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JEE-MAIN EXAMINATION – JANUARY 2025

MATHEMATICS TEST PAPER WITH SOLUTION

Held on Wednesday 22nd January 2025, Time: 9:00 AM to 12:00 NOON

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JEE Main
Mathematics
Morning Session
3 hours

Paper Overview

75
Total Questions
67
Correct
2
Incorrect
6
N/A
iExplain doesn't support the question format

Complete Solutions

Q#ExplanationQuestionCorrectSolutionStatus
1Explain
The number of non-empty equival ence relations on the set {1,2,3} is
(A) 6
(B) 7
(C) 5
(D) 4
3
3
Verified
2Explain
Let f : ℝ → ℝ be a twice-differentiable function such that   f(x + y) = f(x) f(y) for all x, y ∈ ℝ. If f′
(A) e² − 1
(B) e⁴ + 1
(C) e⁴ − 1
(D) e² + 1
1
1
Verified
3Explain
Let the triangle PQR be the image of the triangle with vertices (1,3), (3,1) and (2, 4) in the line x + 2y = 2. If the centroid of triangle PQR is the point (alpha, beta), then 15(alpha – beta) is equal to
(A) 24
(B) 19
(C) 21
(D) 22
4
4
Verified
4Explain
Let (z_{1}, z_{2}, z_{3}) be three complex numbers on the circle (|z| = 1) with (\arg(z_{1}) = -\pi/4), (\arg(z_{2}) = 0) and (\arg(z_{3}) = \pi/4). If (\left|, z_{1}\overline{z_{2}} + z_{2}\overline{z_{3}} + z_{3}\overline{z_{1}} ,\right|^{2} = \alpha + \beta\sqrt{2}), (\alpha, \beta \in \mathbb{Z}), then the value of (\alpha^{2} + \beta^{2}) is
(A) 24
(B) 41
(C) 31
(D) 29
4
4
Verified
5Explain
Using the principal values of the inverse trigonometric functions the sum of the maximum and the minimum values of 16((sec^{-1} x) ^2 + (cosec^{-1} x)^ 2 ) is
(A) 24 2
(B) 18 2
(C) 31 2
(D) 22 2
4
4
Verified
6Explain
A coin is tossed three times. Let X denote the number of times a tail follows a head. If mu and sigma^2 denotes the mean and variance of X, then the value of 64( mu + sigma^2) is
(A) 51
(B) 48
(C) 32
(D) 64
2
2
Verified
7Explain
Let a_{1} , a_{2} , a_{3} ..... be a G.P. of increasing positive terms. If a_{1} a_{5} = 28 and a_{2} + a_{4} = 29, then a_{6} is equal to
(A) 628
(B) 526
(C) 784
(D) 812
3
3
Verified
8Explain
Let L₁ : (x − 1)/2 = (y − 2)/3 = (z − 3)/4 and L₂ : (x − 2)/3 = (y − 4)/4 = (z − 5)/5 be two lines. Which of the following points lies on the line of the shortest distance between L₁ and L₂?
