Mock Test 4 is a full MHT-CET PCM mock written by munotes to the CET Cell's syllabus and pattern: 50 Physics and 50 Chemistry questions at 1 mark each in 90 minutes, then 50 Maths questions at 2 marks each in 90 minutes. 200 marks, no negative marking.
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Q1. A resistor of \(60\ \Omega\) and a capacitor of reactance \(80\ \Omega\) are joined in series across a \(220\ \text{V}\) (rms) AC supply. The rms current in the circuit is
- A
\(1.57\ \text{A}\)
- B
\(2.2\ \text{A}\)
- C
\(2.75\ \text{A}\)
- D
\(3.67\ \text{A}\)
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Q2. The temperature at which the reading on the Fahrenheit scale is twice the reading on the Celsius scale is
- A
\(320^\circ\text{C}\)
- B
\(80^\circ\text{C}\)
- C
\(160^\circ\text{C}\)
- D
\(-40^\circ\text{C}\)
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Q3. A mass hung from a spring oscillates with a period of \(2\ \text{s}\). A second spring, identical to the first, is joined beside it (in parallel) so that the same mass hangs from both. The new period is
- A
\(1\ \text{s}\)
- B
\(\sqrt{2}\ \text{s}\)
- C
\(4\ \text{s}\)
- D
\(2\sqrt{2}\ \text{s}\)
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Q4. Two cells, each of emf \(2\ \text{V}\) and internal resistance \(1\ \Omega\), are joined in parallel (positive to positive) and connected to an external resistor of \(1.5\ \Omega\). The current through the external resistor is
- A
\(1\ \text{A}\)
- B
\(0.8\ \text{A}\)
- C
\(1.33\ \text{A}\)
- D
\(1.14\ \text{A}\)
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Q5. A body of mass \(0.5\ \text{kg}\) performs SHM with an amplitude of \(0.1\ \text{m}\) and an angular frequency of \(10\ \text{rad s}^{-1}\). Its total energy of oscillation is
- A
\(0.025\ \text{J}\)
- B
\(0.25\ \text{J}\)
- C
\(2.5\ \text{J}\)
- D
\(0.5\ \text{J}\)
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Q6. Two identical small metal spheres carry charges of \(+6\ \mu\text{C}\) and \(-2\ \mu\text{C}\) and attract each other with a force \(F\). They are made to touch and are then put back at the same distance apart. The force between them now is
- A
\(\frac{F}{12}\), repulsive
- B
\(\frac{4F}{3}\), repulsive
- C
\(\frac{F}{3}\), repulsive
- D
\(\frac{F}{3}\), attractive
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Q7. Two resistors, \(R_1 = (100 \pm 3)\ \Omega\) and \(R_2 = (200 \pm 4)\ \Omega\), are joined in series. Their equivalent resistance is
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Q8. A very long straight wire carries a uniform charge of \(2\ \mu\text{C}\) per metre. The electric field at a distance of \(10\ \text{cm}\) from the wire is (\(\frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}\ \text{N m}^2\text{C}^{-2}\))
- A
\(3.6 \times 10^{5}\ \text{N C}^{-1}\)
- B
\(1.8 \times 10^{5}\ \text{N C}^{-1}\)
- C
\(7.2 \times 10^{5}\ \text{N C}^{-1}\)
- D
\(3.6 \times 10^{4}\ \text{N C}^{-1}\)
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Q9. A perfect black body has a surface area of \(0.5\ \text{m}^2\) and is at \(1000\ \text{K}\). The energy it radiates each second is about (\(\sigma = 5.67 \times 10^{-8}\ \text{W m}^{-2}\text{K}^{-4}\))
- A
\(1.4 \times 10^{4}\ \text{W}\)
- B
\(2.8 \times 10^{1}\ \text{W}\)
- C
\(5.7 \times 10^{4}\ \text{W}\)
- D
\(2.8 \times 10^{4}\ \text{W}\)
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Q10. A parallel plate capacitor has plates of area \(0.02\ \text{m}^2\) with \(1\ \text{mm}\) of air between them. Its capacitance is about (\(\varepsilon_0 = 8.85 \times 10^{-12}\ \text{C}^2\text{N}^{-1}\text{m}^{-2}\))
- A
\(177\ \text{pF}\)
- B
\(17.7\ \text{pF}\)
- C
\(88.5\ \text{pF}\)
- D
\(354\ \text{pF}\)
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Q11. In a transistor, the emitter current is \(4\ \text{mA}\) and the collector current is \(3.8\ \text{mA}\). Its current gain \(\beta\) in the common emitter configuration is
- A
\(0.05\)
- B
\(0.95\)
- C
\(19\)
- D
\(20\)
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Q12. The magnetic moment of the electron in the first Bohr orbit of hydrogen, \(\frac{eh}{4\pi m_e}\) (the Bohr magneton), is about (\(e = 1.6 \times 10^{-19}\ \text{C}\), \(h = 6.63 \times 10^{-34}\ \text{J s}\), \(m_e = 9.1 \times 10^{-31}\ \text{kg}\))
- A
\(9.3 \times 10^{-24}\ \text{A m}^2\)
- B
\(9.3 \times 10^{-28}\ \text{A m}^2\)
- C
\(4.6 \times 10^{-24}\ \text{A m}^2\)
- D
\(1.9 \times 10^{-23}\ \text{A m}^2\)
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Q13. A seconds pendulum has a period of \(2\ \text{s}\). At a place where \(g = 9.8\ \text{m s}^{-2}\), the length of a seconds pendulum is about
- A
\(0.993\ \text{m}\)
- B
\(3.97\ \text{m}\)
- C
\(1.99\ \text{m}\)
- D
\(0.248\ \text{m}\)
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Q14. The magnetic field at the centre of a circular coil of radius \(R\) is \(B\). On the axis of the coil, at a distance \(\sqrt{3}R\) from its centre, the field is
- A
\(\frac{B}{4}\)
- B
\(\frac{B}{2}\)
- C
\(\frac{B}{8}\)
- D
\(\frac{B}{3\sqrt{3}}\)
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Q15. Two sources of light are coherent when they give out waves of
- A
the same amplitude, whatever their frequencies
- B
different frequencies with a constant phase difference
- C
the same frequency with a phase difference that changes at random
- D
the same frequency with a constant phase difference
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Q16. A wire stretched between two fixed points vibrates in \(3\) loops (segments) when it is made to vibrate at \(450\ \text{Hz}\). The fundamental frequency of the wire is
- A
\(225\ \text{Hz}\)
- B
\(450\ \text{Hz}\)
- C
\(1350\ \text{Hz}\)
- D
\(150\ \text{Hz}\)
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Q17. Two waves of the same frequency and the same amplitude \(a\) travel in the same direction and overlap with a phase difference of \(\frac{\pi}{3}\). The amplitude of the resultant wave is
- A
\(\sqrt{3}\,a\)
- B
\(a\)
- C
\(2a\)
- D
\(\sqrt{2}\,a\)
