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Question 1. If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P., then the common ratio of the G.P. is equal to
(1) 7
(2) 4
(3) 5
(4) 6
Answer: (4)
Question 2. In an A.P., the sixth term is a_{6} = 2.
If the product a_{1} a_{4} a_{5} is greatest, then the common difference of the A.P. is equal to
(2) \frac{8}{5}
(1) \frac{3}{2}
(3) \frac{2}{3}
(4) \frac{5}{8}
Answer (2)
Question 3. If f(x) and g(x) are defined as
f(x)= \begin{cases} 2+2x, & -1 \le x < 0 \ 1-\frac{x}{3}, & 0 \le x \le 3 \end{cases}and
g(x)= \begin{cases} -x, & -3 \le x \le 0 \ x, & 0 < x \le 1 \end{cases}then the range of (f\circ g\left(x\right)) is
(1) (0,1]
(2) [0,3)
(3) [0,1]
(4) [0,1)
Answer (3)
Question 4. A fair die is thrown until 2 appears. The probability that 2 appears in an even number of throws is.
(1) \frac{5}{6}
(2) \frac{1}{6}
(3) \frac{5}{11}
(4) \frac{6}{11}
Answer (3)
Question 5. If z=\frac{1}{2}-2i is such that |z+1|=\alpha z+\beta(1+i),
where i=\sqrt{-1} and \alpha, \beta \in R, then \alpha+\beta
is equal to.
(1) -4
(2) 3
(3) 2
(4) -1
Answer (2)
Question 6. Evaluate \lim_{x \to \frac{\pi}{2}}\left(\frac{1}{\left(x-\frac{\pi}{2}\right)^{2}} \int_{x^{3}}^{\left(\frac{\pi}{2}\right)^{3}} \cos\left(\frac{1}{t^{3}}\right)\,dt\right)
(1) \frac{3\pi}{8}
(2) \frac{3\pi^{2}}{4}
(3) \frac{3\pi^{2}}{8}
(4) \frac{3\pi}{4}
Answer (3)
Question 7. If 2AB = BC and the points A and B are A(4,6) and B(\alpha,\beta) respectively, then \alpha + 2\beta is equal to
(1) 42
(2) 39
(3) 48
(4) 45
Answer (1)
Question 8. Let \vec{a}, \vec{b} and \vec{c} be three non-zero vectors such that \vec{b} and \vec{c} are non-collinear. Given that \vec{a}+5\vec{b} is collinear with \vec{c}, \vec{b}+6\vec{c} is collinear with \vec{a}, and \vec{a}+\alpha\vec{b}+\beta\vec{c}=\vec{0}, then \alpha+\beta is equal to
(1) 35
(2) 30
(3) -30
(4) -25
Answer (1)
Question 9.Let the point \left(5,\frac{a}{4}\right) be the circumcenter of a triangle with vertices A(a,-2), B(a,6) and C\left(\frac{a}{4},-2\right).
Let \alpha denote the circumradius, \beta denote the area, and \gamma denote the perimeter of the triangle. Then \alpha+\beta+\gamma
is equal to
(1) 60
(2) 53
(3) 62
(4) 30
Answer (2)
Question 10. For x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right), let y(x)=\int \frac{\cosec x+\sin x}{\cosec x \sec x+\tan x \sin^{2} x}\,dx and \lim_{x \to \left(\frac{\pi}{2}\right)^{-}} y(x)=0.