4
4
Verified
9Explain
The product of all solutions of the equation ( e^{(5*(\log_e x)^2) + 3} = x^8 ), ( x > 0 ), is
1
1
Verified
10Explain
If ∑₍ᵣ₌₁₎ⁿ Tᵣ = ((2n − 1)(2n + 1)(2n + 3)(2n + 5)) / 64, then lim₍ₙ→∞₎ ∑₍ᵣ₌₁₎ⁿ (1 / Tᵣ) is equal to
(A) 1
(B) 0
(C) 2/3
(D) 1/3
3
3
Verified
11Explain
From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is 'M', is :"
(A) 14950
(B) 6084
(C) 4356
(D) 5148
4
4
Verified
12Explain
Let ( x = x(y) ) be the solution of the differential equation ( y^2 , dx + \left( x - \frac{1}{y} \right) dy = 0 ). If ( x
3
3
Verified
13Explain
**13.** Let the parabola \( y = x^2 + px - 3 \) meet the coordinate axes at the points \( P \), \( Q \), and \( R \). If the circle \( C \) with centre at \( (-1, -1) \) passes through the points \( P \), \( Q \), and \( R \), then the area of \( \triangle PQR \) is: -
(A) 4 -
(B) 6 -
(C) 7 -
(D) 5
2
2
Verified
14Explain
**14.** A circle \( C \) of radius 2 lies in the second quadrant and touches both the coordinate axes. Let \( r \) be the radius of a circle that has centre at the point \( (2, 5) \) and intersects the circle \( C \) at exactly two points. If the set of all possible values of \( r \) is the interval \( (\alpha, \beta) \), then \( 3\beta - 2\alpha \) is equal to: -
(A) 15 -
(B) 14 -
(C) 12 -
(D) 10
1
1
Verified
15Explain
**15.** Let \( f(x) = 7\tan^8 x + 7\tan^6 x - 3\tan^4 x - 3\tan^2 x \), \( I_1 = \int_{0}^{\frac{\pi}{4}} f(x) \, dx \) and \( I_2 = \int_{0}^{\frac{\pi}{4}} x f(x) \, dx \). Then \( 7I_1 + 12I_2 \) is equal to: -
(A) 1 -
(B) 2
3
3
Verified
16Explain
**16.** Let \( f(x) \) be a real differentiable function such that \( f
(A) 2384 -
(B) 2525 -
(C) 5220 -
(D) 2406
2
2
Verified
17Explain
**17.** Let \( A = \{1, 2, 3, \ldots, 10\} \) and \( B = \left\{ \frac{m}{n} : m, n \in A,\ m < n \text{ and } \gcd(m, n) = 1 \right\} \). Then \( n(B) \) is equal to: -
(A) 31 -
(B) 36 -
(C) 37 -
(D) 29
1
1
Verified
18Explain
**18.** The area of the region, inside the circle \( (x - 2\sqrt{3})^2 + y^2 = 12 \) and outside the parabola \( y^2 = 2\sqrt{3}x \) is: -
3
3
Verified
19Explain
**19.** Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is \( \frac{m}{n} \), where \( \gcd(m, n) = 1 \), then \( m + n \) is equal to: -
(A) 14 -
(B) 4 -
(C) 11 -
(D) 13
1
1
Verified
20Explain
**20.** Let the foci of a hyperbola be \( (1, 14) \) and \( (1, -12) \). If it passes through the point \( (1, 6) \), then the length of its latus-rectum is: -
3
3
Verified
21Explain
21. Let the function [ f(x) = \begin{cases} -3a x^2 - 2, & x < 1 \ a^2 + bx, & x \geq 1 \end{cases} ] be differentiable for all ( x \in \mathbb{R} ), where ( a > 1 ), ( b \in \mathbb{R} ). If the area of the region enclosed by ( y = f(x) ) and the line ( y = -20 ) is ( \alpha + \beta \sqrt{3} ), where ( \alpha, \beta \in \mathbb{Z} ), then the value of ( \alpha + \beta ) is ____.
34
34
Verified
22Explain
22. If [ \sum_{r=0}^{5} \frac{{^{11}C_{2r+1}}}{2r + 2} = \frac{m}{n}, \quad \gcd(m, n) = 1, ] then ( m - n ) is equal to _____.
2035
2035
Verified
23Explain
23. Let ( A ) be a square matrix of order 3 such that ( \det(A) = -2 ) and [ \det\left( 3 , \text{adj}(-6 , \text{adj}(3A)) \right) = 2^{m+n} \cdot 3^{mn}, \quad m > n. ] Then ( 4m + 2n ) is equal to _____.
34
34
Verified
24Explain
24. Let [ L_1 : \frac{x - 1}{3} = \frac{y - 1}{-1} = \frac{z + 1}{0} \quad \text{and} \quad L_2 : \frac{x - 2}{2} = \frac{y}{0} = \frac{z + 4}{\alpha}, \ \alpha \in \mathbb{R} ] be two lines which intersect at the point ( B ). If ( P ) is the foot of the perpendicular from the point ( A(1, 1, -1) ) on ( L_2 ), then the value of ( 26\alpha (PB)^2 ) is _____.
216
216
Verified
25Explain
**25.** Let \( \vec{c} \) be the projection vector of \( \vec{b} = \lambda \hat{i} + 4 \hat{k} \), \( \lambda > 0 \), on the vector \( \vec{a} = \hat{i} + 2 \hat{j} + 2 \hat{k} \). If \( |\vec{a} + \vec{c}| = 7 \), then the area of the parallelogram formed by the vectors \( \vec{b} \) and \( \vec{c} \) is _____.