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Q18. In an AC circuit, the voltage is \(V = 200\sin\omega t\) volt and the current is \(I = 5\sin\left(\omega t - \frac{\pi}{3}\right)\) ampere. The average power used in the circuit is
- A
\(433\ \text{W}\)
- B
\(500\ \text{W}\)
- C
\(1000\ \text{W}\)
- D
\(250\ \text{W}\)
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Q19. In a Wheatstone bridge, \(P = 10\ \Omega\), \(Q = 15\ \Omega\) and \(R = 8\ \Omega\). The bridge is balanced when a \(36\ \Omega\) resistor is joined in parallel with the fourth arm \(S\). The resistance \(S\) is
- A
\(9\ \Omega\)
- B
\(24\ \Omega\)
- C
\(12\ \Omega\)
- D
\(18\ \Omega\)
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Q20. The area enclosed by the hysteresis loop (\(B\) against \(H\)) of a ferromagnetic material gives
- A
the magnetic susceptibility of the material
- B
the retentivity of the material
- C
the coercivity of the material
- D
the energy lost as heat per unit volume in each cycle of magnetisation
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Q21. A ball of mass \(0.1\ \text{kg}\) moves at \(10\ \text{m s}^{-1}\). Its de Broglie wavelength is (\(h = 6.63 \times 10^{-34}\ \text{J s}\))
- A
\(6.63 \times 10^{-34}\ \text{m}\)
- B
\(6.63 \times 10^{-32}\ \text{m}\)
- C
\(6.63 \times 10^{-33}\ \text{m}\)
- D
\(6.63 \times 10^{-35}\ \text{m}\)
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Q22. A radioactive substance has a half-life of \(693\ \text{s}\). Its mean life is about
- A
\(1386\ \text{s}\)
- B
\(693\ \text{s}\)
- C
\(1000\ \text{s}\)
- D
\(480\ \text{s}\)
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Q23. A stone is thrown with a speed of \(20\ \text{m s}^{-1}\) at an angle of \(30^\circ\) above the horizontal. With \(g = 10\ \text{m s}^{-2}\), its horizontal range on level ground is
- A
\(20\sqrt{3}\ \text{m}\)
- B
\(40\ \text{m}\)
- C
\(10\sqrt{3}\ \text{m}\)
- D
\(20\ \text{m}\)
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Q24. The driving cell of a potentiometer is kept the same. The sensitivity of the potentiometer can be increased by
- A
using a shorter potentiometer wire
- B
using a longer potentiometer wire
- C
increasing the current through the potentiometer wire
- D
using a driving cell of larger emf
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Q25. A ball of mass \(2\ \text{kg}\) moving at \(3\ \text{m s}^{-1}\) hits a ball of mass \(1\ \text{kg}\) at rest, and the two stick together. The kinetic energy lost in the collision is
- A
\(9\ \text{J}\)
- B
\(3\ \text{J}\)
- C
\(6\ \text{J}\)
- D
\(4.5\ \text{J}\)
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Q26. Charges of \(+2\ \mu\text{C}\), \(-1\ \mu\text{C}\), \(+3\ \mu\text{C}\) and \(-2\ \mu\text{C}\) sit at the four corners of a square whose diagonals are \(20\ \text{cm}\) long. The electric potential at the centre of the square is (\(\frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}\ \text{N m}^2\text{C}^{-2}\))
- A
\(3.6 \times 10^{5}\ \text{V}\)
- B
\(7.2 \times 10^{5}\ \text{V}\)
- C
zero
- D
\(1.8 \times 10^{5}\ \text{V}\)
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Q27. In a photoelectric experiment, the stopping potential \(V_0\) is plotted against the frequency \(\nu\) of the light used. The graph is a straight line whose slope is (\(h\) = Planck's constant, \(e\) = electronic charge, \(\phi_0\) = work function)
- A
\(h\)
- B
\(\frac{\phi_0}{e}\)
- C
\(\frac{h}{e}\)
- D
\(\frac{e}{h}\)
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Q28. The energy of the hydrogen atom in its ground state is \(-13.6\ \text{eV}\). The energy needed to remove the electron from a hydrogen atom that is in its first excited state is
- A
\(1.51\ \text{eV}\)
- B
\(13.6\ \text{eV}\)
- C
\(3.4\ \text{eV}\)
- D
\(10.2\ \text{eV}\)
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Q29. One mole of an ideal gas at \(300\ \text{K}\) expands isothermally until its volume is doubled. The work done by the gas is about (\(R = 8.31\ \text{J mol}^{-1}\text{K}^{-1}\), \(\ln 2 = 0.693\))
- A
\(3456\ \text{J}\)
- B
\(1728\ \text{J}\)
- C
\(864\ \text{J}\)
- D
\(2493\ \text{J}\)
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Q30. A flywheel with a moment of inertia of \(2\ \text{kg m}^2\) turns at \(300\) revolutions per minute. Its rotational kinetic energy is about
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Q31. The radius of the Earth is \(6400\ \text{km}\). The height above the Earth's surface at which the acceleration due to gravity falls to one fourth of its value at the surface is
- A
\(6400\ \text{km}\)
- B
\(1600\ \text{km}\)
- C
\(12800\ \text{km}\)
- D
\(3200\ \text{km}\)
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Q32. A prism of refracting angle \(60^\circ\) gives an angle of minimum deviation of \(30^\circ\). The refractive index of its material is
- A
\(\sqrt{2}\)
- B
\(\sqrt{3}\)
- C
\(\frac{\sqrt{3}}{2}\)
- D
\(1.5\)
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Q33. A listener moves at \(33\ \text{m s}^{-1}\) straight towards a stationary source of sound of frequency \(500\ \text{Hz}\). If the speed of sound is \(330\ \text{m s}^{-1}\), the frequency the listener hears is
- A
\(555.6\ \text{Hz}\)
- B
\(450\ \text{Hz}\)
- C
\(550\ \text{Hz}\)
- D
\(500\ \text{Hz}\)
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Q34. A soap bubble has a radius of \(1\ \text{cm}\). The surface tension of the soap solution is \(0.04\ \text{N m}^{-1}\). The excess pressure inside the bubble is
- A
\(32\ \text{Pa}\)
- B
\(16\ \text{Pa}\)
- C
\(8\ \text{Pa}\)
- D
\(4\ \text{Pa}\)
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Q35. When a p-n junction diode is forward biased,
- A
its depletion region becomes wider and the potential barrier is raised
- B
its depletion region becomes narrower and the potential barrier is lowered
- C
its depletion region and the potential barrier do not change
- D
its depletion region becomes narrower but the potential barrier is raised