Then y\left(\frac{\pi}{4}\right) is equal to
(1) \tan^{-1}\left(\frac{1}{\sqrt{2}}\right)
(2) \frac{1}{2}\tan^{-1}\left(\frac{1}{\sqrt{2}}\right)
(3) -\frac{1}{\sqrt{2}}\tan^{-1}\left(\frac{1}{\sqrt{2}}\right)
(4) \frac{1}{\sqrt{2}}\tan^{-1}\left(-\frac{1}{2}\right)
Answer (4)
Question 11. If \alpha, where -\frac{\pi}{2} < \alpha < \frac{\pi}{2}, is a solution of 4\cos\theta + 5\sin\theta = 1, then the value of \tan\alpha is
(1) \frac{10-\sqrt{10}}{6}
(2) \frac{10-\sqrt{10}}{12}
(3) \frac{\sqrt{10}-10}{12}
(4) \frac{\sqrt{10}-10}{6}
Answer (3)
Question 12. A function y = f(x) satisfies f(x)\sin 2x + \sin x - (1+\cos^{2}x)f'(x) = 0 with the condition f(0)=0. Then f\left(\frac{\pi}{2}\right) is equal to
(1) 1
(2) 0
(3) -1
(4) 2
Answer (1)
Question 13. Let O be the origin. The position vectors of A and B are 2\hat{i}+2\hat{j}+\hat{k} and 2\hat{i}+4\hat{j}+4\hat{k} respectively. If the internal bisector of \angle AOB meets the line AB at C, then the length of OC is
(1) \frac{2}{3}\sqrt{31}
(2) \frac{2}{3}\sqrt{34}
(3) \frac{3}{4}\sqrt{34}
(4) \frac{3}{2}\sqrt{31}
Answer (2)
Question 14. Consider the function f:[\frac{1}{2},1]\rightarrow R defined by f(x)=4\sqrt{2}x^{3}-3\sqrt{2}x-1.
Consider the following statements.
(I) The curve y=f(x) intersects the x-axis exactly at one point.
(II) The curve y=f(x) intersects the x-axis at x=\cos\frac{\pi}{12}.
Then,
(1) Only (II) is correct
(2) Both (I) and (II) are incorrect
(3) Only (I) is correct
(4) Both (I) and (II) are correct
Answer (4)
Question 15. Let A=\begin{bmatrix}1&0&0\\0&\alpha&\beta\\0&\beta&\alpha\end{bmatrix}
and |2A|^{3}=2^{21}, where \alpha,\beta\in Z. Then, a value of \alpha is
(1) 3
(2) 5
(3) 17
(4) 9
Answer (2)
Question 16. Let PQR be a triangle with R(-1,4,2). Suppose M(2,1,2)
is the midpoint of PQ. The distance of the centroid of \triangle PQR
from the point of intersection of the lines \frac{x-2}{0}=\frac{y}{2}=\frac{z+3}{-1}
and \frac{x-1}{1}=\frac{y+3}{-3}=\frac{z+1}{1} is
(1) 69
(2) 9
(3) \sqrt{69}
(4) \sqrt{99}
Answer (3)
Question 17. Let R be a relation on Z\times Z defined by R(c,d) if and only if
ad-bc is divisible by 5. Then R is
(1) Reflexive and symmetric but not transitive
(2) Reflexive but neither symmetric nor transitive
(3) Reflexive, symmetric and transitive
(4) Reflexive and transitive but not symmetric
Answer (1)
Question 18. If the value of the integral \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{x^{2}\cos x}{1+\pi^{x}}+\frac{1+\sin^{2}x}{1+e^{\sin x^{2023}}}\right)dx=\frac{\pi}{4}(\pi+a)-2, then the value of a is
(1) 3
(2) -\frac{3}{2}
(3) 2
(4) \frac{3}{2}
Answer (1)
Question 19. Suppose f(x)=\frac{(2^{x}+2^{-x})\tan x\sqrt{\tan^{-1}(x^{2}-x+1)}}{(7x^{2}+3x+1)^{3}}. Then the value of f'(0) is
(1) \pi
(2) 0
(3) \sqrt{\pi}
(4) \frac{\pi}{2}
Answer (3)
Question 20. Let A be a square matrix such that AA^{T}=I.
Then, \frac{1}{2}A\left[(A+A^{T})^{2}+(A-A^{T})^{2}\right] is equal to
(1) A^{2}+I
(2) A^{3}+I
(3) A^{2}+A^{T}
(4) A^{3}+A^{T}
Answer (4)
Question 21. All the letters of the word “GTWENTY” are written in all possible ways, with or without meaning. These words are arranged in dictionary order. The serial number of the word “GTWENTY” is
Answer : 553
Question 22. Let \alpha,\beta be the roots of the equation x^{2}-x+2=0, with \operatorname{Im}(\alpha)>\operatorname{Im}(\beta).
Then the value of \alpha^{6}+\alpha^{4}+\beta^{4}-5\alpha^{2} is
Answer: 13
Question 23. If the points of intersection of two distinct conics x^{2}+y^{2}=4b and
\frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}=1 lie on the curve y^{2}=3x^{2},
then 3\sqrt{3} times the area of the rectangle formed by the intersection points is ____.
