Mock Test 1 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.
-
Q1. A ball is projected so that its horizontal range is four times its maximum height. The angle of projection with the horizontal is
- A
\(45^\circ\)
- B
\(76^\circ\)
- C
\(60^\circ\)
- D
\(30^\circ\)
-
Q2. In Young's double slit experiment, the slits are \(0.5\ \text{mm}\) apart, the screen is \(1\ \text{m}\) away and light of wavelength \(500\ \text{nm}\) is used. If the whole set-up is put in water (refractive index \(\frac{4}{3}\)), the fringe width becomes
- A
\(0.50\ \text{mm}\)
- B
\(0.75\ \text{mm}\)
- C
\(1.00\ \text{mm}\)
- D
\(1.33\ \text{mm}\)
-
Q3. A curved road of radius \(50\ \text{m}\) is banked so that a car at \(36\ \text{km h}^{-1}\) needs no friction to take the curve. With \(g = 10\ \text{m s}^{-2}\), the angle of banking is
- A
\(\tan^{-1}(2)\)
- B
\(\tan^{-1}(0.5)\)
- C
\(\tan^{-1}(0.72)\)
- D
\(\tan^{-1}(0.2)\)
-
Q4. A pure silicon crystal is doped with a small amount of arsenic (group 15). The crystal becomes
- A
n-type, with electrons as the majority carriers
- B
still intrinsic, because arsenic adds equal numbers of electrons and holes
- C
n-type, with holes as the majority carriers
- D
p-type, with holes as the majority carriers
-
Q5. Light of wavelength \(310\ \text{nm}\) falls on a metal of work function \(2.0\ \text{eV}\) (take \(hc = 1240\ \text{eV nm}\)). The stopping potential is
- A
\(4.0\ \text{V}\)
- B
\(1.0\ \text{V}\)
- C
\(6.0\ \text{V}\)
- D
\(2.0\ \text{V}\)
-
Q6. The ratio of the wavelength of the first line of the Balmer series to that of the first line of the Lyman series in hydrogen is
- A
\(\frac{5}{27}\)
- B
\(\frac{27}{5}\)
- C
\(\frac{9}{4}\)
- D
\(\frac{4}{3}\)
-
Q7. Blocks of mass \(2\ \text{kg}\) and \(3\ \text{kg}\) lie on a smooth horizontal table, joined by a light string. A horizontal force of \(10\ \text{N}\) pulls the \(3\ \text{kg}\) block. The tension in the string is
- A
\(4\ \text{N}\)
- B
\(6\ \text{N}\)
- C
\(2\ \text{N}\)
- D
\(10\ \text{N}\)
-
Q8. The rms speed of oxygen molecules at \(27^\circ\text{C}\) is \(v\). The temperature at which their rms speed is \(2v\) is
- A
\(1200^\circ\text{C}\)
- B
\(108^\circ\text{C}\)
- C
\(54^\circ\text{C}\)
- D
\(927^\circ\text{C}\)
-
Q9. A full-wave rectifier works on a \(50\ \text{Hz}\) mains supply. The frequency of the ripple in its output is
- A
\(200\ \text{Hz}\)
- B
\(25\ \text{Hz}\)
- C
\(50\ \text{Hz}\)
- D
\(100\ \text{Hz}\)
-
Q10. An electron at rest is accelerated through \(100\ \text{V}\). Its de Broglie wavelength is about
- A
\(0.0123\ \text{nm}\)
- B
\(0.123\ \text{nm}\)
- C
\(1.23\ \text{nm}\)
- D
\(12.3\ \text{nm}\)
-
Q11. In SHM of amplitude \(A\), the kinetic energy equals the potential energy at a displacement of
- A
\(\frac{\sqrt{3}A}{2}\)
- B
\(\frac{A}{4}\)
- C
\(\frac{A}{\sqrt{2}}\)
- D
\(\frac{A}{2}\)
-
Q12. A circular coil of \(50\) turns and radius \(10\ \text{cm}\) carries a current of \(2\ \text{A}\). The magnetic field at its centre is (\(\mu_0 = 4\pi \times 10^{-7}\ \text{T m A}^{-1}\))
- A
\(6.28 \times 10^{-5}\ \text{T}\)
- B
\(6.28 \times 10^{-4}\ \text{T}\)
- C
\(12.56 \times 10^{-4}\ \text{T}\)
- D
\(3.14 \times 10^{-4}\ \text{T}\)
-
Q13. Capacitors of \(2\ \mu\text{F}\), \(3\ \mu\text{F}\) and \(6\ \mu\text{F}\) are joined in series across a \(12\ \text{V}\) supply. The total energy stored is
- A
\(144\ \mu\text{J}\)
- B
\(72\ \mu\text{J}\)
- C
\(36\ \mu\text{J}\)
- D
\(792\ \mu\text{J}\)
-
Q14. A thin ring of radius \(R\) carries a charge \(q\) spread uniformly. At its centre, the electric field \(E\) and the potential \(V\) are
- A
\(E = \frac{q}{4\pi\varepsilon_0 R^2},\ V = 0\)
- B
\(E = 0,\ V = \frac{q}{4\pi\varepsilon_0 R}\)
- C
\(E = \frac{q}{4\pi\varepsilon_0 R^2},\ V = \frac{q}{4\pi\varepsilon_0 R}\)
- D
\(E = 0,\ V = 0\)
-
Q15. A proton moves at \(2 \times 10^{6}\ \text{m s}^{-1}\) at right angles to a uniform magnetic field of \(0.5\ \text{T}\). The radius of its circular path is about (\(m_p = 1.67 \times 10^{-27}\ \text{kg}\), \(e = 1.6 \times 10^{-19}\ \text{C}\))
- A
\(4.2\ \text{cm}\)
- B
\(0.42\ \text{cm}\)