16
16
Verified
26Explain
Given below are two statements : Statement I : In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale division. In the light of the above statements, choose the correct answer from the options given below.
(A) Both Statement I and Statement II are false.
(B) Statement I is true but Statement II is false.
(C) Both Statement I and Statement II are true.
(D) Statement I is false but Statement II is true.
2
Verified
27Explain
**27.** A line charge of length \( \frac{a}{2} \) is kept at the center of an edge \( BC \) of a cube \( ABCDEFGH \) having edge length \( a \), as shown in the figure. If the density of line charge is \( \lambda C \) per unit length, then the total electric flux through all the faces of the cube will be _____. (Take \( \varepsilon_0 \) as the free space permittivity) -
1
1
Verified
28Explain
Sliding contact of a potentiometer is in the middle of the potentiomet er wire having resistance R P = 1 as shown in the figure. An ext er nal resistance of R e = 2 is connected via the sliding contact.
(A) 0.3 A
(B) 1.35 A
(C) 1.0 A
(D) 0.9 A
3
DIAGRAM QUESTION N/A
Available
29Explain
29. Given below are two statements. Assertion: If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer. Reason: The speed of light reduces in an optically denser medium than air while its frequency does not change. In the light of the above statements, choose the most appropriate answer from the options below. Option 1: Both Assertion and Reason are true and Reason is the correct explanation of Assertion. Option 2: Assertion is false but Reason is true. Option 3: Both Assertion and Reason are true but Reason is not the correct explanation of Assertion. Option 4: Assertion is true but Reason is false.
1
1
Verified
30Explain
**30.** Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in the same atmosphere. The temperature of the smaller body is 800 K and the temperature of the bigger body is 400 K. If the energy radiated from the smaller body is \( E \), the energy radiated from the bigger body is (assume the effect of the surrounding to be negligible): -
2
2
Verified
31Explain
31. An amount of ice of mass 10^-3 kg and temperature -10°C is transformed to vapour of temperature 110°C by applying heat. The total amount of work required for this conversion is: Take: Specific heat of ice = 2100 J/kg·K, Specific heat of water = 4180 J/kg·K, Specific heat of steam = 1920 J/kg·K, Latent heat of ice = 3.35×10^5 J/kg, Latent heat of steam = 2.25×10^6 J/kg. Option 1: 3022 J Option 2: 3043 J Option 3: 3003 J Option 4: 3024 J
2
2
Verified
32Explain
An electron in the ground state of the hydrogen atom has the orbital radius of 5.3 × 10^-11 m while that for the electron in third excited state is 8.48 × 10^-10 m. The ratio of the de Broglie wavelengths of electron in the ground state to that in excited state is
(A) 4
(B) 9
(C) 3
(D) 16
1
1
Verified
33Explain
In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to [R 1 ] and [R 2 ], i.e., the radii of curvat ure for upper and lower surfaces of the glass lens, the power of the com bination is
2
DIAGRAM QUESTION N/A
Available
34Explain
An electron is made to enters symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the field region with a horizontal component of velocity 10^6 m/s. If the magnitude of the electric between the plates is 9.1 V/cm, then the vertical component of velocity of electron is
(A) 1 × 10^6 m/s
(B) 0
(C) 16 × 10^6 m/s
(D) 16 × 10^4 m/s
3
3
Verified
35Explain
Which of the following resistivity ( ) v/s temperat ure (T) cur ves is most suitable to be used in wire bound standard resistors?
