is
C) were
D) has

Q143. Identify the correctly formed sentence:

A) He insisted to go there.
B) He insisted on going there.
C) He insisted for going there.
D) He insisted go there.

Q144. The closest meaning of “conspicuous” is:

A) Hidden
B) Noticeable
C) Ordinary
D) Uncertain

Q145. Choose the antonym of “hostile”:

A) Aggressive
B) Friendly
C) Violent
D) Unfriendly

Q146. Choose the correct article:

“He is _____ honest officer.”

A) a
B) an
C) the
D) no article

Q147. Choose the correct sentence:

A) The equipment are expensive.
B) The equipments are expensive.
C) The equipment is expensive.
D) The equipment were expensive.

Q148. “Despite the heavy rain, the match continued.” The word “despite” indicates:

A) Cause
B) Contrast
C) Purpose
D) Result

Q149. Choose the correct form:

“By this time tomorrow, we _____ the examination.”

A) finish
B) finished
C) will have finished
D) have finished

Q150. Choose the synonym of “candid”:

A) Frank
B) Secretive
C) Deceptive
D) Hesitant

Q151. Identify the error:

“The captain, along with his officers, were present.”

A) captain
B) along with
C) his officers
D) were

Q152. Choose the correct word:

“The new regulation will _____ all ships entering the port.”

A) effect
B) affect
C) afflict
D) infect

Q153. Choose the correct sentence:

A) I prefer tea than coffee.
B) I prefer tea over coffee.
C) I prefer tea to coffee.
D) Both B and C are acceptable.

Q154. The phrase “at the eleventh hour” means:

A) Very early
B) At the last moment
C) Exactly at 11 AM
D) After eleven hours

Q155. Choose the correct passive voice:

“People speak English all over the world.”

A) English is spoken all over the world.
B) English was spoken all over the world.
C) English has spoken all over the world.
D) English speaks all over the world.

Q156. Choose the word closest in meaning to “deteriorate”:

A) Improve
B) Worsen
C) Stabilize
D) Repair

Q157. Fill in the blank:

“No sooner did the alarm ring _____ everyone rushed outside.”

A) when
B) than
C) then
D) that

Q158. Choose the correct sentence:

A) He has been working here since five years.
B) He has been working here for five years.
C) He is working here since five years.
D) He worked here since five years.

Q159. The antonym of “transparent” in the figurative sense is:

A) Obvious
B) Clear
C) Deceptive
D) Visible

Q160. Choose the most appropriate word:

“The officer gave a _____ explanation of the incident, leaving no major point unanswered.”

A) vague
B) comprehensive
C) reluctant
D) superficial

---

SECTION E — GENERAL APTITUDE & GK

Q161–Q200 | 40 Questions

Q161. A clock gains 5 minutes every hour. If it is set correctly at 8:00 AM, what will it show at 8:00 PM?

A) 8:55 PM
B) 9:00 PM
C) 9:05 PM
D) 9:10 PM

Q162. A train 180 m long crosses a pole in 9 seconds. Its speed is:

A) 60 km/h
B) 72 km/h
C) 80 km/h
D) 90 km/h

Q163. A man can complete a job in 12 days and another in 18 days. Working together, they complete it in:

A) 6 days
B) 7.2 days
C) 8 days
D) 9 days

Q164. A sum becomes ₹12,100 in two years at 10% compound interest annually. The principal is:

A) ₹9,000
B) ₹10,000
C) ₹11,000
D) ₹11,100

Q165. A vessel travels 120 km downstream in 4 hours and the same distance upstream in 6 hours. Speed of the stream is:

A) 4 km/h
B) 5 km/h
C) 6 km/h
D) 10 km/h

Q166. A mixture contains milk and water in ratio 5:2. If 14 L water is added, ratio becomes 5:4. Initial quantity of milk was:

A) 30 L
B) 35 L
C) 40 L
D) 45 L

Q167. If $3A=4B=6C$3A=4B=6C, then $A:B:C$A:B:C is:

A) 3:4:6
B) 4:3:2
C) 2:3:4
D) 6:4:3

Q168. The average of 8 numbers is 24. If one number 18 is replaced by 34, the new average is:

A) 25
B) 26
C) 27
D) 28

Q169. A shopkeeper marks an item 40% above cost and gives a 10% discount. His profit percentage is:

A) 20%
B) 24%
C) 26%
D) 30%

Q170. If $x:y=3:5$x:y=3:5 and $y:z=10:7$y:z=10:7, then $x:y:z$x:y:z is:

A) 3:5:7
B) 6:10:7
C) 3:10:7
D) 6:5:7

Q171. A number is increased by 20% and then decreased by 20%. The net change is:

A) 0%
B) 2% decrease
C) 4% decrease
D) 4% increase

Q172. A boat’s speed in still water is 15 km/h and stream speed is 3 km/h. Time required to travel 36 km downstream is:

A) 2 h
B) 2.5 h
C) 3 h
D) 4 h

Q173. If $CAT$CAT is coded as $DBU$DBU, then $SHIP$SHIP is coded as:

A) TIJQ
B) T H J Q
C) RGHO
D) UJKR

Q174. Find the missing term:

$2, 6, 12, 20, 30, ?$2,6,12,20,30,?