- C
\(2.1\ \text{cm}\)
- D
\(8.4\ \text{cm}\)
-
Q16. If the absolute temperature of a black body rises by \(10\%\), the energy it radiates per second rises by about
- A
\(21\%\)
- B
\(10\%\)
- C
\(46\%\)
- D
\(40\%\)
-
Q17. The component of \(\vec{A} = 2\hat{i} + 3\hat{j} + 6\hat{k}\) along \(\vec{B} = \hat{i} + 2\hat{j} + 2\hat{k}\) is
- A
\(\frac{20}{3}\)
- B
\(\frac{3}{20}\)
- C
\(\frac{20}{7}\)
- D
\(\frac{7}{3}\)
-
Q18. Light of wavelength \(600\ \text{nm}\) falls normally on a single slit of width \(0.3\ \text{mm}\). The angular width of the central maximum is
- A
\(4 \times 10^{-3}\ \text{rad}\)
- B
\(2 \times 10^{-3}\ \text{rad}\)
- C
\(1 \times 10^{-3}\ \text{rad}\)
- D
\(8 \times 10^{-3}\ \text{rad}\)
-
Q19. Two tuning forks A and B give \(4\) beats per second. A has frequency \(256\ \text{Hz}\). When B is loaded with a little wax, the beats fall to \(2\) per second. The original frequency of B was
- A
\(252\ \text{Hz}\)
- B
\(258\ \text{Hz}\)
- C
\(260\ \text{Hz}\)
- D
\(254\ \text{Hz}\)
-
Q20. A train approaching a stationary observer at \(20\ \text{m s}^{-1}\) blows a whistle of frequency \(640\ \text{Hz}\). If the speed of sound is \(340\ \text{m s}^{-1}\), the frequency the observer hears is
- A
\(720\ \text{Hz}\)
- B
\(680\ \text{Hz}\)
- C
\(600\ \text{Hz}\)
- D
\(640\ \text{Hz}\)
-
Q21. A metal rod \(2\ \text{m}\) long expands by \(1.2\ \text{mm}\) when heated from \(20^\circ\text{C}\) to \(80^\circ\text{C}\). The coefficient of area expansion of the metal is
- A
\(3.0 \times 10^{-5}\ {}^\circ\text{C}^{-1}\)
- B
\(1.0 \times 10^{-5}\ {}^\circ\text{C}^{-1}\)
- C
\(0.5 \times 10^{-5}\ {}^\circ\text{C}^{-1}\)
- D
\(2.0 \times 10^{-5}\ {}^\circ\text{C}^{-1}\)
-
Q22. The current in a coil of self-inductance \(0.2\ \text{H}\) falls steadily from \(5\ \text{A}\) to \(1\ \text{A}\) in \(0.1\ \text{s}\). The magnitude of the induced emf is
- A
\(12\ \text{V}\)
- B
\(4\ \text{V}\)
- C
\(8\ \text{V}\)
- D
\(2\ \text{V}\)
-
Q23. A particle performs SHM with amplitude \(10\ \text{cm}\) and period \(2\ \text{s}\). Its speed when it is \(6\ \text{cm}\) from the mean position is
- A
\(4\pi\ \text{cm s}^{-1}\)
- B
\(8\pi\ \text{cm s}^{-1}\)
- C
\(6\pi\ \text{cm s}^{-1}\)
- D
\(10\pi\ \text{cm s}^{-1}\)
-
Q24. Point charges of \(+2\ \mu\text{C}\) and \(+8\ \mu\text{C}\) are \(30\ \text{cm}\) apart. A third charge placed on the line joining them feels no net force when it is
- A
\(20\ \text{cm}\) from the \(2\ \mu\text{C}\) charge, between the two
- B
\(10\ \text{cm}\) from the \(2\ \mu\text{C}\) charge, outside the two
- C
midway between the two charges
- D
\(10\ \text{cm}\) from the \(2\ \mu\text{C}\) charge, between the two
-
Q25. A Carnot engine works between \(527^\circ\text{C}\) and \(127^\circ\text{C}\). Its efficiency is
- A
\(50\%\)
- B
\(25\%\)
- C
\(76\%\)
- D
\(24\%\)
-
Q26. The fundamental frequency of a pipe open at both ends is \(300\ \text{Hz}\). If one end is closed, the frequency of its first overtone is
- A
\(150\ \text{Hz}\)
- B
\(600\ \text{Hz}\)
- C
\(450\ \text{Hz}\)
- D
\(300\ \text{Hz}\)
-
Q27. At a depth \(d\) below the Earth's surface, the acceleration due to gravity equals its value at a height \(\frac{R}{2}\) above the surface (\(R\) = radius of the Earth). Then \(d\) is
- A
\(\frac{2R}{3}\)
- B
\(\frac{4R}{9}\)
- C
\(\frac{5R}{9}\)
- D
\(\frac{R}{2}\)
-
Q28. A radioactive sample has a half-life of \(20\) days. The fraction of the sample that has decayed after \(60\) days is
- A
\(\frac{1}{8}\)
- B
\(\frac{2}{3}\)
- C
\(\frac{7}{8}\)
- D
\(\frac{3}{4}\)
-
Q29. The magnetic susceptibility of a paramagnetic salt is \(2.4 \times 10^{-5}\) at \(300\ \text{K}\). At \(200\ \text{K}\) it is
- A
\(5.4 \times 10^{-5}\)
- B
\(2.4 \times 10^{-5}\)
- C
\(3.6 \times 10^{-5}\)
- D
\(1.6 \times 10^{-5}\)
-
Q30. For an ideal diatomic gas at room temperature (no vibrational modes), the ratio \(\frac{C_p}{C_v}\) is
- A
\(1.40\)
- B
\(1.29\)
- C
\(1.67\)
- D
\(1.33\)
-
Q31. The length and breadth of a rectangle are \((5.0 \pm 0.1)\ \text{cm}\) and \((2.0 \pm 0.1)\ \text{cm}\). The percentage error in its area is
- A
\(7\%\)