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Q36. Two moles of an ideal diatomic gas are heated at constant volume, and the temperature rises by \(10\ \text{K}\). The heat supplied is about (\(R = 8.31\ \text{J mol}^{-1}\text{K}^{-1}\))
- A
\(166.2\ \text{J}\)
- B
\(249.3\ \text{J}\)
- C
\(581.7\ \text{J}\)
- D
\(415.5\ \text{J}\)
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Q37. An ideal gas is taken round a cycle that is a rectangle on a \(P\)-\(V\) diagram: the pressure changes between \(1 \times 10^{5}\ \text{Pa}\) and \(3 \times 10^{5}\ \text{Pa}\), and the volume between \(1\ \text{L}\) and \(4\ \text{L}\). The net work done in one cycle is
- A
\(1200\ \text{J}\)
- B
\(600\ \text{J}\)
- C
\(900\ \text{J}\)
- D
\(300\ \text{J}\)
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Q38. A strong bar magnet is dropped down a long vertical copper pipe. Inside the pipe, the magnet
- A
falls with an acceleration greater than \(g\)
- B
falls freely with acceleration \(g\), since copper is not magnetic
- C
falls with an acceleration less than \(g\)
- D
stops and stays at rest inside the pipe
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Q39. A straight wire \(0.5\ \text{m}\) long carries a current of \(4\ \text{A}\) in a uniform magnetic field of \(0.2\ \text{T}\). The wire makes an angle of \(30^\circ\) with the field. The force on the wire is
- A
\(0.4\ \text{N}\)
- B
\(0.2\ \text{N}\)
- C
\(0.1\ \text{N}\)
- D
\(0.35\ \text{N}\)
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Q40. In Young's double slit experiment, the intensities of the light from the two slits are in the ratio \(9 : 1\). The ratio of the maximum to the minimum intensity in the fringe pattern is
- A
\(81 : 1\)
- B
\(9 : 1\)
- C
\(4 : 1\)
- D
\(3 : 1\)
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Q41. In a hydraulic lift, the small piston has an area of \(5\ \text{cm}^2\) and the large piston an area of \(250\ \text{cm}^2\). With \(g = 10\ \text{m s}^{-2}\), the force on the small piston needed to hold up a car of mass \(1000\ \text{kg}\) on the large piston is
- A
\(2000\ \text{N}\)
- B
\(500\ \text{N}\)
- C
\(50\ \text{N}\)
- D
\(200\ \text{N}\)
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Q42. The ratio of the radius of the nucleus \({}^{27}_{13}\text{Al}\) to the radius of the nucleus \({}^{125}_{52}\text{Te}\) is
- A
\(3 : 5\)
- B
\(9 : 25\)
- C
\(27 : 125\)
- D
\(5 : 3\)
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Q43. A stone of mass \(0.2\ \text{kg}\) tied to a string is whirled in a vertical circle. With \(g = 10\ \text{m s}^{-2}\), the tension in the string at the lowest point is greater than the tension at the highest point by
- A
\(4\ \text{N}\)
- B
\(6\ \text{N}\)
- C
\(2\ \text{N}\)
- D
\(12\ \text{N}\)
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Q44. A toroid of mean radius \(10\ \text{cm}\) has \(500\) turns and carries a current of \(0.5\ \text{A}\). The magnetic field inside its core is (\(\mu_0 = 4\pi \times 10^{-7}\ \text{T m A}^{-1}\))
- A
\(1 \times 10^{-3}\ \text{T}\)
- B
\(2.5 \times 10^{-4}\ \text{T}\)
- C
\(5 \times 10^{-4}\ \text{T}\)
- D
\(3.14 \times 10^{-3}\ \text{T}\)
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Q45. For two non-zero vectors \(\vec{A}\) and \(\vec{B}\), the magnitude of their vector product equals their scalar product: \(|\vec{A} \times \vec{B}| = \vec{A} \cdot \vec{B}\). The angle between the vectors is
- A
\(0^\circ\)
- B
\(45^\circ\)
- C
\(60^\circ\)
- D
\(90^\circ\)
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Q46. A long solenoid of length \(50\ \text{cm}\) and cross-sectional area \(10\ \text{cm}^2\) has \(500\) turns. Its self-inductance is about (\(\mu_0 = 4\pi \times 10^{-7}\ \text{T m A}^{-1}\))
- A
\(1.26\ \text{mH}\)
- B
\(6.28\ \text{mH}\)
- C
\(0.628\ \text{mH}\)
- D
\(0.314\ \text{mH}\)
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Q47. The internal energy of \(2\) moles of an ideal monatomic gas at \(300\ \text{K}\) is about (\(R = 8.31\ \text{J mol}^{-1}\text{K}^{-1}\))
- A
\(7.48\ \text{kJ}\)
- B
\(4.99\ \text{kJ}\)
- C
\(12.5\ \text{kJ}\)
- D
\(3.74\ \text{kJ}\)
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Q48. A uniform disc has a mass of \(2\ \text{kg}\) and a radius of \(10\ \text{cm}\). Its moment of inertia about an axis through a point on its rim, perpendicular to its plane, is
- A
\(0.01\ \text{kg m}^2\)
- B
\(0.025\ \text{kg m}^2\)
- C
\(0.02\ \text{kg m}^2\)
- D
\(0.03\ \text{kg m}^2\)
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Q49. A series LCR circuit is at resonance. Its capacitance is now made four times as large. To keep the same resonant frequency, its inductance must be made
- A
half its value
- B
one fourth of its value
- C
twice its value
- D
four times its value
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Q50. Each of the two inputs of an OR gate is first passed through a NOT gate. The combination works as
- A
a NAND gate
- B
a NOR gate
- C
an AND gate
- D
an OR gate
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Q51. A reaction has \(\Delta H > 0\) and \(\Delta S > 0\). The reaction is spontaneous
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Q52. Chloroform is kept in dark coloured bottles filled to the top because
- A
it explodes when it is exposed to light
- B
in light, air slowly oxidises it to the poisonous gas phosgene
- C
in light it slowly changes into methane
- D
it absorbs moisture from the air and turns acidic at once
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Q53. A \(5\%\) (mass by volume) solution of cane sugar (molar mass \(342\ \text{g mol}^{-1}\)) is isotonic with a solution of urea (molar mass \(60\ \text{g mol}^{-1}\)) of strength about
- A
\(0.877\%\)
- B
\(28.5\%\)
- C
\(1.75\%\)
- D
\(5\%\)
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Q54. A concentrated aqueous solution of sodium propanoate, \(\ce{CH3CH2COONa}\), is electrolysed (Kolbe's method). The alkane formed at the anode is
- A
propane
- B
butane
- C
hexane
- D
ethane
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Q55. Which substance is used as the catalyst in the contact process for making sulphuric acid?