A) 36
B) 40
C) 42
D) 44

Q175. Find the next term:

$3, 9, 27, 81, ?$3,9,27,81,?

A) 162
B) 189
C) 243
D) 324

Q176. A person walks 5 km north, then 12 km east. His straight-line distance from the starting point is:

A) 13 km
B) 15 km
C) 17 km
D) 7 km

Q177. If all navigators are sailors and some sailors are engineers, which conclusion is definitely valid?

A) All engineers are navigators
B) Some navigators are engineers
C) All navigators are sailors
D) No sailor is an engineer

Q178. A cube is painted on all faces and cut into 27 equal smaller cubes. How many small cubes have exactly two painted faces?

A) 4
B) 8
C) 12
D) 16

Q179. A man faces north. He turns $90^\circ$90∘ clockwise, then $180^\circ$180∘ anticlockwise. He is now facing:

A) North
B) South
C) East
D) West

Q180. If today is Wednesday, what day will it be 100 days later?

A) Monday
B) Wednesday
C) Friday
D) Saturday

Q181. The headquarters of the International Maritime Organization (IMO) is in:

A) Geneva
B) London
C) New York
D) Rotterdam

Q182. IMO stands for:

A) International Marine Organization
B) International Maritime Organization
C) International Maritime Office
D) Indian Maritime Organization

Q183. SOLAS primarily deals with:

A) Prevention of pollution
B) Safety of life at sea
C) Maritime labour
D) Cargo taxation

Q184. MARPOL is primarily concerned with:

A) Maritime pollution prevention
B) Ship construction
C) Crew recruitment
D) Navigation licences

Q185. The Suez Canal connects:

A) Arabian Sea and Red Sea
B) Mediterranean Sea and Red Sea
C) Black Sea and Mediterranean Sea
D) Atlantic and Pacific Oceans

Q186. The Panama Canal connects:

A) Atlantic and Pacific Oceans
B) Indian and Pacific Oceans
C) Mediterranean and Red Seas
D) Arctic and Atlantic Oceans

Q187. The Strait of Malacca lies between:

A) India and Sri Lanka
B) Malay Peninsula and Sumatra
C) Africa and Arabia
D) Europe and Asia Minor

Q188. Which instrument measures atmospheric pressure?

A) Hygrometer
B) Barometer
C) Anemometer
D) Hydrometer

Q189. Which SI unit is used for force?

A) Joule
B) Pascal
C) Newton
D) Watt

Q190. The SI unit of pressure is:

A) Newton
B) Pascal
C) Joule
D) Bar

Q191. Which ocean is the largest?

A) Atlantic
B) Indian
C) Pacific
D) Arctic

Q192. The Equator passes through which of these?

A) India
B) Indonesia
C) Japan
D) Australia

Q193. The Tropic of Cancer passes through:

A) Sri Lanka
B) India
C) Indonesia
D) Maldives

Q194. The deepest known oceanic trench is:

A) Java Trench
B) Mariana Trench
C) Tonga Trench
D) Peru–Chile Trench

Q195. The Coriolis effect is primarily caused by:

A) Earth’s revolution only
B) Earth’s rotation
C) Ocean tides
D) Solar radiation

Q196. In the Northern Hemisphere, large-scale moving air is deflected generally toward the:

A) Left
B) Right
C) Equator only
D) Poles only

Q197. Which Indian state has the longest coastline?

A) Tamil Nadu
B) Andhra Pradesh
C) Gujarat
D) Maharashtra

Q198. The headquarters of the Indian Maritime University is located in:

A) Mumbai
B) Chennai
C) Kochi
D) Kolkata

Q199. Which organization is primarily responsible for regulating international civil aviation?

A) IMO
B) ILO
C) ICAO
D) WTO

Q200. A nautical mile is approximately equal to:

A) 1.0 km
B) 1.609 km
C) 1.852 km
D) 2.0 km

SECTION B — PHYSICS

Q51–Q100 | 50 Questions

Q51. A particle is projected with speed $u$u at an angle $\theta$θ to the horizontal. If its maximum height equals one-fourth of its horizontal range, then $\tan\theta$tanθ is:

A) $1/2$1/2
B) 1
C) 2
D) 4

Q52. A body is projected vertically upward from the ground with speed $30\,m/s$30m/s. Taking $g=10\,m/s^2$g=10m/s2, the ratio of distances travelled during the 3rd and 5th seconds is:

A) 1:1
B) 3:1
C) 1:3
D) 5:3

Q53. A car moves around a circular track of radius $50\,m$50m at $10\,m/s$10m/s. If its speed is increasing at $2\,m/s^2$2m/s2, the magnitude of its total acceleration is:

A) $2\,m/s^2$2m/s2
B) $2\sqrt2\,m/s^2$22​m/s2
C) $2.4\,m/s^2$2.4m/s2
D) $4\,m/s^2$4m/s2

Q54. A block of mass $m$m rests on a rough inclined plane of angle $\theta$θ. The coefficient of static friction is $\mu$μ. The block is just about to slide downward. Then:

A) $\mu=\sin\theta$μ=sinθ
B) $\mu=\cos\theta$μ=cosθ
C) $\mu=\tan\theta$μ=tanθ
D) $\mu=\cot\theta$μ=cotθ

Q55. Two blocks of masses $2\,kg$2kg and $3\,kg$3kg are connected by a light string over a frictionless pulley. The acceleration of the system is:

A) $g/5$g/5
B) $g/3$g/3
C) $2g/5$2g/5
D) $3g/5$3g/5

Q56. A particle moves under a force $F=(3x^2+2x)\,N$F=(3×2+2x)N. The work done in moving it from $x=0$x=0 to $x=2\,m$x=2m is:

A) 8 J
B) 10 J
C) 12 J
D) 16 J

Q57. A body of mass $m$m moving with speed $v$v collides perfectly inelastically with another body of mass $2m$2m initially at rest. The fraction of initial kinetic energy lost is:

A) $1/3$1/3
B) $2/3$2/3
C) $1/2$1/2
D) $3/4$3/4

Q58. A satellite revolves around Earth in a circular orbit. If its orbital radius is increased by a factor of 4, its orbital speed becomes:

A) $4v$4v
B) $2v$2v
C) $v/2$v/2
D) $v/4$v/4

Q59. A planet has the same radius as Earth but twice Earth’s mass. Its escape velocity is:

A) $v_e/2$ve​/2
B) $v_e/\sqrt2$ve​/2​
C) $\sqrt2v_e$2​ve​
D) $2v_e$2ve​

Q60. A uniform rod of length $L$L and mass $M$M is pivoted at one end. Its moment of inertia about the pivot is:

A) $ML^2/2$ML2/2
B) $ML^2/3$ML2/3
C) $ML^2/6$ML2/6
D) $ML^2/12$ML2/12

Q61. A disc and a ring of equal mass and radius roll down an inclined plane without slipping. Which reaches the bottom first?

A) Ring
B) Disc
C) Both simultaneously
D) Depends only on their masses

Q62. A simple pendulum has time period $T$T on Earth. At a height equal to Earth’s radius above the surface, its time period becomes:

A) $T/\sqrt2$T/2​
B) $\sqrt2T$2​T
C) $2T$2T
D) $4T$4T

Q63. In SHM, when displacement is $A/2$A/2, the ratio of kinetic energy to potential energy is:

A) 1:1
B) 1:3
C) 3:1
D) 4:1

Q64. Two SHMs of equal amplitude and frequency have a phase difference of $120^\circ$120∘. Their resultant amplitude is:

A) $A$A
B) $\sqrt2A$2​A
C) $\sqrt3A$3​A
D) $2A$2A

Q65. A wave is represented by$$y=0.02\sin(100\pi t-4\pi x).$$y=0.02sin(100πt−4πx).

Its velocity is:

A) 12.5 m/s
B) 25 m/s
C) 50 m/s
D) 100 m/s

Q66. A source of sound of frequency 500 Hz moves toward a stationary observer with speed $20\,m/s$20m/s. Taking speed of sound as $340\,m/s$340m/s, observed frequency is approximately:

A) 471 Hz
B) 500 Hz
C) 531 Hz
D) 560 Hz

Q67. One mole of an ideal gas expands isothermally from volume $V$V to $2V$2V. The work done is:

A) $RT$RT
B) $RT\ln2$RTln2
C) $2RT$2RT
D) $RT/2$RT/2

Q68. An ideal gas undergoes an adiabatic expansion. During the process:

A) Temperature remains constant
B) Heat is absorbed
C) Work is done at the expense of internal energy
D) Internal energy remains constant

Q69. Two moles of a monoatomic ideal gas are heated at constant volume through $50\,K$50K. The increase in internal energy is:

A) $100R$100R
B) $150R$150R
C) $200R$200R
D) $250R$250R

Q70. A Carnot engine operates between $500\,K$500K and $300\,K$300K. Its efficiency is:

A) 20%
B) 30%
C) 40%
D) 60%

Q71. Two charges $+q$+q and $-q$−q are separated by distance $2a$2a. At the midpoint, the electric potential is:

A) $kq/a$kq/a
B) $-kq/a$−kq/a
C) $2kq/a$2kq/a
D) 0

Q72. A charge $q$q is placed at the centre of a cube. The electric flux through one face is:

A) $q/\epsilon_0$q/ϵ0​
B) $q/(2\epsilon_0)$q/(2ϵ0​)
C) $q/(4\epsilon_0)$q/(4ϵ0​)
D) $q/(6\epsilon_0)$q/(6ϵ0​)

Q73. A capacitor is charged to potential $V$V and disconnected from the battery. If its plate separation is doubled, its stored energy becomes:

A) $U/2$U/2
B) $U$U
C) $2U$2U
D) $4U$4U

Q74. Three capacitors $2\mu F,3\mu F,6\mu F$2μF,3μF,6μF are connected in parallel. Equivalent capacitance is:

A) $1\mu F$1μF
B) $6\mu F$6μF
C) $9\mu F$9μF
D) $11\mu F$11μF

Q75. A wire has resistance $R$R. It is stretched uniformly to twice its original length without changing volume. Its new resistance is:

A) $R/2$R/2
B) $R$R
C) $2R$2R
D) $4R$4R

Q76. A battery of emf $12V$12V and internal resistance $1\Omega$1Ω supplies a current of $2A$2A. The terminal voltage is:

A) 8 V
B) 10 V
C) 12 V
D) 14 V

Q77. A current-carrying wire is placed perpendicular to a magnetic field. If current is doubled and magnetic field is halved, magnetic force becomes:

A) Half
B) Same
C) Double
D) Four times

Q78. An electron enters a uniform magnetic field perpendicular to the field. Its path is:

A) Straight line
B) Parabola
C) Circle
D) Ellipse

Q79. A charged particle enters a magnetic field with velocity having both parallel and perpendicular components. Its trajectory is:

A) Circular
B) Helical
C) Parabolic
D) Straight

Q80. A coil of 100 turns experiences a change in magnetic flux from $5\times10^{-3}\,Wb$5×10−3Wb to zero in $0.1s$0.1s. Average induced emf is:

A) 0.5 V
B) 2 V
C) 5 V
D) 10 V

Q81. In an AC circuit, $V_{rms}=220V$Vrms​=220V. The peak voltage is approximately:

A) 110 V
B) 220 V
C) 311 V
D) 440 V

Q82. In a pure inductive AC circuit, current:

A) Leads voltage by $90^\circ$90∘
B) Lags voltage by $90^\circ$90∘
C) Is in phase with voltage
D) Lags by $180^\circ$180∘

Q83. An ideal transformer has 1000 turns in primary and 200 turns in secondary. If primary voltage is 220 V, secondary voltage is:

A) 11 V
B) 44 V
C) 110 V
D) 440 V

Q84. In Young’s double-slit experiment, fringe width is $\beta$β. If wavelength is doubled and slit separation is halved, the new fringe width is:

A) $\beta/4$β/4
B) $\beta/2$β/2
C) $2\beta$2β
D) $4\beta$4β

Q85. In a double-slit experiment, the intensity at the central maximum is $I_0$I0​. If one slit is closed, intensity becomes:

A) $I_0/4$I0​/4
B) $I_0/2$I0​/2
C) $I_0$I0​
D) $2I_0$2I0​

Q86. The critical angle for glass-air interface is $30^\circ$30∘. Refractive index of glass is:

A) $1/2$1/2
B) $\sqrt2$2​
C) 2
D) $1/\sqrt2$1/2​

Q87. A convex lens of focal length 20 cm forms a real image twice the size of the object. The object distance is:

A) 10 cm
B) 20 cm
C) 30 cm
D) 40 cm

Q88. A concave mirror forms a real image equal in size to the object. The object is placed:

A) At focus
B) Between focus and centre
C) At centre of curvature
D) Beyond centre

Q89. The de Broglie wavelength of an electron accelerated through potential $V$V is proportional to:

A) $V$V
B) $1/V$1/V
C) $\sqrt V$V​
D) $1/\sqrt V$1/V​

Q90. In the photoelectric effect, increasing the intensity of incident light while keeping frequency fixed above threshold primarily increases:

A) Maximum kinetic energy
B) Stopping potential
C) Photoelectric current
D) Work function

Q91. The half-life of a radioactive substance is 10 days. The fraction remaining after 30 days is:

A) $1/2$1/2
B) $1/4$1/4
C) $1/8$1/8
D) $1/16$1/16

Q92. In Bohr’s model, the radius of the $n$n-th orbit is proportional to:

A) $n$n
B) $n^2$n2
C) $1/n$1/n
D) $1/n^2$1/n2

Q93. A nucleus has mass defect $0.01u$0.01u. Its binding energy is approximately:

A) 0.931 MeV
B) 9.31 MeV
C) 93.1 MeV
D) 931 MeV

Q94. A semiconductor diode is forward biased when:

A) P-side is connected to negative terminal
B) N-side is connected to positive terminal
C) P-side is connected to positive terminal
D) Both terminals are grounded