Answer : 432
Question 24. If the mean and variance of the data 65,68,58,44, 48, 45, 60, \alpha,\beta,60 where \alpha>\beta, are 56 and 66.2 respectively, then the value of \alpha^{2}+\beta^{2} is
Answer: 6344
Question 25. If \frac{{}^{11}C_{1}}{2}+\frac{{}^{11}C_{2}}{3}+\cdots+\frac{{}^{11}C_{9}}{10}=\frac{n}{m} with \gcd(n,m)=1, then the value of n + m is
Answer: 2041
Question 26. In the given circuit, the breakdown voltage of the Zener diode is 3.0 V.
Find the value of I_{z}.
(1) 3.3 mA
(2) 5.5 mA
(3) 10 mA
(4) 7 mA
Answer: (2)
Question 27 The electric current through a wire varies with time as I=I_{0}+\beta t.
Here, I_{0}=20 A \beta=3 A/s The amount of electric charge crossing a section of the wire in 20 s is :
(1) 80 C
(2) 1000 C
(3) 800 C
(4) 1600 C
Answer: (2)
Question 28. Given below are two statements.
Statement I:
If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water.
Statement II:
If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water.
In the light of the above statements, choose the most appropriate option.
(1) Both Statement I and Statement II are true
(2) Both Statement I and Statement II are false
(3) Statement I is true but Statement II is false
(4) Statement I is false but Statement II is true
Answer: (3)
Question 29. A convex mirror of radius of curvature 30 cm forms an image that is half the size of the object.
The object distance is :
(1) -15 cm
(2) 45 cm
(3) -45 cm
(4) 15 cm
Answer: (1)
Question 30. Two charges of 5Q and -2Q are situated at the points ( 3a,0 )
and ( -5a,0 ) respectively. The electric flux through a sphere of radius 4a having center at the origin is :
(1) \frac{2Q}{\varepsilon_{0}}
(2) \frac{5Q}{\varepsilon_{0}}
(3) \frac{7Q}{\varepsilon_{0}}
(4) \frac{3Q}{\varepsilon_{0}}
Answer: (2)
Question 31. A body starts moving from rest with constant acceleration. It covers displacement S_{1} in the first p-1 seconds. It covers displacement S_{2} in the first p seconds. The time in which the displacement S_{1}+S_{2} is covered is :
(1) 2p+1 s
(2) \sqrt{2p^{2}-2p+1} s
(3) 2p-1 s
(4) 2p^{2}-2p+1 s
Answer: (2)
Question 32. The potential energy function of a particle in a region of space is U=2x^{2}+3y^{3}+2z J. Here, x, y and z are in meter. The magnitude of the x-component of force acting on the particle at the point
P(1,2,3) m is :
(1) 2
(2) 6
(3) 4
(4) 8
Answer: (3)
Question 33.The resistance is given by R=\frac{V}{I}. The measured values are
V=(200\pm5) V I=(20\pm0.2) A The percentage error in the measurement of resistance is :
(1) 3.5\%
(2) 7\%
(3) 3\%
(4) 5.5\%
Answer: (1)
Question 34. A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. The coefficient of friction between the surfaces is 0.4. The work done against friction is :
(1) 4200
(2) 3900
(3) 4000
(4) 4500
Answer: (3)
Question 35. Match List I with List II.
| List I | List II |
|---|---|
| A. \oint \vec{B}\cdot\vec{dl}=\mu_{0}i_{c}+\mu_{0}\varepsilon_{0}\frac{d\phi_{E}}{dt} | I. Gauss’ law for electricity |
| B. \oint \vec{E}\cdot\vec{dl}=\frac{d\phi_{B}}{dt} | II. Gauss’ law for magnetism |
| C. \oint \vec{E}\cdot\vec{dA}=\frac{Q}{\varepsilon_{0}} | III. Faraday law |
| D. \oint \vec{B}\cdot\vec{dA}=0 | IV. Ampere–Maxwell law |
Choose the correct option.