- B
\(3.5\%\)
- C
\(5\%\)
- D
\(2\%\)
-
Q32. In a metre bridge, an unknown resistance \(X\) is in the left gap and \(30\ \Omega\) in the right gap. The null point is \(40\ \text{cm}\) from the left end. Then \(X\) is
- A
\(45\ \Omega\)
- B
\(20\ \Omega\)
- C
\(12\ \Omega\)
- D
\(30\ \Omega\)
-
Q33. A skater spinning at \(2\) revolutions per second pulls in her arms, which reduces her moment of inertia to \(40\%\) of its earlier value. Her new rate of spin is
-
Q34. Unpolarised light falls on glass of refractive index \(\sqrt{3}\) at the polarising angle. The angle of refraction is
- A
\(30^\circ\)
- B
\(60^\circ\)
- C
\(45^\circ\)
- D
\(90^\circ\)
-
Q35. The energy stored in an inductor of \(50\ \text{mH}\) carrying a current of \(4\ \text{A}\) is
- A
\(0.8\ \text{J}\)
- B
\(0.1\ \text{J}\)
- C
\(0.2\ \text{J}\)
- D
\(0.4\ \text{J}\)
-
Q36. An ideal gas at \(300\ \text{K}\) with \(\gamma = 1.5\) is compressed adiabatically to one fourth of its volume. Its final temperature is
- A
\(600\ \text{K}\)
- B
\(2400\ \text{K}\)
- C
\(424\ \text{K}\)
- D
\(1200\ \text{K}\)
-
Q37. A small steel ball falls through glycerine with terminal velocity \(v\). A ball of the same steel with twice the radius falls with terminal velocity
- A
\(2v\)
- B
\(8v\)
- C
\(\frac{v}{2}\)
- D
\(4v\)
-
Q38. The output of a NOR gate is fed into a NOT gate. The combination works as
- A
an XOR gate
- B
an AND gate
- C
an OR gate
- D
a NAND gate
-
Q39. A cell balances at \(75\ \text{cm}\) of a potentiometer wire. When it is shunted by a \(10\ \Omega\) resistor, the balance point moves to \(60\ \text{cm}\). The internal resistance of the cell is
- A
\(1.25\ \Omega\)
- B
\(7.5\ \Omega\)
- C
\(2.5\ \Omega\)
- D
\(5\ \Omega\)
-
Q40. A series LCR circuit has \(L = 0.1\ \text{H}\) and \(C = 10\ \mu\text{F}\). Its resonant angular frequency is
- A
\(10000\ \text{rad s}^{-1}\)
- B
\(1000\ \text{rad s}^{-1}\)
- C
\(316\ \text{rad s}^{-1}\)
- D
\(100\ \text{rad s}^{-1}\)
-
Q41. An object is placed \(30\ \text{cm}\) in front of a concave mirror of focal length \(20\ \text{cm}\). The magnification of the image is
- A
\(+2\)
- B
\(-0.5\)
- C
\(+0.5\)
- D
\(-2\)
-
Q42. Water rises to a height of \(6\ \text{cm}\) in a vertical capillary tube. If the tube is tilted so that it makes \(60^\circ\) with the vertical, the length of the water column inside the tube is
- A
\(12\ \text{cm}\)
- B
\(6\sqrt{3}\ \text{cm}\)
- C
\(3\ \text{cm}\)
- D
\(6\ \text{cm}\)
-
Q43. Soft iron is preferred for the core of an electromagnet because it has
- A
low permeability and high coercivity
- B
high retentivity and high coercivity
- C
negative susceptibility
- D
high permeability and low retentivity
-
Q44. The work done in blowing a soap bubble of radius \(2\ \text{cm}\) (surface tension of soap solution \(0.03\ \text{N m}^{-1}\)) is
- A
\(2.4\pi \times 10^{-5}\ \text{J}\)
- B
\(9.6\pi \times 10^{-5}\ \text{J}\)
- C
\(19.2\pi \times 10^{-5}\ \text{J}\)
- D
\(4.8\pi \times 10^{-5}\ \text{J}\)
-
Q45. An ideal refrigerator keeps its inside at \(-3^\circ\text{C}\) in a room at \(27^\circ\text{C}\). Its coefficient of performance is
- A
\(1.11\)
- B
\(0.9\)
- C
\(10\)
- D
\(9\)
-
Q46. A solid sphere rolls without slipping on a horizontal surface. The fraction of its total kinetic energy that is rotational is
- A
\(\frac{2}{5}\)
- B
\(\frac{1}{3}\)
- C
\(\frac{2}{7}\)
- D
\(\frac{5}{7}\)
-
Q47. In a series LCR circuit, \(R = 30\ \Omega\), \(X_L = 80\ \Omega\) and \(X_C = 40\ \Omega\). The power factor is
- A
\(0.75\)
- B
\(0.6\)
- C
\(0.8\)
- D
\(0.5\)
-
Q48. A parallel plate capacitor is charged and then disconnected from the battery. A dielectric slab of constant \(4\) is then made to fill the space between the plates. The energy stored, earlier \(U\), becomes
- A
\(\frac{U}{4}\)
- B
\(4U\)
- C
\(\frac{U}{2}\)
- D
\(U\)
-
Q49. A mass hung from a spring oscillates with period \(T\). The spring is cut into two equal halves and the same mass is hung from one half. The new period is
- A
\(2T\)
- B
\(\frac{T}{\sqrt{2}}\)
- C
\(\sqrt{2}\,T\)
- D
\(\frac{T}{2}\)
-
