JEE Main 2023 April 8 Shift 2 Question Paper with Solution PDF- Download Here

Let A = \(\left\{ \theta \in (0, 2\pi) : \frac{1 + 2i \sin \theta}{1 - i \sin \theta} \text{ is purely imaginary} \right\}\). Then the sum of the elements in A is.

• (1) 2π
• (2) 3π
• (3) 4π
• (4) π

25¹⁹⁰ - 19¹⁹⁰ - 8¹⁹⁰ + 2¹⁹⁰ is divisible by

• (1) both 14 and 34
• (2) 14 but not 34
• (3) 34 but not 14
• (4) neither 14 nor 34

The integral \(\int \left(\frac{x}{2}\right)^x + \left(\frac{2}{x}\right)^x \log x \, dx\) is equal to:

• (1) \(\left(\frac{x}{2}\right)^x \log_2 \left(\frac{2}{x}\right) + C\)
• (2) \(\left(\frac{x}{2}\right)^x - \left(\frac{2}{x}\right)^x + C\)
• (3) \(\left(\frac{x}{2}\right)^x \log_2 \left(\frac{x}{2}\right) + C\)
• (4) \(\left(\frac{x}{2}\right)^x + \left(\frac{2}{x}\right)^x + C\)

If the probability that the random variable \( X \) takes values \( x \) is given by \( P(X = x) = k(x + 1) 3^{-x}, x = 0, 1, 2, \dots \), where \( k \) is a constant, then \( P(X \geq 2) \) is equal to:

• (1) \(\frac{5}{18}\)
• (2) \(\frac{10}{18}\)
• (3) \(\frac{20}{27}\)
• (4) \(\frac{7}{27}\)

Let \( A = \{1, 2, 3, 4, 5, 6, 7\} \). Then the relation \( R = \{(x, y) \in A \times A : x + y = 7\} \) is:

• (1) Symmetric but neither reflexive nor transitive
• (2) Transitive but neither symmetric nor reflexive
• (3) An equivalence relation
• (4)  Reflexive but neither symmetric nor transitive

Let the mean and variance of 12 observations be \( \frac{9}{2} \) and 4, respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is \( \frac{m}{n} \), where \( m \) and \( n \) are coprime, then \( m + n \) is equal to:

• (1) 314
• (2) 315
• (3) 316
• (4) 317

The absolute difference of the coefficients of \(x^{10}\) and \(x^7\) in the expansion of \(\left(2x^2 + \frac{1}{2x}\right)^{11}\) is equal to:

• (1) \(10^3 - 10\)
• (2) \(12^3 - 12\)
• (3) \(11^3 - 11\)
• (4) \(13^3 - 13\)

The area of the quadrilateral having vertices as (1,2), (5,6), (7,6), (-1,-6) is?

If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which C and S do not come together, is (6!)k , is equal to

• (1) 5670
• (2) 1890
• (3) 595
• (4) 657

If \( A = \begin{bmatrix} 1 & 5 \\ \lambda & 10 \end{bmatrix} \), \( A^{-1} = \alpha A + \beta I \) and \( \alpha + \beta = -2 \), then \( 4\alpha^2 + \beta^2 + \lambda^2 \) is equal to:

• (1) 10
• (2) 12
• (3) 14
• (4) 19

If α > β > 0 are the roots of the equation ax2 + bx + 1 = 0, and \(\lim\limits_{x \to \frac{1}{\alpha}}\left(\frac{1-cos(x^2+bx+a)}{2(1-ax)^2}\right)^{1/2}=\frac{1}{k}\left(\frac{1}{\beta}-\frac{1}{\alpha}\right),\) then k is equal to

• (1) α
• (2) β
• (3) 2α
• (4) 2β

The value of \( 36 \big(4 \cos^2 9^\circ - 1\big) \big(4 \cos^2 27^\circ - 1\big) \big(4 \cos^2 81^\circ - 1\big) \big(4 \cos^2 243^\circ - 1\big) \) is:

• (1) 18
• (2) 27
• (3) 36
• (4) 54

Let S be the set of all values of θ Ε [-π, π] for which the system of linear equations
x+y+√3z=0
-x+(tanθ)y+ √7z=0
x+y+(tanθ)z = 0 has non-trivial solution.
Then 120/π ∑θ_θ∈s is equal to

• (1) 10
• (2) 20
• (3) 30
• (4) 40

Let O be the origin and OP and OQ be the tangents to the circle \( x^2 + y^2 - 6x + 4y + 8 = 0 \) at the points P and Q on it. If the circumcircle of the triangle OPQ passes through the point \( \left( \alpha, \frac{1}{2} \right) \), then a value of \( \alpha \) is.