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Q56. Which halogen has the most negative electron gain enthalpy?
- A
iodine
- B
bromine
- C
chlorine
- D
fluorine
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Q57. The \(\alpha\)-helix, a secondary structure of proteins, is held in shape mainly by
- A
disulphide bonds between cysteine units
- B
peptide bonds between the side chains
- C
ionic bonds between the end groups of the chain
- D
hydrogen bonds between the C=O and N-H groups of the peptide chain
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Q58. Phenol is treated with concentrated nitric acid in the presence of concentrated sulphuric acid. The main product is
- A
1,3,5-trinitrobenzene
- B
a mixture of 2-nitrophenol and 4-nitrophenol
- C
2,4,6-trinitrophenol (picric acid)
- D
3-nitrophenol
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Q59. A gas has a density of \(1.25\ \text{g L}^{-1}\) at STP. Its molar mass is about (molar volume at STP: \(22.4\ \text{L mol}^{-1}\))
- A
\(32\ \text{g mol}^{-1}\)
- B
\(17.9\ \text{g mol}^{-1}\)
- C
\(14\ \text{g mol}^{-1}\)
- D
\(28\ \text{g mol}^{-1}\)
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Q60. The solubility product of \(\ce{BaSO4}\) is \(1.1 \times 10^{-10}\). Equal volumes of \(2 \times 10^{-5}\ \text{M}\ \ce{BaCl2}\) and \(2 \times 10^{-5}\ \text{M}\ \ce{Na2SO4}\) are mixed. Then
- A
a precipitate forms, because the ionic product, \(4.0 \times 10^{-10}\), is more than \(K_{sp}\)
- B
no precipitate forms, because the ionic product, \(1.0 \times 10^{-10}\), is less than \(K_{sp}\)
- C
no precipitate forms, because barium sulphate is freely soluble in water
- D
a precipitate forms, because barium sulphate is insoluble in any amount
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Q61. In a cubic crystal, atoms of A sit at the corners of the cube and atoms of B at the centres of the faces. The formula of the compound is
- A
\(\ce{A3B}\)
- B
\(\ce{AB2}\)
- C
\(\ce{AB3}\)
- D
\(\ce{A8B6}\)
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Q62. Following green chemistry, which of these is a safer solvent that can replace harmful organic solvents in many processes?
-
Q63. Which order of thermal stability of the hydrides of group 16 is correct?
- A
\(\ce{H2S} > \ce{H2O} > \ce{H2Se} > \ce{H2Te}\)
- B
\(\ce{H2Te} > \ce{H2Se} > \ce{H2S} > \ce{H2O}\)
- C
\(\ce{H2Te} > \ce{H2O} > \ce{H2S} > \ce{H2Se}\)
- D
\(\ce{H2O} > \ce{H2S} > \ce{H2Se} > \ce{H2Te}\)
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Q64. Benzoic acid is treated with bromine in the presence of iron(III) bromide. The main product is
- A
4-bromobenzoic acid
- B
2-bromobenzoic acid
- C
3-bromobenzoic acid
- D
bromobenzene
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Q65. Phenol is heated with zinc dust. The organic product is
- A
benzene
- B
benzoic acid
- C
cyclohexanol
- D
toluene
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Q66. The most common oxidation state shown by the lanthanoids is
- A
\(+3\)
- B
\(+6\)
- C
\(+4\)
- D
\(+2\)
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Q67. Dilute acid is added to a yellow solution of potassium chromate. The colour of the solution changes to
- A
violet, because permanganate ions form
- B
orange, because dichromate ions form
- C
colourless
- D
green, because \(\ce{Cr^3+}\) ions form
-
Q68. Which statement about the molecularity of an elementary reaction is correct?
-
Q69. To make 4-bromoaniline from aniline in good yield, aniline is first
- A
converted to nitrobenzene, then brominated
- B
acetylated to acetanilide, then brominated, then hydrolysed
- C
treated directly with excess bromine water
- D
diazotised, then treated with bromine
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Q70. An aqueous solution of which salt is acidic?
- A
\(\ce{NaCl}\)
- B
\(\ce{Na2CO3}\)
- C
\(\ce{NH4Cl}\)
- D
\(\ce{CH3COONa}\)
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Q71. Which ionic solid mainly shows the Frenkel defect?