Q50. A conducting rod \(0.5\ \text{m}\) long moves at \(4\ \text{m s}^{-1}\) at right angles to a uniform magnetic field of \(0.2\ \text{T}\), and to its own length. The emf induced across its ends is
- A
\(0.04\ \text{V}\)
- B
\(4\ \text{V}\)
- C
\(0.4\ \text{V}\)
- D
\(1.6\ \text{V}\)
-
Q51. \(\ce{[Ni(CN)4]^{2-}}\) is square planar and diamagnetic. The hybridisation of nickel in it is
- A
\(dsp^2\)
- B
\(sp^3\)
- C
\(sp^3d^2\)
- D
\(d^2sp^3\)
-
Q52. The numbers of radial nodes and angular nodes in a \(4d\) orbital are, respectively,
- A
\(2\) and \(2\)
- B
\(2\) and \(1\)
- C
\(0\) and \(2\)
- D
\(1\) and \(2\)
-
Q53. In the reaction \[\begin{aligned} &\ce{2MnO4^- + 5C2O4^{2-} + 16H+} \\ &\ce{-> 2Mn^{2+} + 10CO2 + 8H2O} \end{aligned}\] the oxidation number of manganese
- A
increases by \(5\)
- B
decreases by \(2\)
- C
decreases by \(3\)
- D
decreases by \(5\)
-
Q54. For \(\ce{N2(g) + 3H2(g) -> 2NH3(g)}\), \(\Delta H = -92\ \text{kJ}\) and \(\Delta S = -199\ \text{J K}^{-1}\). Assuming both stay constant, the reaction stops being spontaneous above about
- A
\(300\ \text{K}\)
- B
\(925\ \text{K}\)
- C
\(199\ \text{K}\)
- D
\(462\ \text{K}\)
-
Q55. The spin-only magnetic moment of \(\ce{Fe^{3+}}\) (atomic number of Fe = \(26\)) is about
- A
\(5.92\ \text{BM}\)
- B
\(4.90\ \text{BM}\)
- C
\(1.73\ \text{BM}\)
- D
\(3.87\ \text{BM}\)
-
Q56. The IUPAC name of \(\ce{[Co(NH3)5Cl]Cl2}\) is
- A
pentaamminechloridocobalt(III) chloride
- B
pentaamminecobalt(III) trichloride
- C
pentaamminechloridocobalt(II) chloride
- D
chloridopentaamminecobalt(III) chloride
-
Q57. Which of these is the strongest acid?
- A
\(\ce{ClCH2COOH}\)
- B
\(\ce{Cl2CHCOOH}\)
- C
\(\ce{CH3COOH}\)
- D
\(\ce{Cl3CCOOH}\)
-
Q58. For the cell \(\text{Zn} \mid \text{Zn}^{2+} \parallel \text{Cu}^{2+} \mid \text{Cu}\), \(E^\circ_{\ce{Zn^{2+}/Zn}} = -0.76\ \text{V}\) and \(E^\circ_{\ce{Cu^{2+}/Cu}} = +0.34\ \text{V}\). The standard Gibbs energy change of the cell reaction is (\(F = 96500\ \text{C mol}^{-1}\))
- A
\(+212.3\ \text{kJ}\)
- B
\(-424.6\ \text{kJ}\)
- C
\(-106.2\ \text{kJ}\)
- D
\(-212.3\ \text{kJ}\)
-
Q59. Which observation shows that the six carbon atoms of glucose are joined in a straight chain?
- A
It forms a pentaacetate
- B
Heating with HI gives n-hexane
- C
It reduces Tollens' reagent
- D
It forms an oxime with hydroxylamine
-
Q60. In acidic medium, the equivalent mass of \(\ce{KMnO4}\) (molar mass \(158\ \text{g mol}^{-1}\)) is
- A
\(31.6\)
- B
\(158\)
- C
\(79\)
- D
\(52.7\)
-
Q61. Which of these is a colloid of a liquid dispersed in a gas?
- A
Fog
- B
Milk
- C
Smoke
- D
Cheese
-
Q62. Which of these is the strongest base in aqueous solution?
- A
\(\ce{(CH3)2NH}\)
- B
\(\ce{(CH3)3N}\)
- C
\(\ce{C6H5NH2}\)
- D
\(\ce{CH3NH2}\)
-
Q63. A gas occupies \(600\ \text{mL}\) at \(27^\circ\text{C}\) and \(1\ \text{atm}\). Its volume at \(127^\circ\text{C}\) and \(2\ \text{atm}\) is
- A
\(800\ \text{mL}\)
- B
\(400\ \text{mL}\)
- C
\(300\ \text{mL}\)
- D
\(450\ \text{mL}\)
-
Q64. Which alkali metal carbonate decomposes on ordinary heating to give carbon dioxide?
- A
\(\ce{K2CO3}\)
- B
\(\ce{Li2CO3}\)
- C
\(\ce{Na2CO3}\)
- D
\(\ce{Rb2CO3}\)
-
Q65. Ozonolysis of but-2-ene, followed by treatment with zinc and water, gives
- A
ethanal only
- B
ethanal and methanal
- C
propanal and methanal
- D
propanone
-
Q66. The packing efficiency of a face centred cubic (cubic close packed) lattice is about
- A
\(68\%\)
- B
\(90.7\%\)
- C
\(74\%\)
- D
\(52.4\%\)
-
Q67. The shape of the \(\ce{XeF4}\) molecule is
- A
tetrahedral
- B
square planar
- C
octahedral
- D
see-saw
-
Q68. The rate constant of a reaction doubles when the temperature rises from \(300\ \text{K}\) to \(310\ \text{K}\). Its activation energy is about (\(R = 8.314\ \text{J K}^{-1}\text{mol}^{-1}\))
- A
\(5.36\ \text{kJ mol}^{-1}\)
- B
\(107.2\ \text{kJ mol}^{-1}\)
- C
\(26.8\ \text{kJ mol}^{-1}\)
- D
\(53.6\ \text{kJ mol}^{-1}\)
-
Q69. Acetophenone can be converted directly into ethylbenzene using
-
Q70. Phenol is heated with chloroform and aqueous sodium hydroxide, and the product is acidified. The main product is
-
Q71. Which of these gives a positive iodoform test?