Q95. In a transistor, if emitter current is $10mA$10mA and collector current is $9.5mA$9.5mA, the base current is:

A) 0.05 mA
B) 0.5 mA
C) 1.5 mA
D) 19.5 mA

Q96. An ideal logic gate gives output 0 only when both inputs are 1. The gate is:

A) OR
B) AND
C) NAND
D) NOR

Q97. A body of mass $2kg$2kg is attached to a spring of spring constant $200N/m$200N/m. Its angular frequency is:

A) 5 rad/s
B) 10 rad/s
C) 20 rad/s
D) 100 rad/s

Q98. A projectile has maximum range $R$R. If its initial velocity is doubled, the maximum range becomes:

A) $2R$2R
B) $3R$3R
C) $4R$4R
D) $R/2$R/2

Q99. A body is moving in a circular path with constant speed. Which quantity is necessarily changing?

A) Speed
B) Kinetic energy
C) Velocity
D) Mass

Q100. A 4 kg block is pulled by a horizontal force of 20 N on a frictionless surface. Starting from rest, its kinetic energy after 5 s is:

A) 250 J
B) 500 J
C) 625 J
D) 1000 J

---

SECTION C — CHEMISTRY

Q101–Q120 | 20 Questions

Q101. For a reaction, doubling the concentration of reactant doubles the rate, while doubling the concentration of another reactant makes the rate four times. The overall order is:

A) 1
B) 2
C) 3
D) 4

Q102. For a first-order reaction, the half-life is independent of:

A) Temperature
B) Rate constant
C) Initial concentration
D) Activation energy

Q103. The pH of $10^{-3}M$10−3M HCl is approximately:

A) 1
B) 2
C) 3
D) 11

Q104. A buffer solution resists change in:

A) Temperature
B) Pressure
C) pH
D) Volume

Q105. Which has the highest boiling point?

A) CH₄
B) NH₃
C) H₂O
D) HF

Q106. The hybridisation of carbon in $CO_2$CO2​ is:

A) sp
B) sp²
C) sp³
D) dsp²

Q107. Which molecule has zero dipole moment?

A) H₂O
B) NH₃
C) CO₂
D) SO₂

Q108. The oxidation state of chromium in $K_2Cr_2O_7$K2​Cr2​O7​ is:

A) +3
B) +4
C) +6
D) +7

Q109. Which species is paramagnetic?

A) $N_2$N2​
B) $O_2$O2​
C) $CO_2$CO2​
D) $CH_4$CH4​

Q110. The strongest reducing agent among alkali metals in aqueous solution is generally:

A) Li
B) Na
C) K
D) Cs

Q111. The IUPAC name of $CH_3CH(CH_3)CH_2OH$CH3​CH(CH3​)CH2​OH is:

A) 2-methylpropan-1-ol
B) 2-methylpropan-2-ol
C) butan-2-ol
D) 3-methylpropan-1-ol

Q112. Benzene primarily undergoes:

A) Addition reactions
B) Electrophilic substitution
C) Nucleophilic substitution
D) Elimination

Q113. Which reagent distinguishes aldehydes from ketones?

A) NaOH
B) Tollens’ reagent
C) HCl
D) NaCl

Q114. The major product of dehydration of 2-butanol is predominantly:

A) 1-butene
B) cis-2-butene only
C) trans-2-butene predominantly
D) butane

Q115. The monomer used to produce PVC is:

A) Ethene
B) Propene
C) Vinyl chloride
D) Styrene

Q116. The coordination number of Co in $[Co(NH_3)_6]Cl_3$[Co(NH3​)6​]Cl3​ is:

A) 3
B) 4
C) 6
D) 9

Q117. Which has the greatest lattice energy generally?

A) NaCl
B) MgO
C) KCl
D) CaO

Q118. According to Le Chatelier’s principle, increasing pressure favors the side having:

A) More gaseous moles
B) Fewer gaseous moles
C) Equal gaseous moles only
D) Higher temperature

Q119. For an exothermic reaction at equilibrium, increasing temperature generally:

A) Increases $K$K
B) Decreases $K$K
C) Does not affect $K$K
D) Makes $K=1$K=1

Q120. The number of sigma and pi bonds in benzene respectively is:

A) 6, 3
B) 9, 3
C) 12, 3
D) 12, 6

---

SECTION D — ENGLISH

Q121–Q160 | 40 Questions

Q121. Choose the word closest in meaning to “meticulous”:

A) Careless
B) Thorough
C) Rapid
D) Uncertain

Q122. Choose the antonym of “obsolete”:

A) Ancient
B) Outdated
C) Current
D) Useless

Q123. Identify the grammatically correct sentence:

A) Neither of the boys have completed their work.
B) Neither of the boys has completed his work.
C) Neither of the boys have completed his work.
D) Neither boys has completed their work.