1
DIAGRAM QUESTION N/A
Available
36Explain
"A closed organ and an open organ tube filled by two different gases having same bulk modulus but different densities ρ1 and ρ2 respectively. The frequency of 9th harmonic of closed tube is identical with 4th harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is ρ1 : ρ2 = 1 : 16, then the length of the open tube is :"
(A) 20 / 7
(B) 15 / 7
(C) 20 / 9
(D) 15 / 9
3
3
Verified
37Explain
A uniform circular disc of radius ‘R’ and mass ‘M’ is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius R/2 is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above
4
4
Verified
38Explain
A small point of mass m is placed at a distance 2R from the centre ‘O’ of a big uniform solid sphere of mass M and radius R. The gravitational force on ‘m’ due to M is F1. A spherical part of radius R/3 is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of M is found to be F2. The value of ratio F1 : F2 is
(A) 16 : 9
(B) 11 : 10
(C) 12 : 11
(D) 12 : 9
3
3
Verified
39Explain
The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV, respectively. If we incident a light of wavelength 550 nm on these two metal surface, then photo-electric effect is possible for the case of
(A) Li only
(B) Cs only
(C) Neither Cs nor Li
(D) Both Cs and Li
2
2
Verified
40Explain
If B is magnetic field and μ0\mu_0 is permeability of free space, then the dimensions of (B/μ0\mu_0) is"
(A) MT –2 A –1
(B) L –1 A
(C) LT –2 A –1
(D) ML 2 T –2 A –1
2
2
Verified
41Explain
A bob of mass m is suspended at a point O by a light string of length l and left to perform vertical motion (circul ar) as shown in figure. Initially, by appl ying horizontal vel ocity 0 string becomes slack when, the bob reaches at the at the points B and C is ______.
(A) 2
(B) 1
(C) 4
(D) 3
1
DIAGRAM QUESTION N/A
Available
42Explain
Given below are two statements : Statement-I : The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs. Statement-II : The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries. In the light of the above statements, choose the correct answer from the options given below."
(A) Statement-I is true but Statement-II is false
(B) Both Statement-I and Statement-II are false
(C) Both Statement-I and Statement-II are true
(D) Statement-I is false but Statement-II is true
4
4
Verified
43Explain
Which of the following ci rcuits represents a forward biased diode ? (A) (B) (C) (D) (E) Choose the correct answer from the options given bel ow
3
DIAGRAM QUESTION N/A
Available
44Explain
A parallel-plate capacitor of capacitance 40µF is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant K = 2. Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are
(A) 2 mC and 0.2 J
(B) 8 mC and 2.0 J
(C) 4 mC and 0.2 J
(D) 2 mC and 0.4 J
3
3
Verified
45Explain
Given is a thin convex lens of glass (refractive index mu) and each side having radius of curvature R. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself.
(A) R/mu
(B) muR
4
4
Verified
46Explain
Two soap bubbles of radius 2 cm and 4 cm, respectively, are in contact with each other. The radius of curvature of the common surface, in cm, is ______ .
4
4
Verified
47Explain
The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature R = 2 m. Another car approaches him from behind with a uniform speed of 90 km/hr. When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the side view mirror is ‘a’. The value of 100a is ______ m/s 2
8
8.67
Alternative
48Explain
Three conductions of same length having thermal conductivity k1, k2 and k3 are connected as shown in figure. 1. k1 2. k2 3. k3 100°C °C 0°C Area of cross sections of 1st and 2nd conductor are same and for 3rd conductor it is double of the 1st conductor. The temperatures are given in the figure. In steady state condition, the value of  is __________ °C. [Given : k1 = 60 Js-1 m-1 K-1 , k2 = 120 Js-1 m-1 K-1 , k3 = 135 Js-1 m-1 K-1 ]
40
Diagram Question
Available
49Explain
49. The position vectors of two 1 kg particles, A and B, are given by: rA = (alpha1 t^2 i + alpha2 t j + alpha3 t k) m and rB = (beta1 t i + beta2 t^2 j + beta3 t k) m, respectively. Where: alpha1 = 1 m/s^2, alpha2 = 3n m/s, alpha3 = 2 m/s; beta1 = 2 m/s, beta2 = -1 m/s^2, beta3 = 4p m/s. t is time, and n, p are constants. At t = 1 s, |VA| = |VB|, and the velocities VA and VB are orthogonal to each other. At t = 1 s, the magnitude of angular momentum of particle A with respect to the position of particle B is sqrt(L) kg·m^2/s. The value of L is _____.
90
90
Verified
50Explain
A particle is projected at an angle of 30° from horizontal at a speed of 60 m/s. The height traversed by the particle in the first second is h0 and height traversed in the last second, before it reaches the maximum height, is h1. The ratio h0 : h1 is ______ .
5
5
Verified
51Explain
A solution of aluminium chloride is electrolysed for 30 minutes using a current of 2A. The amount of the aluminium deposited at the cathode is ___ . [Given : molar mass of aluminium and chlorine are 27 g mol –1 and 35.5 g mol –1 respectively, Faraday constant = 96500 C mol –1 ]
(A) 1.660 g
(B) 1.007 g
(C) 0.336 g
(D) 0.441 g
3
3
Verified
52Explain
Select one of the following statement which is not true for radioactive decay
(A) Amount of radioactive substance remained after three half lives is 1/8 th of original amount.