• (1) \(\frac{5}{2}\)
• (2) \(-\frac{1}{2}\)
• (3) 1
• (4) \(\frac{3}{2}\)

Let a_n be the n^th term of the series 5 + 8 + 14 + 23 + 35 + 50 +.... and Sn = \(\displaystyle\sum_{k=1}^{n} a_k.\) Then S³⁰ - a⁴⁰ is equal to

• (1) 11260
• (2) 11280
• (3) 11290
• (4) 11310

Let the vectors \(\mathbf{u}_1 = \hat{i} + \hat{j} + a\hat{k}, \mathbf{u}_2 = \hat{i} + b\hat{j} + \hat{k}\), and \(\mathbf{u}_3 = c\hat{i} + \hat{j} + \hat{k}\) be coplanar. If the vectors \(\mathbf{v}_1 = (a + b)\hat{i} + c\hat{j} + c\hat{k}, \mathbf{v}_2 = a\hat{i} + (b + c)\hat{j} + a\hat{k}, \mathbf{v}_3 = b\hat{i} + b\hat{j} + (c + a)\hat{k}\) are also coplanar, then \(6(a + b + c)\) is equal to:

• (1) 0
• (2) 4
• (3) 6
• (4) 12

For \(a, b \in \mathbb{Z}\) and \(|a - b| \leq 10\), let the angle between the plane \(P: ax + y - z = b\) and the line \(L: x - 1 = a - y = z + 1\) be \(\cos^{-1}\left(\frac{1}{3}\right)\). If the distance of the point \((6, -6, 4)\) from the plane \(P\) is \(3\sqrt{6}\), then \(a^4 + b^2\) is equal to:

• (1) 25
• (2) 32
• (3) 48
• (4) 85

The negation of \( (p \land (\sim q)) \lor (\sim p) \) is equivalent to:

• (1) \( p \land (\sim q) \)
• (2) \( p \land q \)
• (3) \( p \land (q \land (\sim p)) \)
• (4) \( p \lor (q \lor (\sim p)) \)

Let P be the plane passing through the line \(\frac{x-1}{1}=\frac{y-2}{-3}=\frac{z+5}{7}\) and the point (2, 4, –3). If the image of the point (-1, 3, 4) in the plane P is (α, β, γ) then α + β + γ is equal to

• (1) 9
• (2) 10
• (3) 11
• (4) 12

Let \( A(0, 1) \), \( B(1, 1) \), and \( C(1, 0) \) be the midpoints of the sides of a triangle with incentre at the point \( D \). If the focus of the parabola \( y^2 = 4ax \) passing through \( D \) is \( (\alpha + \beta \sqrt{3}, 0) \), where \( \alpha \) and \( \beta \) are rational numbers, then \( \frac{\alpha}{\beta^2} \) is equal to:

• (1) 9/2
• (2) 6
• (3) 8
• (4) 12

Let [t] denote the greatest integer function. If \(\int\limits_0^{2.4}[x^2]dx=α+β√2+γ√3+δ√5,\) then α+β+γ +δ is equal to _____.

Let the area enclosed by the lines \( x + y = 2 \), \( y = 0 \), \( x = 0 \), and the curve \( f(x) = \min \left\{ x^2 + \frac{3}{4}, 1 + [x] \right\} \), where \( [x] \) denotes the greatest integer less than or equal to \( x \), be \( A \). Then the value of \( 12A \) is ____________.

Let \( m \) and \( n \) be the numbers of real roots of the quadratic equations \( x^2 - 12x + [x] + 31 = 0 \) and \( x^2 - 5|x+2| - 4 = 0 \), respectively, where \( [x] \) denotes the greatest integer less than or equal to \( x \). Then \( m^2 + mn + n^2 \) is equal to ___________.