Q124. Choose the correctly spelt word:

A) Accomodation
B) Acommodation
C) Accommodation
D) Accommadation

Q125. “To hit the nail on the head” means:

A) To make a mistake
B) To describe something exactly
C) To work carelessly
D) To avoid an issue

Q126. Choose the correct passive form:

“They will have completed the project by Monday.”

A) The project will complete by Monday.
B) The project will be completed by Monday.
C) The project will have been completed by Monday.
D) The project has been completed by Monday.

Q127. Choose the correct indirect speech:

He said, “I am working hard.”

A) He said that I am working hard.
B) He said that he was working hard.
C) He said that he is working hard.
D) He says that he was working hard.

Q128. Fill in the blank:

“Hardly had the ship left the harbour _____ the storm began.”

A) than
B) when
C) then
D) while

Q129. Choose the correct preposition:

“He is proficient _____ mathematics.”

A) at
B) in
C) on
D) with

Q130. Identify the error:

“Each of the candidates have submitted their application.”

A) Each
B) candidates
C) have
D) application

Q131. The word “ambiguous” means:

A) Clear
B) Having more than one possible meaning
C) Incorrect
D) Extremely difficult

Q132. Choose the best replacement:

“He is senior than me.”

A) senior from me
B) senior to me
C) senior with me
D) senior over me

Q133. Choose the correctly punctuated sentence:

A) However we decided to continue.
B) However, we decided to continue.
C) However we, decided to continue.
D) However; we decided, to continue.

Q134. Choose the synonym of “prudent”:

A) Reckless
B) Wise
C) Aggressive
D) Impulsive

Q135. Choose the antonym of “scarce”:

A) Rare
B) Limited
C) Abundant
D) Insufficient

Q136. “The captain called off the operation.” Here “called off” means:

A) Started
B) Cancelled
C) Announced
D) Delayed briefly

Q137. Choose the correct sentence:

A) The news are shocking.
B) The news is shocking.
C) The news were shocking.
D) The news have shocking.

Q138. Complete the sentence:

“If I had known about the problem, I _____ helped you.”

A) will have
B) would
C) would have
D) had

Q139. Choose the correct spelling:

A) Questionnaire
B) Questionaire
C) Questionnair
D) Questionnare

Q140. The phrase “in lieu of” means:

A) In addition to
B) Instead of
C) Because of
D) In spite of

Q141. Choose the word that best completes the sentence:

“The evidence was _____ to prove his innocence.”

A) insufficient
B) sufficient
C) reluctant
D) ambiguous

Q142. Choose the correct form:

“Neither the captain nor the engineers _____ available.”

A) was
B) is
C) were
D) has

Q143. Identify the correctly formed sentence:

A) He insisted to go there.
B) He insisted on going there.
C) He insisted for going there.
D) He insisted go there.

Q144. The closest meaning of “conspicuous” is:

A) Hidden
B) Noticeable
C) Ordinary
D) Uncertain

Q145. Choose the antonym of “hostile”:

A) Aggressive
B) Friendly
C) Violent
D) Unfriendly

Q146. Choose the correct article:

“He is _____ honest officer.”

A) a
B) an
C) the
D) no article

Q147. Choose the correct sentence:

A) The equipment are expensive.
B) The equipments are expensive.
C) The equipment is expensive.
D) The equipment were expensive.

Q148. “Despite the heavy rain, the match continued.” The word “despite” indicates:

A) Cause
B) Contrast
C) Purpose
D) Result

Q149. Choose the correct form:

“By this time tomorrow, we _____ the examination.”

A) finish
B) finished
C) will have finished
D) have finished

Q150. Choose the synonym of “candid”:

A) Frank
B) Secretive
C) Deceptive
D) Hesitant

Q151. Identify the error:

“The captain, along with his officers, were present.”

A) captain
B) along with
C) his officers
D) were

Q152. Choose the correct word:

“The new regulation will _____ all ships entering the port.”

A) effect
B) affect
C) afflict
D) infect

Q153. Choose the correct sentence:

A) I prefer tea than coffee.
B) I prefer tea over coffee.
C) I prefer tea to coffee.
D) Both B and C are acceptable.

Q154. The phrase “at the eleventh hour” means:

A) Very early
B) At the last moment
C) Exactly at 11 AM
D) After eleven hours

Q155. Choose the correct passive voice:

“People speak English all over the world.”

A) English is spoken all over the world.
B) English was spoken all over the world.
C) English has spoken all over the world.
D) English speaks all over the world.

Q156. Choose the word closest in meaning to “deteriorate”:

A) Improve
B) Worsen
C) Stabilize
D) Repair

Q157. Fill in the blank:

“No sooner did the alarm ring _____ everyone rushed outside.”

A) when
B) than
C) then
D) that

Q158. Choose the correct sentence:

A) He has been working here since five years.
B) He has been working here for five years.
C) He is working here since five years.
D) He worked here since five years.