(1) A–IV, B–I, C–III, D–II
(2) A–II, B–III, C–I, D–IV
(3) A–IV, B–III, C–I, D–II
(4) A–I, B–II, C–III, D–IV
Answer: (3)
Question 36. If the radii of curvature of the paths of two particles of the same mass are in the ratio
3:4, then in order to have constant centripetal force, the ratio of their velocities is :
(1) \sqrt{3}:2
(2) 1:\sqrt{3}
(3) \sqrt{3}:1
(4) 2:\sqrt{3}
Answer: (1)
Question 37. A galvanometer having a coil resistance of 10 Ω shows full scale deflection for a current of 3 mA. To measure a current of 8 A, the value of the shunt required is :
(1) 3\times10^{-3}\Omega
(2) 4.85\times10^{-3}\Omega
(3) 3.75\times10^{-3}\Omega
(4) 2.75\times10^{-3}\Omega
Answer: (3)
Question 38. The de-Broglie wavelength of an electron is the same as that of a photon. The velocity of the electron is 25% of the velocity of light. The ratio of kinetic energy of the electron to the energy of the photon is :
(1) 1:1
(2) 1:8
(3) 8:1
(4) 1:4
Answer: (2)
Question 39. The deflection in a moving coil galvanometer falls from 25 divisions to 5 divisions when a shunt of 24 Ω is applied. The resistance of the galvanometer coil is :
(1) 12\Omega
(2) 96\Omega
(3) 48\Omega
(4) 100\Omega
Answer: (2)
Question 40. A biconvex lens of refractive index 1.5 has a focal length of 20 cm in air. Its focal length when immersed in a liquid of refractive index 1.6 is :
(1) -16 cm
(2) -160 cm
(3) +160 cm
(4) +16 cm
Answer: (2)
Question 41. A thermodynamic system is taken from an original state A to an intermediate state B by a linear process as shown in the figure. Its volume is then reduced to the original value from B to C by an isobaric process. The total work done by the gas from A to B and B to C is :
(1) 33800 J
(2) 2200 J
(3) 800 J
(4) 1200 J
Answer: 800 J
Question 42. At what distance above and below the surface of the Earth will a body have the same weight?
Take the radius of the Earth as R.
(1) \sqrt{5}R-R
(2) \frac{\sqrt{3}R-R}{2}
(3) \frac{R}{2}
(4) \frac{\sqrt{5}R-R}{2}
Answer: (4)
Question 43. A capacitor of capacitance 100 μF is charged to a potential of 12 V and connected to a 6.4 mH inductor to produce oscillations. The maximum current in the circuit is :
(1) 3.2 A
(2) 1.5 A
(3) 2.0 A
(4) 1.2 A
Answer: (2)
Question 44. The explosive in a hydrogen bomb is a mixture of {}_1H^2,\;{}_1H^3 and {}_3Li^6 in some condensed form. The chain reaction is given by
{}_3{Li}^6+{}_0n^1\rightarrow{}_2{He}^4+{}_1H^3 {}_1H^2+{}_1H^3\rightarrow{}_2{He}^4+{}_0n^1During the explosion, the energy released is approximately Given:
M(Li)=6.01690 amu M({}_1H^2)=2.01471
amu M({}_2{He}^4)=4.00388
amu 1 amu =931.5 MeV
(1) 28.12 MeV
(2) 12.64 MeV
(3) 16.48 MeV
(4) 22.22 MeV
Answer: (4)
Question 45. Two vessels A and B are of the same size. Both vessels are at the same temperature.
Vessel A contains 1 g of hydrogen. Vessel B contains 1 g of oxygen.
P_{A} and P_{B} are the pressures of gases in A and B respectively.
Then \frac{P_{A}}{P_{B}} is:
(1) 16
(2) 8
(3) 4
(4) 32
Answer: (1)
Question 46. When a hydrogen atom goes from n=2 to n=1, it emits a photon.
Due to emission, the atom recoils. The recoil speed is \frac{X}{5} m/s.
Find the value of X. Mass of hydrogen atom is 1.6\times10^{-27} kg.
(Use standard constants.)
Answer: 17
Question 47. The magnetic potential due to a magnetic dipole at a point on its axis is measured. The point is at a distance of 20 cm from the centre of the dipole. The magnetic potential is 1.5\times10^{-5} Tm. Find the magnetic moment of the dipole. The magnetic moment is ____ Am^{2}.
Given, \frac{\mu_{0}}{4\pi}=10^{-7} TmA⁻¹
Answer: 6
Question 48. When the displacement of a simple harmonic oscillator is one third of its amplitude,
find the ratio of total energy to kinetic energy. The ratio is \frac{X}{8}. Find the value of X.