- A
\(\ce{CsCl}\)
- B
\(\ce{NaCl}\)
- C
\(\ce{ZnS}\)
- D
\(\ce{KCl}\)
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Q72. \(4\ \text{g}\) of sodium hydroxide is dissolved in water and the solution is made up to \(250\ \text{mL}\). The molarity of the solution is (Na = \(23\), O = \(16\), H = \(1\))
- A
\(1.6\ \text{M}\)
- B
\(0.4\ \text{M}\)
- C
\(0.1\ \text{M}\)
- D
\(0.04\ \text{M}\)
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Q73. The enthalpy of neutralisation of a strong acid by a strong base is \(-57.1\ \text{kJ mol}^{-1}\). The heat given out when \(200\ \text{mL}\) of \(0.5\ \text{M}\) HCl is mixed with \(200\ \text{mL}\) of \(0.5\ \text{M}\) NaOH is
- A
\(57.1\ \text{kJ}\)
- B
\(5.71\ \text{kJ}\)
- C
\(11.42\ \text{kJ}\)
- D
\(2.86\ \text{kJ}\)
-
Q74. For the reaction \(\ce{2N2O5 -> 4NO2 + O2}\), oxygen is formed at \(0.02\ \text{mol L}^{-1}\text{s}^{-1}\). The rate of formation of \(\ce{NO2}\) is
- A
\(0.02\ \text{mol L}^{-1}\text{s}^{-1}\)
- B
\(0.005\ \text{mol L}^{-1}\text{s}^{-1}\)
- C
\(0.08\ \text{mol L}^{-1}\text{s}^{-1}\)
- D
\(0.04\ \text{mol L}^{-1}\text{s}^{-1}\)
-
Q75. For a reaction at \(300\ \text{K}\), \(\Delta H = -10\ \text{kJ mol}^{-1}\) and \(\Delta S = -20\ \text{J K}^{-1}\text{mol}^{-1}\). Its \(\Delta G\) is
- A
\(+5990\ \text{kJ mol}^{-1}\)
- B
\(-16\ \text{kJ mol}^{-1}\)
- C
\(+4\ \text{kJ mol}^{-1}\)
- D
\(-4\ \text{kJ mol}^{-1}\)
-
Q76. Benzoyl chloride is reduced with hydrogen over palladium on barium sulphate (Rosenmund reduction). The product is
- A
benzaldehyde
- B
toluene
- C
benzoic acid
- D
benzyl alcohol
-
Q77. Which of these is an electrophile?
- A
\(\ce{NH3}\)
- B
\(\ce{NO2+}\)
- C
\(\ce{CN-}\)
- D
\(\ce{H2O}\)
-
Q78. Which mixture shows a negative deviation from Raoult's law?
-
Q79. Glucose is oxidised by bromine water. The product is
- A
glucose pentaacetate
- B
n-hexane
- C
saccharic acid
- D
gluconic acid
-
Q80. Which ligand causes the largest crystal field splitting in an octahedral complex of a given metal ion?
- A
\(\ce{CN-}\)
- B
\(\ce{F-}\)
- C
\(\ce{H2O}\)
- D
\(\ce{Cl-}\)
-
Q81. \(1\ \text{g}\) of a non-volatile non-electrolyte dissolved in \(50\ \text{g}\) of benzene lowers its freezing point by \(0.40\ \text{K}\). If \(K_f\) of benzene is \(5.12\ \text{K kg mol}^{-1}\), the molar mass of the solute is
- A
\(256\ \text{g mol}^{-1}\)
- B
\(128\ \text{g mol}^{-1}\)
- C
\(512\ \text{g mol}^{-1}\)
- D
\(25.6\ \text{g mol}^{-1}\)
-
Q82. The activation energy of a reaction is \(80\ \text{kJ mol}^{-1}\) and its enthalpy change is \(\Delta H = -20\ \text{kJ mol}^{-1}\). The activation energy of the reverse reaction is
- A
\(20\ \text{kJ mol}^{-1}\)
- B
\(80\ \text{kJ mol}^{-1}\)
- C
\(60\ \text{kJ mol}^{-1}\)
- D
\(100\ \text{kJ mol}^{-1}\)
-
Q83. Which set of quantum numbers is NOT possible for an electron?
- A
\(n = 3,\ l = 2,\ m_l = -2,\ m_s = -\frac{1}{2}\)
- B
\(n = 2,\ l = 1,\ m_l = -1,\ m_s = +\frac{1}{2}\)
- C
\(n = 4,\ l = 0,\ m_l = 0,\ m_s = -\frac{1}{2}\)
- D
\(n = 2,\ l = 2,\ m_l = 0,\ m_s = +\frac{1}{2}\)
-
Q84. Which compound is used as an antiseptic in a dilute solution (about \(0.2\%\)) and as a disinfectant in a stronger one (about \(1\%\))?
- A
saccharin
- B
phenol
- C
paracetamol
- D
aspirin
-
Q85. In allene, \(\ce{CH2=C=CH2}\), the hybridisation of the three carbon atoms, taken from left to right, is
- A
\(sp^3\), \(sp\), \(sp^3\)
- B
\(sp\), \(sp^2\), \(sp\)
- C
\(sp^2\), \(sp\), \(sp^2\)
- D
\(sp^2\), \(sp^2\), \(sp^2\)
-
Q86. Bulk gold is yellow. A solution containing gold nanoparticles of about \(10\ \text{nm}\) usually looks
-
Q87. According to the Freundlich adsorption isotherm, \(\frac{x}{m} = kP^{1/n}\). A graph of \(\log\frac{x}{m}\) against \(\log P\) is a straight line whose slope is
- A
\(k\)
- B
\(\frac{1}{n}\)
- C
\(n\)
- D
\(\log k\)
-
Q88. The degree of dissociation of a \(0.01\ \text{M}\) solution of ammonium hydroxide (\(K_b = 1.8 \times 10^{-5}\)) is about
- A
\(4.24\%\)
- B
\(0.18\%\)
- C
\(1.8\%\)
- D
\(0.42\%\)
-
Q89. Which order of reactivity towards nucleophilic addition is correct?