Q159. The antonym of “transparent” in the figurative sense is:

A) Obvious
B) Clear
C) Deceptive
D) Visible

Q160. Choose the most appropriate word:

“The officer gave a _____ explanation of the incident, leaving no major point unanswered.”

A) vague
B) comprehensive
C) reluctant
D) superficial

---

SECTION E — GENERAL APTITUDE & GK

Q161–Q200 | 40 Questions

Q161. A clock gains 5 minutes every hour. If it is set correctly at 8:00 AM, what will it show at 8:00 PM?

A) 8:55 PM
B) 9:00 PM
C) 9:05 PM
D) 9:10 PM

Q162. A train 180 m long crosses a pole in 9 seconds. Its speed is:

A) 60 km/h
B) 72 km/h
C) 80 km/h
D) 90 km/h

Q163. A man can complete a job in 12 days and another in 18 days. Working together, they complete it in:

A) 6 days
B) 7.2 days
C) 8 days
D) 9 days

Q164. A sum becomes ₹12,100 in two years at 10% compound interest annually. The principal is:

A) ₹9,000
B) ₹10,000
C) ₹11,000
D) ₹11,100

Q165. A vessel travels 120 km downstream in 4 hours and the same distance upstream in 6 hours. Speed of the stream is:

A) 4 km/h
B) 5 km/h
C) 6 km/h
D) 10 km/h

Q166. A mixture contains milk and water in ratio 5:2. If 14 L water is added, ratio becomes 5:4. Initial quantity of milk was:

A) 30 L
B) 35 L
C) 40 L
D) 45 L

Q167. If $3A=4B=6C$3A=4B=6C, then $A:B:C$A:B:C is:

A) 3:4:6
B) 4:3:2
C) 2:3:4
D) 6:4:3

Q168. The average of 8 numbers is 24. If one number 18 is replaced by 34, the new average is:

A) 25
B) 26
C) 27
D) 28

Q169. A shopkeeper marks an item 40% above cost and gives a 10% discount. His profit percentage is:

A) 20%
B) 24%
C) 26%
D) 30%

Q170. If $x:y=3:5$x:y=3:5 and $y:z=10:7$y:z=10:7, then $x:y:z$x:y:z is:

A) 3:5:7
B) 6:10:7
C) 3:10:7
D) 6:5:7

Q171. A number is increased by 20% and then decreased by 20%. The net change is:

A) 0%
B) 2% decrease
C) 4% decrease
D) 4% increase

Q172. A boat’s speed in still water is 15 km/h and stream speed is 3 km/h. Time required to travel 36 km downstream is:

A) 2 h
B) 2.5 h
C) 3 h
D) 4 h

Q173. If $CAT$CAT is coded as $DBU$DBU, then $SHIP$SHIP is coded as:

A) TIJQ
B) T H J Q
C) RGHO
D) UJKR

Q174. Find the missing term:

$2, 6, 12, 20, 30, ?$2,6,12,20,30,?

A) 36
B) 40
C) 42
D) 44

Q175. Find the next term:

$3, 9, 27, 81, ?$3,9,27,81,?

A) 162
B) 189
C) 243
D) 324

Q176. A person walks 5 km north, then 12 km east. His straight-line distance from the starting point is:

A) 13 km
B) 15 km
C) 17 km
D) 7 km

Q177. If all navigators are sailors and some sailors are engineers, which conclusion is definitely valid?

A) All engineers are navigators
B) Some navigators are engineers
C) All navigators are sailors
D) No sailor is an engineer

Q178. A cube is painted on all faces and cut into 27 equal smaller cubes. How many small cubes have exactly two painted faces?

A) 4
B) 8
C) 12
D) 16

Q179. A man faces north. He turns $90^\circ$90∘ clockwise, then $180^\circ$180∘ anticlockwise. He is now facing:

A) North
B) South
C) East
D) West

Q180. If today is Wednesday, what day will it be 100 days later?

A) Monday
B) Wednesday
C) Friday
D) Saturday

Q181. The headquarters of the International Maritime Organization (IMO) is in:

A) Geneva
B) London
C) New York
D) Rotterdam

Q182. IMO stands for:

A) International Marine Organization
B) International Maritime Organization
C) International Maritime Office
D) Indian Maritime Organization

Q183. SOLAS primarily deals with:

A) Prevention of pollution
B) Safety of life at sea
C) Maritime labour
D) Cargo taxation

Q184. MARPOL is primarily concerned with:

A) Maritime pollution prevention
B) Ship construction
C) Crew recruitment
D) Navigation licences

Q185. The Suez Canal connects:

A) Arabian Sea and Red Sea
B) Mediterranean Sea and Red Sea
C) Black Sea and Mediterranean Sea
D) Atlantic and Pacific Oceans

Q186. The Panama Canal connects:

A) Atlantic and Pacific Oceans
B) Indian and Pacific Oceans
C) Mediterranean and Red Seas
D) Arctic and Atlantic Oceans

Q187. The Strait of Malacca lies between:

A) India and Sri Lanka
B) Malay Peninsula and Sumatra
C) Africa and Arabia
D) Europe and Asia Minor

Q188. Which instrument measures atmospheric pressure?