- A
methanal
- B
ethanal
- C
pentan-3-one
- D
propanal
-
Q72. Which alkyl bromide reacts fastest by the \(S_N1\) mechanism?
- A
\(\ce{CH3CH2Br}\)
- B
\(\ce{(CH3)2CHBr}\)
- C
\(\ce{(CH3)3CBr}\)
- D
\(\ce{CH3Br}\)
-
Q73. A first order reaction is \(75\%\) complete in \(60\) minutes. Its half-life is
- A
\(60\ \text{min}\)
- B
\(15\ \text{min}\)
- C
\(30\ \text{min}\)
- D
\(45\ \text{min}\)
-
Q74. The limiting molar conductivities of HCl, NaCl and \(\ce{CH3COONa}\) are \(426\), \(126\) and \(91\ \text{S cm}^2\text{mol}^{-1}\). The limiting molar conductivity of acetic acid is
- A
\(209\ \text{S cm}^2\text{mol}^{-1}\)
- B
\(391\ \text{S cm}^2\text{mol}^{-1}\)
- C
\(461\ \text{S cm}^2\text{mol}^{-1}\)
- D
\(643\ \text{S cm}^2\text{mol}^{-1}\)
-
Q75. A buffer contains acetic acid (\(\text{p}K_a = 4.74\)) and sodium acetate, with \(\frac{[\text{salt}]}{[\text{acid}]} = 10\). Its pH is
- A
\(5.74\)
- B
\(4.74\)
- C
\(3.74\)
- D
\(9.26\)
-
Q76. Which base is found in RNA but not in DNA?
- A
thymine
- B
cytosine
- C
adenine
- D
uracil
-
Q77. \(3\ \text{g}\) of urea (molar mass \(60\ \text{g mol}^{-1}\)) is dissolved in \(250\ \text{g}\) of water. If \(K_b\) of water is \(0.52\ \text{K kg mol}^{-1}\), the elevation in boiling point is
- A
\(0.052\ \text{K}\)
- B
\(0.208\ \text{K}\)
- C
\(0.104\ \text{K}\)
- D
\(1.04\ \text{K}\)
-
Q78. Which of these is the strongest acid?
- A
p-nitrophenol
- B
phenol
- C
p-cresol
- D
ethanol
-
Q79. The rate constant of a reaction has the unit \(\text{mol}^{-1}\,\text{L}\,\text{s}^{-1}\). The order of the reaction is
- A
\(1\)
- B
\(0\)
- C
\(3\)
- D
\(2\)
-
Q80. A nanomaterial has at least one dimension in the range
- A
\(100\) to \(1000\ \text{nm}\)
- B
\(1\) to \(100\ \text{nm}\)
- C
\(1\) to \(100\ \mu\text{m}\)
- D
\(0.01\) to \(0.1\ \text{nm}\)
-
Q81. Which of these complex ions is optically active?
- A
trans-\(\ce{[Co(en)2Cl2]+}\)
- B
\(\ce{[Co(NH3)6]^{3+}}\)
- C
\(\ce{[Co(NH3)5Cl]^{2+}}\)
- D
cis-\(\ce{[Co(en)2Cl2]+}\)
-
Q82. Given \(\ce{C(s) + O2(g) -> CO2(g)}\), \(\Delta H = -393.5\ \text{kJ}\) and \(\ce{CO(g) + 1/2O2(g) -> CO2(g)}\), \(\Delta H = -283.0\ \text{kJ}\). The enthalpy of \(\ce{C(s) + 1/2O2(g) -> CO(g)}\) is
- A
\(-110.5\ \text{kJ}\)
- B
\(+110.5\ \text{kJ}\)
- C
\(-221.0\ \text{kJ}\)
- D
\(-676.5\ \text{kJ}\)
-
Q83. Which \(0.1\ \text{m}\) aqueous solution has the lowest freezing point?