- A
\(\ce{CH3COCH3} > \ce{CH3CHO} > \ce{HCHO}\)
- B
\(\ce{CH3COCH3} > \ce{HCHO} > \ce{CH3CHO}\)
- C
\(\ce{CH3CHO} > \ce{HCHO} > \ce{CH3COCH3}\)
- D
\(\ce{HCHO} > \ce{CH3CHO} > \ce{CH3COCH3}\)
-
Q90. The standard emf of a Daniell cell, in which \(2\) electrons are transferred, is \(1.10\ \text{V}\). Its standard Gibbs energy change is about (\(F = 96500\ \text{C mol}^{-1}\))
- A
\(+212.3\ \text{kJ mol}^{-1}\)
- B
\(-212.3\ \text{kJ mol}^{-1}\)
- C
\(-106.2\ \text{kJ mol}^{-1}\)
- D
\(-21.2\ \text{kJ mol}^{-1}\)
-
Q91. Ethanamine, \(\ce{C2H5NH2}\), is treated with nitrous acid (sodium nitrite and dilute HCl) in the cold. The organic product and the gas given off are
- A
ethanenitrile and hydrogen
- B
a stable ethanediazonium chloride, and no gas
- C
ethanol and nitrogen dioxide
- D
ethanol and nitrogen
-
Q92. Which of these is a disproportionation reaction?
- A
\(\ce{CaCO3 -> CaO + CO2}\)
- B
\(\ce{2H2O2 -> 2H2O + O2}\)
- C
\(\ce{2KClO3 -> 2KCl + 3O2}\)
- D
\(\ce{Zn + CuSO4 -> ZnSO4 + Cu}\)
-
Q93. The effective atomic number (EAN) of iron in \(\ce{K4[Fe(CN)6]}\) is (atomic number of Fe = \(26\))
- A
\(36\)
- B
\(30\)
- C
\(24\)
- D
\(38\)
-
Q94. Chlorobenzene is much less reactive than chloroethane towards nucleophilic substitution, because in chlorobenzene
- A
the C-Cl bond has partial double bond character due to resonance
- B
the C-Cl bond is purely ionic
- C
the C-Cl bond is longer and weaker
- D
chlorine is attached to an \(sp^3\) carbon atom
-
Q95. The number of geometrical isomers of the square planar complex \(\ce{[Pt(NH3)2Cl2]}\) is
- A
\(2\)
- B
\(3\)
- C
\(4\)
- D
none
-
Q96. When a lead storage battery gives out current (discharges), the substance formed at both electrodes is
- A
\(\ce{PbO2}\)
- B
\(\ce{PbO}\)
- C
\(\ce{PbSO4}\)
- D
\(\ce{Pb}\)
-
Q97. A concentrated aqueous solution of sodium chloride (brine) is electrolysed with inert electrodes. The products are
- A
chlorine at the cathode and hydrogen at the anode
- B
sodium at the cathode and chlorine at the anode
- C
hydrogen at the cathode and chlorine at the anode
- D
hydrogen at the cathode and oxygen at the anode
-
Q98. The vapour of an alcohol is passed over heated copper at \(573\ \text{K}\), and an alkene is formed. The alcohol is
- A
ethanol
- B
butan-1-ol
- C
2-methylpropan-2-ol
- D
propan-2-ol
-
Q99. Buna-S rubber is a copolymer of
- A
isoprene only
- B
chloroprene only
- C
buta-1,3-diene and acrylonitrile
- D
buta-1,3-diene and styrene
-
Q100. Which alkali metal combines directly with nitrogen to form a nitride?
- A
caesium
- B
sodium
- C
lithium
- D
potassium
-
Q101. The modulus of \(z = \frac{(3 + 4i)(1 - i)}{1 + 2i}\) is
- A
\(10\)
- B
\(\sqrt{2}\)
- C
\(5\)
- D
\(\sqrt{10}\)
-
Q102. \(\displaystyle\int \frac{\cos 2x}{(\sin x + \cos x)^2}\,dx\) is
- A
\(\log|\cos x - \sin x| + c\)
- B
\(\log|\sin x + \cos x| + c\)
- C
\(\frac{1}{\sin x + \cos x} + c\)
- D
\(\log|\cos 2x| + c\)
-
Q103. The volume of the tetrahedron with vertices \(O(0, 0, 0)\), \(A(1, 2, 1)\), \(B(2, 1, 3)\) and \(C(-1, 1, 2)\) is
- A
\(4\) cubic units
- B
\(12\) cubic units
- C
\(6\) cubic units
- D
\(2\) cubic units
-
Q104. A family has two children. Given that at least one of them is a boy, the probability that both are boys is (boys and girls equally likely)
- A
\(\frac{1}{3}\)
- B
\(\frac{1}{4}\)
- C
\(\frac{1}{2}\)
- D
\(\frac{2}{3}\)
-
Q105. Two switches \(S_1\) and \(S_2\) are joined in parallel, and this pair is joined in series with a third switch \(S_3\). If \(p\), \(q\) and \(r\) stand for '\(S_1\), \(S_2\), \(S_3\) is closed', the circuit is represented by
-
Q106. The points with position vectors \(60\hat{i} + 3\hat{j}\), \(40\hat{i} - 8\hat{j}\) and \(a\hat{i} - 52\hat{j}\) are collinear. Then \(a\) is
- A
\(-20\)
- B
\(40\)
- C
\(20\)
- D
\(-40\)
-
Q107. A particle moves along a line so that its distance from a fixed point after \(t\) seconds is \(s = t^3 - 6t^2 + 9t\) metres. Its acceleration at the second moment when its velocity is zero is
- A
\(12\ \text{m s}^{-2}\)
- B
\(6\ \text{m s}^{-2}\)
- C
\(0\ \text{m s}^{-2}\)
- D
\(-6\ \text{m s}^{-2}\)
-