A) Hygrometer
B) Barometer
C) Anemometer
D) Hydrometer

Q189. Which SI unit is used for force?

A) Joule
B) Pascal
C) Newton
D) Watt

Q190. The SI unit of pressure is:

A) Newton
B) Pascal
C) Joule
D) Bar

Q191. Which ocean is the largest?

A) Atlantic
B) Indian
C) Pacific
D) Arctic

Q192. The Equator passes through which of these?

A) India
B) Indonesia
C) Japan
D) Australia

Q193. The Tropic of Cancer passes through:

A) Sri Lanka
B) India
C) Indonesia
D) Maldives

Q194. The deepest known oceanic trench is:

A) Java Trench
B) Mariana Trench
C) Tonga Trench
D) Peru–Chile Trench

Q195. The Coriolis effect is primarily caused by:

A) Earth’s revolution only
B) Earth’s rotation
C) Ocean tides
D) Solar radiation

Q196. In the Northern Hemisphere, large-scale moving air is deflected generally toward the:

A) Left
B) Right
C) Equator only
D) Poles only

Q197. Which Indian state has the longest coastline?

A) Tamil Nadu
B) Andhra Pradesh
C) Gujarat
D) Maharashtra

Q198. The headquarters of the Indian Maritime University is located in:

A) Mumbai
B) Chennai
C) Kochi
D) Kolkata

Q199. Which organization is primarily responsible for regulating international civil aviation?

A) IMO
B) ILO
C) ICAO
D) WTO

Q200. A nautical mile is approximately equal to:

A) 1.0 km
B) 1.609 km
C) 1.852 km
D) 2.0 km

Mathematics — Q1–Q50

Q	Ans	Q	Ans	Q	Ans	Q	Ans	Q	Ans
1	B	11	C	21	C	31	B	41	—
2	—	12	C	22	B	32	B	42	B
3	C	13	B	23	B	33	B	43	B
4	A	14	—	24	B	34	B	44	B
5	B	15	C	25	B	35	—	45	B
6	A	16	B	26	—	36	—	46	B
7	A	17	A	27	B	37	—	47	B
8	C	18	—	28	B	38	C	48	A
9	C	19	B	29	B	39	C	49	C
10	B	20	C	30	B	40	C	50	B

Problems in the original paper:

• Q2: insufficient information; $a+b$a+b isn’t uniquely determined.
• Q14: correct probability is $5/12$5/12, but that option wasn’t provided.
• Q18: minimum is 7, but that option wasn’t provided.
• Q26: $y(\pi/4)=\frac{1}{\sqrt2}+\frac{\pi}{8}$y(π/4)=2​1​+8π​ — no listed option.
• Q35: angle satisfies $\cos\theta=4/9$cosθ=4/9, no listed option.
• Q36: more than one/none depending interpretation; question needs correction.
• Q37: maximum is $\frac{1+2\sqrt2}{2}$21+22​​, no listed option.
• Q41: no integer $n$n satisfies the condition.

Physics — Q51–Q100

Q	Ans	Q	Ans	Q	Ans	Q	Ans	Q	Ans
51	C	61	B	71	D	81	C	91	C
52	C	62	C	72	D	82	B	92	B
53	B	63	C	73	C	83	B	93	B
54	C	64	C	74	D	84	D	94	C
55	C	65	B	75	D	85	B	95	B
56	A	66	C	76	B	86	C	96	C
57	C	67	B	77	B	87	C	97	B
58	C	68	C	78	C	88	C	98	C
59	C	69	B	79	B	89	D	99	C
60	B	70	A	80	C	90	C	100	—

English — Q121–Q160

Q	Ans	Q	Ans	Q	Ans	Q	Ans
121	B	131	B	141	B	151	D
122	C	132	B	142	C	152	B
123	B	133	B	143	B	153	D
124	C	134	B	144	B	154	B
125	B	135	C	145	B	155	A
126	C	136	B	146	B	156	B
127	B	137	B	147	C	157	B
128	B	138	C	148	B	158	B
129	B	139	A	149	C	159	C
130	C	140	B	150	A	160	B

Aptitude & GK — Q161–Q200

Q	Ans	Q	Ans	Q	Ans	Q	Ans
161	B	171	C	181	B	191	C
162	B	172	A	182	B	192	B
163	B	173	A	183	B	193	B
164	B	174	C	184	A	194	B
165	B	175	C	185	B	195	B
166	B	176	A	186	A	196	B
167	B	177	C	187	B	197	C
168	B	178	C	188	B	198	B
169	C	179	D	189	C	199	C
170	B	180	C	190	B	200	C