(B) Decay constant does not depend upon temperature.
(C) Decay constant increases with increase in temperature.
3
4
Verified
53Explain
**53.** How many different stereoisomers are possible for the given molecule? CH₃–CH–CH=CH–CH₃ | OH Options: -
(A) 3 -
(B) 1 -
(C) 2 -
(D) 4
4
4
Verified
54Explain
Which of the following electronegativity order is incorrect?
(A) Al < Mg < B < N
(B) Al < Si < C < N
(C) Mg < Be < B < N
(D) S < Cl < O < F
1
1
Verified
55Explain
Lanthanoid ions with 4f 7 configuration are : (A) Eu 2+ (B) Gd 3+ (C) Eu 3+ (D) Tb 3+ (E) Sm 2+ Choose the correct answer from the options given below
1
1
Verified
56Explain
56. Match List-I with List-II. List-I: (A) Al3+ < Mg2+ < Na+ < F- (B) B < C < O < N (C) B < Al < Mg < K (D) Si < P < S < Cl. List-II: (I) Ionisation Enthalpy (II) Metallic Character (III) Electronegativity (IV) Ionic Radii. Choose the correct answer from the options given below: Option 1: A-IV, B-I, C-III, D-II Option 2: A-II, B-III, C-IV, D-I Option 3: A-IV, B-I, C-II, D-III Option 4: A-III, B-IV, C-II, D-I
3
3
Verified
57Explain
Which of the following acids is a vitamin ?
(A) Adipic acid
(B) Aspartic acid
(C) Ascorbic acid
(D) Saccharic acid
3
3
Verified
58Explain
A liquid when kept inside a thermally insulated closed vessel at 25°C was mechanically stirred from outside. What will be the correct option for the following thermodynamic parameters ?
(A) triangle of U > 0, q = 0, w > 0
(B) triangle of U = 0, q = 0, w = 0
(C) triangle of U < 0, q = 0, w > 0
(D) triangle of U = 0, q < 0, w > 0
1
1
Verified
59Explain
**59.** Radius of the first excited state of Helium ion is given as: \( a_0 \rightarrow \) radius of first stationary state of hydrogen atom. Options: -
4
4
Verified
60Explain
60. Given below are two statements. Statement I: CH3-O-CH2-Cl will undergo SN1 reaction though it is a primary halide. Statement II: (CH3)2CH-CH2-Cl will not undergo SN2 reaction very easily though it is a primary halide. In the light of the above statements, choose the most appropriate answer from the options given below. Option 1: Statement I is incorrect but Statement II is correct. Option 2: Both Statement I and Statement II are incorrect. Option 3: Statement I is correct but Statement II is incorrect. Option 4: Both Statement I and Statement II are correct.
4
4
Verified
61Explain
Given below are two statements : Statement I : One mole of propyne reacts with excess of sodium to liberate half a mole of H2 gas. Statement II : Four g of propyne reacts with NaNH2 to liberate NH3 gas which occupies 224 mL at STP. In the light of the above statements, choose the most appropriate answer from the options given below
(A) Statement I is correct but Statement II is incorrect.
(B) Both Statement I and Statement II are incorrect
(C) Statement I is incorrect but Statement II is correct
(D) Both Statement I and Statement II are correct.
1
1
Verified
62Explain
A vessel at 1000 K contains CO2 with a pressure of 0.5 atm. Some of CO2 is converted into CO on addition of graphite. If total pressure at equilibrium is 0.8 atm, then KP is
(A) 0.18 atm
(B) 1.8 atm
(C) 0.3 atm
(D) 3 atm.
2
2
Verified
63Explain
**63.** The IUPAC name of the following compound is: \ce{CH3-CH(COOH)-CH2-CH(CH3)-COOCH3}
(A) 2-Carboxy-5-methoxycarbonylhexane
(B) Methyl-6-carboxy-2,5-dimethylhexanoate
(C) Methyl-5-carboxy-2-methylhexanoate
(D) 6-Methoxycarbonyl-2,5-dimethylhexanoic acid
4
4
Verified
64Explain
Which of the following electrolyte can be used to obtain H2S2O8 by the process of electrolysis?