Answer: 9
Question 49. An electron moves under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density +\sigma. The electron at t = 0 is at a distance of 1 m from S and has a speed of 1 m/s. The maximum value of \sigma if the electron strikes S at t = 1 s is \alpha\left[\frac{m\in_0}e\right]\frac C{m^2} the vlaue of \alpha is
Answer: 8
Question 50. In a wind tunnel test on a model aeroplane, the speed of air over the upper surface of the wing is 70 m/s. The speed of air over the lower surface of the wing is 65 m/s. The area of the wing is 2 m². Find the lift produced by the wing. Density of air is 1.2 kg m⁻³. The lift of the wing is ____ N.
Answer: 810
Question 51. Given below are two statements.
One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The first ionisation enthalpy decreases across a period.
Reason R: The increasing nuclear charge outweighs the shielding across the period.
In the light of the above statements, choose the most appropriate option.
(1) Both A and R are true and R is the correct explanation of A
(2) A is true but R is false
(3) A is false but R is true
(4) Both A and R are true but R is NOT the correct explanation of A
Answer: (3)
Question 52. Match List I with List II.
| LIST I (Substances) | LIST II (Element Present) |
|---|---|
| A. Ziegler catalyst | I. Rhodium |
| B. Blood pigment | II. Cobalt |
| C. Wilkinson catalyst | III. Iron |
| D. Vitamin \mathrm{B}_{12} | IV. Titanium |
Choose the correct answer from the options given below.
(1) A-II, B-IV, C-I, D-III
(2) A-II, B-III, C-IV, D-I
(3) A-III, B-II, C-IV, D-I
(4) A-IV, B-III, C-I, D-II
Answer: (4)
Question 53. In chromyl chloride test for confirmation of \mathrm{Cl}^{-} ion, a yellow solution is obtained. On acidification and addition of amyl alcohol and 10\%{\mathrm H}_2{\mathrm O}_2 , the organic layer turns blue. This indicates the formation of chromium pentoxide. The oxidation state of chromium in chromium pentoxide is:
(1) +6
(2) +5
(3) +10
(4) +3
Answer: (1)
Question 54. The difference in energy between the actual structure and the lowest energy resonance structure for the given compound is:
(1) Electromeric energy
(2) Resonance energy
(3) Ionization energy
(4) Hyperconjugation energy
Answer: (2)
Question 55. Given below are two statements.
Statement I: The electronegativity of group 14 elements from Si to Pb gradually decreases.
Statement II: Group 14 contains non-metallic, metallic, as well as metalloid elements.
In the light of the above statements, choose the most appropriate option.
(1) Statement I is false but Statement II is true
(2) Statement I is true but Statement II is false
(3) Both Statement I and Statement II are true
(4) Both Statement I and Statement II are false
Answer: (1)
Question 56. The correct set of four quantum numbers for the valence electron of rubidium atom (Z = 37) is:
(1) 5,0,0,+\frac{1}{2}
(2) 5,0,1,+\frac{1}{2}
(3) 5,1,0,+\frac{1}{2}
(4) 5,1,1,+\frac{1}{2}
Answer: (1)
Question 57. The major product in the following reaction is:
Answer: (4)
Question 58. The arenium ion which is not involved in the bromination of aniline is:
Answer: (3)
Question 59. Appearance of blood red colour on treatment of the sodium fusion extract of an organic compound with {\mathrm{FeSO}}_4 in the presence of concentrated {\mathrm H}_2{\mathrm{SO}}_4 indicates the presence of element or elements:
(1) Br
(2) N
(3) N and S
(4) S
Answer: (3)
Question 60. Given below are two statements.
One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Aryl halides cannot be prepared by replacement of hydroxyl group of phenol by halogen atom.
Reason R: Phenols react with halogen acids violently.
In the light of the above statements, choose the most appropriate option.