- A
glucose
- B
\(\ce{CaCl2}\)
- C
urea
- D
\(\ce{NaCl}\)
-
Q84. A current of \(2\ \text{A}\) is passed for \(965\ \text{s}\) through copper sulphate solution. The mass of copper deposited is (\(\ce{Cu} = 63.5\), \(F = 96500\ \text{C}\))
- A
\(6.35\ \text{g}\)
- B
\(0.635\ \text{g}\)
- C
\(1.27\ \text{g}\)
- D
\(0.3175\ \text{g}\)
-
Q85. The solubility of \(\ce{Ag2CrO4}\) in water is \(1 \times 10^{-4}\ \text{mol L}^{-1}\). Its solubility product is
- A
\(4 \times 10^{-12}\)
- B
\(1 \times 10^{-8}\)
- C
\(2 \times 10^{-8}\)
- D
\(1 \times 10^{-12}\)
-
Q86. The oxidation state of sulphur in peroxodisulphuric acid, \(\ce{H2S2O8}\), is
- A
\(+5\)
- B
\(+6\)
- C
\(+8\)
- D
\(+7\)
-
Q87. A metal (molar mass \(64\ \text{g mol}^{-1}\)) forms a face centred cubic lattice with edge length \(400\ \text{pm}\). Its density is about (\(N_A = 6.022 \times 10^{23}\ \text{mol}^{-1}\))
- A
\(8.92\ \text{g cm}^{-3}\)
- B
\(3.32\ \text{g cm}^{-3}\)
- C
\(6.64\ \text{g cm}^{-3}\)
- D
\(13.3\ \text{g cm}^{-3}\)
-
Q88. \(2\) mol of an ideal gas expand isothermally and reversibly at \(300\ \text{K}\) from \(1\ \text{L}\) to \(10\ \text{L}\). The work done on the gas is about (\(R = 8.314\ \text{J K}^{-1}\text{mol}^{-1}\))
- A
\(-5.7\ \text{kJ}\)
- B
\(-11.5\ \text{kJ}\)
- C
\(+11.5\ \text{kJ}\)
- D
\(-2.5\ \text{kJ}\)
-
Q89. The atom economy of \(\ce{CH4 + Cl2 -> CH3Cl + HCl}\), with chloromethane as the desired product, is about (C = \(12\), H = \(1\), Cl = \(35.5\))
- A
\(100\%\)
- B
\(58\%\)
- C
\(50\%\)
- D
\(42\%\)
-
Q90. \(50\ \text{mL}\) of \(0.2\ \text{M}\) HCl is mixed with \(50\ \text{mL}\) of \(0.1\ \text{M}\) NaOH. The pH of the mixture is
- A
\(2.00\)
- B
\(1.00\)
- C
\(1.30\)
- D
\(0.70\)
-
Q91. Nylon-6,6 is made from
-
Q92. Chlorobenzene and chloromethane react with sodium in dry ether to give toluene. This is the
- A
Wurtz-Fittig reaction
- B
Finkelstein reaction
- C
Sandmeyer reaction
- D
Fittig reaction
-
Q93. Zirconium and hafnium have almost the same atomic radius because of
-
Q94. Which defect lowers the density of an ionic crystal?
-
Q95. The osmotic pressure of a \(0.1\ \text{M}\) solution of a non-electrolyte at \(27^\circ\text{C}\) is (\(R = 0.0821\ \text{L atm K}^{-1}\text{mol}^{-1}\))
- A
\(2.46\ \text{atm}\)
- B
\(1.23\ \text{atm}\)
- C
\(24.6\ \text{atm}\)
- D
\(0.246\ \text{atm}\)
-
Q96. The number of moles of oxygen atoms in \(9.8\ \text{g}\) of \(\ce{H2SO4}\) (molar mass \(98\ \text{g mol}^{-1}\)) is
- A
\(0.8\)
- B
\(0.2\)
- C
\(0.4\)
- D
\(0.1\)
-
Q97. Hoffmann bromamide degradation of propanamide gives
- A
ethanamide
- B
butan-1-amine
- C
ethanamine
- D
propan-1-amine
-
Q98. Which of these molecules has zero dipole moment?
- A
\(\ce{H2O}\)
- B
\(\ce{NH3}\)
- C
\(\ce{BF3}\)
- D
\(\ce{NF3}\)
-
Q99. Ranitidine is used as
- A
an analgesic
- B
an artificial sweetener
- C
an antibiotic
- D
an antacid
-
Q100. Which carbocation is the most stable?
- A
\(\ce{CH3+}\)
- B
\(\ce{CH3CH2+}\)
- C
\(\ce{(CH3)3C+}\)
- D
\(\ce{(CH3)2CH+}\)
-
Q101. The distance between the parallel lines \(3x + 4y = 7\) and \(6x + 8y = 9\) is
- A
\(\frac{5}{2}\)
- B
\(1\)
- C
\(\frac{2}{5}\)
- D
\(\frac{1}{2}\)
-
Q102. \(\displaystyle\int_{-1}^{1} |x|\,dx\) is
- A
\(\frac{1}{2}\)
- B
\(1\)
- C
\(2\)
- D
\(0\)
-
Q103. Two fair dice are thrown. The probability that the sum of the numbers is a prime number is
- A
\(\frac{5}{12}\)
- B
\(\frac{1}{2}\)
- C
\(\frac{7}{18}\)
- D
\(\frac{1}{3}\)
-
Q104. The function \(f(x) = \frac{x^2 - 9}{x - 3}\) for \(x \neq 3\), and \(f(3) = k\), is continuous at \(x = 3\) when \(k\) is
- A
\(6\)
- B
\(3\)
- C
\(0\)
- D
\(9\)
-
Q105. The area enclosed by the ellipse \(\frac{x^2}{16} + \frac{y^2}{9} = 1\) is
- A
\(25\pi\) square units
- B
\(7\pi\) square units
- C
\(144\pi\) square units
- D
\(12\pi\) square units
-
Q106. If \(z = \frac{1 + i}{1 - i}\), then \(z^{2026}\) is
- A
\(-1\)
- B
\(1\)
- C
\(-i\)
- D
\(i\)
-
Q107. The general solution of \(\tan\theta = \sqrt{3}\) is