(A) Dilute solution of sodium sulphate
(B) Dilute solution of sulphuric acid
(C) Concentrated solution of sulphuric acid
(D) Acidified dilute solution of sodium sulphate
3
3
Verified
65Explain
**65.** The compounds which give **positive Fehling’s test** are: **(A)** \( \ce{C6H5CHO} \) **(B)** \( \ce{C6H5COCH3} \) **(C)** \( \ce{HOCH2CO(CHOH)3CH2OH} \) **(D)** \( \ce{CH3CHO} \) **(E)** \( \ce{C6H4CH2CHO} \) Choose the **CORRECT** answer from the options given below: -
3
3
Verified
66Explain
**66.** In which of the following complexes the CFSE, \( \Delta_0 \), will be equal to zero? -
4
4
Verified
67Explain
Arrange the following solutions in order of their increasing boiling points. (i) 10^–4 M NaCl (ii) 10^–4 M Urea (iii) 10^–3 M NaCl (iv) 10^-2 M NaCl
1
1
Verified
68Explain
68. The products formed in the following reaction sequence are: Starting compound: C6H4NO2CH3 (p-nitrotoluene). Reagents: 1. Br2, AcOH 2. Sn, HCl 3. NaNO2, HCl, 273K 4. C2H5OH. C6H4NO2CH3 --(i-iv)--> A + B. Option 1: A = C6H3Br(OH)CH3, B = C6H3Br(OEt)CH3. Option 2: A = C6H3Br(OEt)CH3, B = CH3COOH. Option 3: A = C6H4BrCH3, B = CH3CHO. Option 4: A = C6H3Br(OH)CH3, B = CH3CHO.
3
3
Verified
69Explain
69. From the magnetic behaviour of [NiCl4]2− (paramagnetic) and [Ni(CO)4] (diamagnetic), choose the correct geometry and oxidation state. Option 1: [NiCl4]2− : Ni2+, square planar; [Ni(CO)4] : Ni
(A) , square planar.
2
2
Verified
70Explain
The incorrect statements regarding geometrical isomerism are : (A) Propene shows geometrical isomerism. (B) Trans isomer has identical atoms/groups on the opposite sides of the double bond. (C) Cis-but-2-ene has higher dipole moment than trans-but-2-ene. (D) 2-methylbut-2-ene shows two geometrical isomers. (E) Trans-isomer has lower melting point that cis isomer. Choose the CORRECT answer from the options given below
1
1
Verified
71Explain
Some CO2 gas was kept in a sealed container at a pressure of 1 atm and at 273 K. This entire amount of CO2 gas was later passed through an aqueous solution of Ca(OH)2. The excess unreacted Ca(OH)2 was later neutralized with 0.1 M of 40 mL HCl. If the volume of the sealed container of CO2 was x, then x is ______ cm 3 (nearest integer). [Given : The entire amount of CO2(g) reacted with exactly half the initial amount of Ca(OH)2 present in the aqueous solution.]
45
45
Verified
72Explain
In Carius method for estimation of halogens, 180 mg of an organic compound produced 143.5 mg of AgCl. The percentage composition of chlorine in the compound is ______ %. [Given : molar mass in g mol –1 of Ag : 108, Cl = 35.5]
20
19.7
Verified
73Explain
The number of molecules/ions that show linear geometry among the following is ______. SO2, BeCl2, CO2, N3 – , NO2, F2O, XeF2, NO2 + , I3 – , O3
6
6
Verified
74Explain
Consider the following sequence of reactions : A -> B The molecule A changes into its isomeric form B by following a first order kinetics at a temperature of 1000 K. If the energy barrier with respect to reactant energy for such isomeric transformation is 191.48 kJ mol –1 and the frequency factor is 10 20, the time required for 50%, molecules of A to become B is ______ picoseconds (nearest integer). [R = 8.314 J K –1 mol –1 ]
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75Explain
**75.** Consider the following sequence of reactions: Starting compound: Nitrobenzene (\ce{C6H5NO2}) **Reagents:** 1. Sn + HCl 2. NaNO₂, HCl (0°C) 3. Cu₂Cl₂ 4. Na, Ether The final product formed is \( A \). **Question:** Molar mass of the product formed (A) is ______ g mol\(^{-1}\).
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