(1) Both A and R are true but R is NOT the correct explanation of A
(2) A is false but R is true
(3) A is true but R is false
(4) Both A and R are true and R is the correct explanation of A
Answer: (3)
Question 61. Identify product A and product B:
Answer: (4)
Question 62. Identify the incorrect pair from the following:
(1) Fluorspar – {\mathrm{BF}}_3
(2) Cryolite – {\mathrm{Na}}_3{\mathrm{AlF}}_6
(3) Fluoroapatite – 3{\mathrm{Ca}}_3{({\mathrm{PO}}_4)}_2\cdot{\mathrm{CaF}}_2
(4) Carnallite – \mathrm{KCl}\cdot{\mathrm{MgCl}}_2\cdot6{\mathrm H}_2\mathrm O
Answer: (1)
Question 63. The interaction between \pi bond and lone pair of electrons present on an adjacent atom is responsible for:
(1) Hyperconjugation
(2) Inductive effect
(3) Electromeric effect
(4) Resonance effect
Answer: (4)
Question 64. KMnO4 decomposes on heating at 513 K to form O2 along with:
(1) MnO_2\;\&\;K_2O_2
(2) K_2MnO_4\;\&\;Mn
(3) Mn\;\&\;KO_2
(4) K_2MnO_4\;\&\;MnO_2
Answer: (4)
Question 65. In which one of the following metal carbonyls, CO forms a bridge between metal atoms?
(1) \lbrack CO_2{(CO)}_8\;\rbrack
(2) \lbrack Mn_2{(CO)}_{10}\rbrack
(3) \lbrack OS_3(CO)_{12}\rbrack
(4) \lbrack Ru_3{(CO)}_{12}\rbrack
Answer: (1)
Question 66. Type of amino acids obtained by hydrolysis of proteins is:
(1) \beta
(2) \alpha
(3) \delta
(4) \gamma
Answer: (2)
Question 67. The final product A formed in the following multistep reaction sequence is:
Answer: (1)
Question 68. Which of the following is not correct?
(1) \Delta \mathrm{G} is negative for a spontaneous reaction
(2) \Delta \mathrm{G} is positive for a spontaneous reaction
(3) \Delta \mathrm{G} is zero for a reversible reaction
(4) \Delta \mathrm{G} is positive for a non-spontaneous reaction
Answer: (2)
Question 69. Chlorine undergoes disproportionation in alkaline medium as shown below:
\mathrm a\,{\mathrm{Cl}}_2+\mathrm b\,\mathrm{OH}^-\rightarrow\mathrm c\,\mathrm{ClO}^-+\mathrm d\,\mathrm{Cl}^-+\mathrm e\,{\mathrm H}_2\mathrm OThe values of \mathrm{a},\mathrm{b},\mathrm{c} and \mathrm{d} in the balanced redox reaction are:
(1) 1, 2, 1 and 1
(2) 2, 2, 1 and 3
(3) 3, 4, 4 and 2
(4) 2, 4, 1 and 3
Answer: (1)
Question 70. In alkaline medium, \mathrm{MnO}_{4}^{-} oxidises \mathrm{I}^{-} to
(1) {\mathrm{IO}}_4^-
(2) \mathrm{IO}^{-}
(3) {\mathrm I}_2
(4) \mathrm{IO}_{3}^{-}
Answer: (4)
Question 71. The mass of zinc produced by the electrolysis of zinc sulphate solution with a steady current of 0.015 A for 15 minutes is ____\times10^{-4} g.
(Atomic mass of zinc = 65.4 amu)
Answer: (45.75) or (46)
Question 72. For a reaction taking place in three steps at the same temperature, the overall rate constant is \mathrm{K}=\frac{\mathrm{K}{1}\mathrm{K}{2}}{\mathrm{K}_{3}}. If \mathrm E{\mathrm a}_1, \mathrm E{\mathrm a}_2 and \mathrm E{\mathrm a}_3 are 40, 50 and 60 kJ/mol respectively, the overall activation energy is ____ kJ/mol.
Answer: (30)
Question 73. For the reaction {\mathrm N}_2{\mathrm O}_4(\mathrm g)\rightleftharpoons2{\mathrm{NO}}_2(\mathrm g), \mathrm{K}{\mathrm{p}}=0.492 atm at 300 K. The value of \mathrm{K}_{\mathrm{c}} for the reaction at the same temperature is ____ \times10^{-2}.
(Given: \mathrm{R}=0.082 L atm mol⁻¹ K⁻¹)
Answer: (2)
Question 74. A solution of H2SO4 is 31.4% H2SO4 by mass. The density of the solution is 1.25 g/mL. The molarity of the H2SO4 solution is ____ M (nearest integer).
Given molar mass of H2SO4 = 98 g mol⁻¹.
Answer: (4)
Question 75. The osmotic pressure of a dilute solution is 7\times10^{5} Pa at 273 K. The osmotic pressure of the same solution at 283 K is____ \times10^{4} N m⁻².
Answer: (72.56) or (73)
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