- A
\(\theta = n\pi + \frac{\pi}{6},\ n \in \mathbb{Z}\)
- B
\(\theta = n\pi + \frac{\pi}{3},\ n \in \mathbb{Z}\)
- C
\(\theta = n\pi \pm \frac{\pi}{3},\ n \in \mathbb{Z}\)
- D
\(\theta = 2n\pi + \frac{\pi}{3},\ n \in \mathbb{Z}\)
-
Q108. The equation of the plane through \((1, 2, 3)\) perpendicular to the vector \(2\hat{i} - \hat{j} + 2\hat{k}\) is
- A
\(2x - y + 2z = 0\)
- B
\(2x + y + 2z = 10\)
- C
\(2x - y + 2z = 6\)
- D
\(x + 2y + 3z = 9\)
-
Q109. The number of ways of arranging the letters of the word ORANGE so that the three vowels are always together is
- A
\(144\)
- B
\(36\)
- C
\(720\)
- D
\(72\)
-
Q110. The contrapositive of 'If it rains, then the match is cancelled' is
- A
It rains and the match is not cancelled
- B
If the match is cancelled, then it rains
- C
If it does not rain, then the match is not cancelled
- D
If the match is not cancelled, then it does not rain
-
Q111. \(\sin^{-1}\frac{3}{5} + \cos^{-1}\frac{12}{13}\) equals
- A
\(\sin^{-1}\frac{56}{65}\)
- B
\(\cos^{-1}\frac{56}{65}\)
- C
\(\sin^{-1}\frac{16}{65}\)
- D
\(\sin^{-1}\frac{63}{65}\)
-
Q112. The order and degree of \(\left(\frac{d^2y}{dx^2}\right)^3 + \left(\frac{dy}{dx}\right)^4 + y = 0\) are
- A
order \(2\), degree \(3\)
- B
order \(3\), degree \(2\)
- C
order \(4\), degree \(3\)
- D
order \(2\), degree \(4\)
-
Q113. \(\displaystyle\int_0^{\pi} x\sin x\,dx\) is
- A
\(\pi\)
- B
\(0\)
- C
\(\frac{\pi}{2}\)
- D
\(2\pi\)
-
Q114. If \(A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}\), then \(A^2 - 5A\) equals
- A
\(I\)
- B
\(-2I\)
- C
\(2I\)
- D
\(O\)
-
Q115. The area of the triangle with vertices \(A(1, 1, 1)\), \(B(1, 2, 3)\) and \(C(2, 3, 1)\) is
- A
\(\frac{\sqrt{14}}{2}\)
- B
\(\sqrt{21}\)
- C
\(\frac{21}{2}\)
- D
\(\frac{\sqrt{21}}{2}\)
-
Q116. A population grows at a rate proportional to its size and doubles in \(10\) years. It becomes eight times its size in
- A
\(80\) years
- B
\(40\) years
- C
\(20\) years
- D
\(30\) years
-
Q117. The maximum value of \(z = 3x + 2y\) subject to \(x + y \le 4\), \(x \le 3\), \(x \ge 0\), \(y \ge 0\) is
- A
\(8\)
- B
\(9\)
- C
\(11\)
- D
\(12\)
-
Q118. If \(y = x^x\) (\(x > 0\)), then \(\frac{dy}{dx}\) is
- A
\(x^x(1 + \log x)\)
- B
\(x^x \log x\)
- C
\(x^x(1 - \log x)\)
- D
\(x \cdot x^{x - 1}\)
-
Q119. The angle between two lines with direction ratios \(1, 1, 2\) and \(\sqrt{3} - 1, -\sqrt{3} - 1, 4\) is
- A
\(45^\circ\)
- B
\(60^\circ\)
- C
\(30^\circ\)
- D
\(90^\circ\)
-
Q120. If \(A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}\), then \(A^{-1}\) is
- A
\(\frac{1}{5}\begin{bmatrix} 4 & -3 \\ -1 & 2 \end{bmatrix}\)
- B
\(\frac{1}{5}\begin{bmatrix} 4 & 3 \\ 1 & 2 \end{bmatrix}\)
- C
\(\frac{1}{11}\begin{bmatrix} 4 & -3 \\ -1 & 2 \end{bmatrix}\)
- D
\(\frac{1}{5}\begin{bmatrix} 2 & -3 \\ -1 & 4 \end{bmatrix}\)
-
Q121. \(\displaystyle\int \frac{dx}{x^2 + 4x + 13}\) is
- A
\(\frac{1}{3}\tan^{-1}\left(\frac{x - 2}{3}\right) + c\)
- B
\(\frac{1}{9}\tan^{-1}\left(\frac{x + 2}{9}\right) + c\)
- C
\(\frac{1}{3}\tan^{-1}\left(\frac{x + 2}{3}\right) + c\)
- D
\(\tan^{-1}\left(\frac{x + 2}{3}\right) + c\)
-
Q122. Using derivatives, the approximate value of \(\sqrt{25.1}\) is
- A
\(5.02\)
- B
\(5.1\)
- C
\(5.001\)
- D
\(5.01\)
-
Q123. If \(y = \sin^{-1}\left(\frac{2x}{1 + x^2}\right)\) for \(|x| < 1\), then \(\frac{dy}{dx}\) is
-
Q124. The distance of the point \((2, 1, -1)\) from the plane \(x - 2y + 4z = 9\) is
- A
\(\frac{13}{\sqrt{21}}\)
- B
\(\frac{13}{21}\)
- C
\(\frac{\sqrt{21}}{13}\)
- D
\(\frac{5}{\sqrt{21}}\)
-
Q125. The joint equation of the lines through the origin perpendicular to the lines \(3x^2 - 7xy + 2y^2 = 0\) is
- A
\(3x^2 + 7xy + 2y^2 = 0\)
- B
\(2x^2 - 7xy + 3y^2 = 0\)
- C
\(2x^2 + 7xy + 3y^2 = 0\)
- D
\(2x^2 + 7xy - 3y^2 = 0\)
-
Q126. \(\displaystyle\int x\log x\,dx\) is
- A
\(\frac{x^2}{2}\log x + \frac{x^2}{4} + c\)
- B
\(\frac{x^2}{2}\log x - \frac{x}{2} + c\)
- C
\(\frac{x^2}{2}\log x - \frac{x^2}{4} + c\)