Q108. If \(A = \begin{bmatrix} 1 & 2 \\ 3 & -1 \end{bmatrix}\) and \(B = \begin{bmatrix} 1 & 0 \\ -1 & 2 \end{bmatrix}\), then \(AB - BA\) is
- A
\(\begin{bmatrix} -2 & 2 \\ -1 & 2 \end{bmatrix}\)
- B
\(\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}\)
- C
\(\begin{bmatrix} 2 & -2 \\ 1 & -2 \end{bmatrix}\)
- D
\(\begin{bmatrix} -2 & 2 \\ 1 & 2 \end{bmatrix}\)
-
Q109. If \(x^y = e^{x - y}\) (\(x > 0\)), then \(\frac{dy}{dx}\) is
- A
\(\frac{x}{(1 + \log x)^2}\)
- B
\(\frac{1}{(1 + \log x)^2}\)
- C
\(\frac{\log x}{1 + \log x}\)
- D
\(\frac{\log x}{(1 + \log x)^2}\)
-
Q110. The general solution of \(\sqrt{3}\cos\theta + \sin\theta = \sqrt{2}\) is (\(n \in \mathbb{Z}\))
- A
\(\theta = n\pi + (-1)^n\frac{\pi}{4} + \frac{\pi}{6}\)
- B
\(\theta = 2n\pi \pm \frac{\pi}{4} + \frac{\pi}{6}\)
- C
\(\theta = 2n\pi \pm \frac{\pi}{4} - \frac{\pi}{6}\)
- D
\(\theta = n\pi \pm \frac{\pi}{4} + \frac{\pi}{6}\)
-
Q111. The problem: maximise \(z = x + y\) subject to \(x + y \ge 4\), \(x + y \le 2\), \(x \ge 0\), \(y \ge 0\)
- A
has the maximum value \(4\)
- B
has the maximum value \(2\)
- C
has no feasible solution
- D
has an unbounded solution
-
Q112. A random variable \(X\) has \(P(X = x) = k(x + 1)\) for \(x = 0, 1, 2, 3\). Then \(P(X \ge 2)\) is
- A
\(\frac{3}{10}\)
- B
\(\frac{7}{10}\)
- C
\(\frac{2}{5}\)
- D
\(\frac{1}{2}\)
-
Q113. \(\displaystyle\int_0^{2} \sqrt{4 - x^2}\,dx\) is
- A
\(2\pi\)
- B
\(\frac{\pi}{2}\)
- C
\(4\pi\)
- D
\(\pi\)
-
Q114. The equation \(x^2 + 4xy + ky^2 = 0\) represents two real and distinct lines through the origin when
- A
\(k > -4\)
- B
\(k > 4\)
- C
\(k < 4\)
- D
\(k = 4\)
-
Q115. For \(f(x) = \frac{2x - 3}{5}\), \(x \in \mathbb{R}\), the inverse function \(f^{-1}(x)\) is
- A
\(\frac{2x + 3}{5}\)
- B
\(\frac{5x - 3}{2}\)
- C
\(\frac{5}{2x - 3}\)
- D
\(\frac{5x + 3}{2}\)
-
Q116. The area of the triangle formed by the lines \(x^2 - y^2 = 0\) and the line \(x = 4\) is
- A
\(8\) square units
- B
\(16\) square units
- C
\(4\) square units
- D
\(32\) square units
-
Q117. The equation of the plane that cuts off intercepts \(2\), \(3\) and \(4\) on the \(x\), \(y\) and \(z\) axes is
- A
\(4x + 6y + 3z = 12\)
- B
\(6x + 4y + 3z = 24\)
- C
\(6x + 4y + 3z = 12\)
- D
\(2x + 3y + 4z = 12\)
-
Q118. If \(y = \sin(m\sin^{-1}x)\), then \((1 - x^2)\frac{d^2y}{dx^2} - x\frac{dy}{dx}\) equals
- A
\(-my\)
- B
\(m^2 y\)
- C
\(-m^2 y\)
- D
\(0\)
-
Q119. The acute angle between the lines \(2x - y + 3 = 0\) and \(3x + y - 1 = 0\) is
- A
\(90^\circ\)
- B
\(60^\circ\)
- C
\(45^\circ\)
- D
\(30^\circ\)
-
Q120. The direction ratios of the line of intersection of the planes \(x + y + z = 1\) and \(x - y + 2z = 3\) are
- A
\(3, 1, -2\)
- B
\(2, 1, 3\)
- C
\(3, -1, -2\)
- D
\(1, -1, 2\)
-
Q121. The diagonals of a parallelogram are \(3\hat{i} + \hat{j} - 2\hat{k}\) and \(\hat{i} - 3\hat{j} + 4\hat{k}\). The area of the parallelogram is
-
Q122. If \(A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}\), then for every natural number \(n\), \(A^n\) is
- A
\(2^{n - 1}A\)
- B
\(2^n A\)
- C
\(nA\)
- D
\(2^{n + 1}A\)
-
Q123. A continuous random variable \(X\) has the probability density function \(f(x) = 2x\) for \(0 \le x \le 1\) (and \(0\) elsewhere). Its expected value \(E(X)\) is
- A
\(1\)
- B
\(\frac{1}{2}\)
- C
\(\frac{2}{3}\)
- D
\(\frac{1}{3}\)
-
Q124. The equation of the normal to the curve \(y = x^2\) at the point \((1, 1)\) is
- A
\(x + 2y = 3\)
- B
\(x + 2y = 1\)
- C
\(x - 2y + 1 = 0\)
- D
\(2x - y = 1\)
-
Q125. In \(\triangle ABC\), \(a = 4\), \(b = 6\) and \(C = 60^\circ\). The area of the triangle is
- A
\(12\)
- B
\(6\sqrt{3}\)
- C
\(6\)
- D
\(12\sqrt{3}\)
-
Q126. \(\displaystyle\int_0^{1} \frac{x}{x^2 + 1}\,dx\) is
- A
\(\log 2\)
- B
\(\frac{\pi}{4}\)
- C
\(\frac{1}{2}\log 2\)
- D
\(2\log 2\)
-
Q127. The statement \(p \leftrightarrow q\) is logically equivalent to
- A
\(\sim p \leftrightarrow q\)
- B
\((p \rightarrow q) \wedge (q \rightarrow p)\)
- C
\((p \rightarrow q) \vee (q \rightarrow p)\)
- D
\((p \wedge q) \vee (\sim p \wedge q)\)
-
Q128. The equation of the circle with the points \((1, 2)\) and \((5, 6)\) as the ends of a diameter is
- A
\(x^2 + y^2 - 6x - 8y + 25 = 0\)
- B
\(x^2 + y^2 - 6x - 8y + 17 = 0\)
- C
\(x^2 + y^2 - 6x - 8y - 17 = 0\)
- D
\(x^2 + y^2 + 6x + 8y + 17 = 0\)
-
Q129. The number of different arrangements of the letters of the word BANANA is
- A
\(360\)
- B
\(120\)
- C
\(60\)
- D
\(720\)
-
Q130. The slope of one of the lines represented by \(x^2 + kxy + 2y^2 = 0\) is twice the slope of the other. Then \(k\) is
- A
\(\pm 3\)
- B
\(\pm 2\sqrt{2}\)
- C
\(\pm 2\)
- D
\(\pm 6\)
-
Q131. The general solution of the differential equation \(\frac{dy}{dx} = \frac{x + y}{x}\) (\(x > 0\)) is
- A
\(y = x\log x + c\)
- B
\(y = x^2\log x + cx\)
- C
\(y = x\log x + cx\)
- D
\(y = \log x + cx\)
-
Q132. The area of the region enclosed by the parabolas \(y = x^2\) and \(y^2 = x\) is
- A
\(\frac{1}{3}\) square units
- B
\(\frac{2}{3}\) square units
- C
\(1\) square unit
- D
\(\frac{1}{6}\) square units
-
Q133. The eccentricity of the hyperbola \(\frac{x^2}{16} - \frac{y^2}{9} = 1\) is
- A
\(\frac{5}{3}\)
- B
\(\frac{5}{4}\)
- C
\(\frac{4}{5}\)
- D
\(\frac{3}{4}\)
-
Q134. The converse of the statement 'If a number is divisible by \(6\), then it is divisible by \(3\)' is
- A
'If a number is divisible by \(3\), then it is divisible by \(6\)'
- B
'A number is divisible by \(6\) and it is not divisible by \(3\)'
- C
'If a number is not divisible by \(3\), then it is not divisible by \(6\)'
- D
'If a number is not divisible by \(6\), then it is not divisible by \(3\)'
-
Q135. \(A\) is a square matrix of order \(3\) with \(|A| = 5\). Then \(|2A|\) is
- A
\(30\)
- B
\(10\)
- C
\(40\)
- D
\(80\)
-
Q136. The function \(f(x) = \frac{e^{3x} - 1}{\sin x}\) for \(x \neq 0\), with \(f(0) = k\), is continuous at \(x = 0\) when \(k\) is
- A
\(0\)
- B
\(\frac{1}{3}\)
- C
\(3\)
- D
\(1\)
-
Q137. \(\displaystyle\int \frac{dx}{\sqrt{x^2 + 6x + 13}}\) is
- A
\(\log\left|x + 3 + \sqrt{x^2 + 6x + 13}\right| + c\)
- B
\(\frac{1}{2}\tan^{-1}\frac{x + 3}{2} + c\)
- C
\(\sin^{-1}\frac{x + 3}{2} + c\)
- D
\(\log\left|x + 3 - \sqrt{x^2 + 6x + 13}\right| + c\)
-
Q138. The least value of \(f(x) = x^2 + \frac{16}{x}\) for \(x > 0\) is
- A
\(12\)
- B
\(16\)
- C
\(20\)
- D
\(8\)
-
Q139. The lines \(\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}\) and \(\frac{x - 2}{3} = \frac{y - 3}{4} = \frac{z - 4}{5}\)
- A
intersect at the point \((-1, -1, -1)\)
- B
are skew lines (neither parallel nor intersecting)
- C
intersect at the point \((1, 2, 3)\)
- D
are parallel
-
Q140. The derivative of \(\sin x\) with respect to \(\cos x\) is
- A
\(\cot x\)
- B
\(-\cot x\)
- C
\(\tan x\)
- D
\(-\tan x\)
-
Q141. The minimum value of \(z = 3x + 5y\) subject to \(x + y \ge 2\), \(x + 3y \ge 3\), \(x \ge 0\), \(y \ge 0\) is
- A
\(9\)
- B
\(10\)
- C
\(6\)
- D
\(7\)
-
Q142. \(A\) and \(B\) are acute angles with \(\sin A = \frac{3}{5}\) and \(\cos B = \frac{5}{13}\). Then \(\sin(A + B)\) is
- A
\(\frac{56}{65}\)
- B
\(\frac{16}{65}\)
- C
\(\frac{33}{65}\)
- D
\(\frac{63}{65}\)
-
Q143. \(\displaystyle\lim_{x \to 0} (1 + 3x)^{\frac{2}{x}}\) is
- A
\(e^{3/2}\)
- B
\(e^3\)
- C
\(e^{2/3}\)
- D
\(e^6\)
-
Q144. The area of the region bounded by the curve \(y = \log x\), the \(x\)-axis and the line \(x = e\) is
-
Q145. The integrating factor of the differential equation \(\frac{dy}{dx} + y\tan x = \sec x\) is
- A
\(\sec x\)
- B
\(\cos x\)
- C
\(e^{\tan x}\)
- D
\(\tan x\)
-
Q146. \(\displaystyle\int \tan^{-1}x\,dx\) is
- A
\(\frac{1}{1 + x^2} + c\)
- B
\(x\tan^{-1}x + \frac{1}{2}\log(1 + x^2) + c\)
- C
\(x\tan^{-1}x - \log(1 + x^2) + c\)
- D
\(x\tan^{-1}x - \frac{1}{2}\log(1 + x^2) + c\)
-
Q147. The value of \(\tan^{-1} 1 + \tan^{-1} 2 + \tan^{-1} 3\) is
- A
\(\frac{3\pi}{4}\)
- B
\(\pi\)
- C
\(0\)
- D
\(\frac{\pi}{2}\)
-
Q148. The probability that a bulb of a certain kind fuses within a year is \(0.05\). The probability that none of \(5\) such bulbs fuses within a year is
- A
\((0.95)^5\)
- B
\(1 - (0.05)^5\)
- C
\((0.05)^5\)
- D
\(5(0.05)(0.95)^4\)
-
Q149. In \(4\) independent trials, the probability of success in each trial is \(\frac{1}{3}\). The probability of exactly \(2\) successes is
- A
\(\frac{2}{9}\)
- B
\(\frac{4}{81}\)
- C
\(\frac{16}{81}\)
- D
\(\frac{8}{27}\)
-
Q150. \(\displaystyle\int_0^{\pi} |\cos x|\,dx\) is
- A
\(0\)
- B
\(2\)
- C
\(1\)
- D
\(\pi\)