- D
\(x^2\log x - \frac{x^2}{2} + c\)
-
Q127. A fair coin is tossed \(6\) times. The probability of getting exactly \(4\) heads is
- A
\(\frac{5}{16}\)
- B
\(\frac{1}{4}\)
- C
\(\frac{15}{64}\)
- D
\(\frac{3}{32}\)
-
Q128. In \(\triangle ABC\), \(a = 3\), \(b = 5\) and \(c = 7\). The angle \(C\) is
- A
\(\frac{\pi}{2}\)
- B
\(\frac{\pi}{3}\)
- C
\(\frac{5\pi}{6}\)
- D
\(\frac{2\pi}{3}\)
-
Q129. The negation of the statement 'All students are honest' is
-
Q130. If \(x = a\cos^3 t\) and \(y = a\sin^3 t\), then \(\frac{dy}{dx}\) is
- A
\(\tan t\)
- B
\(-\tan t\)
- C
\(\cot t\)
- D
\(-\cot t\)
-
Q131. \(f(x) = kx^2\) for \(0 \le x \le 3\) (and \(0\) elsewhere) is a probability density function. Then \(k\) is
- A
\(3\)
- B
\(\frac{1}{9}\)
- C
\(\frac{1}{3}\)
- D
\(\frac{1}{27}\)
-
Q132. The lines represented by \(kx^2 + 4xy - y^2 = 0\) are perpendicular to each other when \(k\) is
- A
\(1\)
- B
\(4\)
- C
\(-1\)
- D
\(0\)
-
Q133. The statement \(p \rightarrow (q \rightarrow p)\) is
-
Q134. If \(f(x) = \frac{3x + 2}{5x - 3}\) for \(x \neq \frac{3}{5}\), then \(f(f(x))\) is
-
Q135. The acute angle between the lines represented by \(x^2 - 4xy + y^2 = 0\) is
- A
\(30^\circ\)
- B
\(60^\circ\)
- C
\(45^\circ\)
- D
\(90^\circ\)
-
Q136. The local maximum value of \(f(x) = x^3 - 6x^2 + 9x + 1\) is
- A
\(13\)
- B
\(9\)
- C
\(1\)
- D
\(5\)
-
Q137. If \(\tan A = \frac{1}{2}\) and \(\tan B = \frac{1}{3}\), where \(A\) and \(B\) are acute, then \(A + B\) is
- A
\(\frac{\pi}{6}\)
- B
\(\frac{\pi}{2}\)
- C
\(\frac{\pi}{3}\)
- D
\(\frac{\pi}{4}\)
-
Q138. The radius of a circle grows at \(0.5\ \text{cm s}^{-1}\). When the radius is \(4\ \text{cm}\), its area grows at
- A
\(8\pi\ \text{cm}^2\text{s}^{-1}\)
- B
\(4\pi\ \text{cm}^2\text{s}^{-1}\)
- C
\(16\pi\ \text{cm}^2\text{s}^{-1}\)
- D
\(2\pi\ \text{cm}^2\text{s}^{-1}\)
-
Q139. \(A\) is a square matrix of order \(3\) with \(|A| = 4\). Then \(|\text{adj}\,A|\) is
- A
\(\frac{1}{4}\)
- B
\(4\)
- C
\(16\)
- D
\(64\)
-
Q140. \(A\) and \(B\) have position vectors \(2\hat{i} + \hat{j} - \hat{k}\) and \(\hat{i} - 3\hat{j} + 5\hat{k}\). The point dividing \(AB\) externally in the ratio \(2 : 1\) has position vector
- A
\(-7\hat{j} + 9\hat{k}\)
- B
\(-7\hat{j} + 11\hat{k}\)
- C
\(3\hat{i} + 5\hat{j} - 7\hat{k}\)
- D
\(\frac{4}{3}\hat{i} - \frac{5}{3}\hat{j} + 3\hat{k}\)
-
Q141. The length of the tangent from the point \((1, 2)\) to the circle \(x^2 + y^2 - 6x + 8y - 11 = 0\) is
- A
\(4\)
- B
\(6\)
- C
\(2\)
- D
\(\sqrt{6}\)
-
Q142. \(\displaystyle\int_0^{\pi/2} \frac{\sin x}{\sin x + \cos x}\,dx\) is
- A
\(0\)
- B
\(\pi\)
- C
\(\frac{\pi}{2}\)
- D
\(\frac{\pi}{4}\)
-
Q143. The vectors \(2\hat{i} - \hat{j} + \hat{k}\), \(\hat{i} + 2\hat{j} - 3\hat{k}\) and \(3\hat{i} + \lambda\hat{j} + 5\hat{k}\) are coplanar when \(\lambda\) is
- A
\(4\)
- B
\(2\)
- C
\(-2\)
- D
\(-4\)
-
Q144. The area of the region bounded by \(y = x^2\) and \(y = x\) is
- A
\(\frac{1}{2}\) square unit
- B
\(\frac{1}{6}\) square unit
- C
\(\frac{5}{6}\) square unit
- D
\(\frac{1}{3}\) square unit
-
Q145. A random variable \(X\) has \(P(X = x) = kx\) for \(x = 1, 2, 3, 4\). The expected value \(E(X)\) is
- A
\(\frac{1}{10}\)
- B
\(2.5\)
- C
\(3\)
- D
\(\frac{10}{3}\)
-
Q146. The eccentricity of the ellipse \(9x^2 + 25y^2 = 225\) is
- A
\(\frac{5}{4}\)
- B
\(\frac{4}{5}\)
- C
\(\frac{9}{25}\)
- D
\(\frac{3}{5}\)
-
Q147. \(\displaystyle\lim_{x \to 0} \frac{1 - \cos 4x}{x^2}\) is
- A
\(2\)
- B
\(16\)
- C
\(8\)
- D
\(4\)
-
Q148. For a linear programming problem with a non-empty bounded feasible region, the maximum of the objective function
- A
occurs only at the origin
- B
occurs at a corner point of the region
- C
occurs only at an interior point of the region
- D
may not exist
-
Q149. \(\displaystyle\int e^x(\sin x + \cos x)\,dx\) is
-
Q150. A binomial variable has mean \(4\) and variance \(3\). The number of trials \(n\) is
- A
\(20\)
- B
\(8\)
- C
\(16\)
- D
\(12\)