Let \( R = \{a, b, c, d, e\} \) and \( S = \{1, 2, 3, 4\} \). Total number of onto functions \( f: R \to S \) such that \( f(a) \neq 1 \), is equal to:

• (1) 240
• (2) 180
• (3) 204
• (4) 216

Let \( k \) and \( m \) be positive real numbers such that the function} \[ f(x) = \begin{cases} 3x^2 + \frac{k}{\sqrt{x} + 1}, & 0 < x < 1, \\ mx^2 + k^2, & x \geq 1 \end{cases} \] is differentiable for all \( x > 0 \). Then \( 8f'(8) \left(\frac{1}{f(8)}\right) \) is equal to __________

Let the solution curve \( x = x(y) \), \( 0 < y \leq \frac{\pi}{2} \), of the differential equation \[ (\log_e (\cos y))^2 \cos y \, dx - (1 + 3x \log_e (\cos y)) \sin y \, dy = 0 \] satisfy \( x \left( \frac{\pi}{3} \right) = \frac{1}{2 \log_e 2} \). If \( x \left( \frac{\pi}{6} \right) = \frac{1}{\log_e m - \log_e n} \), where \( m \) and \( n \) are co-prime integers, then \( mn \) is equal to ______.

f domain of the function \[ f(x) = \log_e \left(\frac{6x^2 + 5x + 1}{2x - 1}\right) + \cos^{-1}\left(\frac{2x^2 - 3x + 4}{3x - 5}\right) \] is \( (\alpha, \beta) \cup (\gamma, \delta) \), then \( 18(\alpha^2 + \beta^2 + \gamma^2 + \delta^2) \) is equal to __________.

Let P₁ be the plane 3x-y-7z = 11 and P₂ be the plane passing through the points (2,-1,0), (2,0,-1), and (5,1,1). If the foot of the perpendicular drawn from the point (7,4,-1) on the line of intersection of the planes P₁ and P₂ is (α, β, γ), then a + ẞ+ y is equal to

A parabola with focus (3, 0) and directrix x = –3. Points P and Q lie on the parabola and their ordinates are in the ratio 3 : 1. The point of intersection of tangents drawn at points P and Q lies on the parabola

• (1) y² = 16x
• (2) y² = 4x
• (3) y² = 8x
• (4) x² = 4y

Let \( 0 < z < y < x \) be three real numbers such that \( \frac{1}{x}, \frac{1}{y}, \frac{1}{z} \) are in an arithmetic progression and \( x, \sqrt{2}y, z \) are in a geometric progression. If \( xy + yz + zx = \frac{3}{\sqrt{2}} xyz \), then \( 3(x + y + z)^2 \) is equal to ____________.

A hydraulic automobile lift is designed to lift vehicles of mass 5000 kg. The area of cross section of the cylinder carrying the load is 250 cm². The maximum pressure the smaller piston would have to bear is [Assume g = 10 m/s²]:

• (1) 20 × 10⁺⁶ Pa
• (2) 2 × 10⁺⁵ Pa
• (3) 200 × 10⁺⁶ Pa
• (4) 2 × 10⁺⁶ Pa

An emf of 0.08 V is induced in a metal rod of length 10 cm held normal to a uniform magnetic field of 0.4 T, when moves with a velocity of:

• (1) 20 ms^-1
• (2) 2 ms^-1
• (3) 0.5 ms^-1
• (4) 3.2 ms^-1

For particle P revolving round the centre O with radius of circular path r and angular velocity ω, as shown in below figure, the projection of OP on the x-axis at time t is

• (1) x(t) = rcos (ωt )
• (2) x(t) = rcos (ωt - \(\frac{π}{6}\) ω)
• (3) x(t) = rcos (ωt + \(\frac{π}{6}\))
• (4) x(t) = rsin (ωt + \(\frac{π}{6}\))

In photo electric effect
A. The photocurrent is proportional to the intensity of the incident radiation.
B. Maximum Kinetic energy with which photoelectrons are emitted depends on the intensity of incident light.
C. Max. K.E with which photoelectrons are emitted depends on the frequency of incident light.
D. The emission of photoelectrons require a minimum threshold intensity of incident radiation.
E. Max. K.E of the photoelectrons is independent of the frequency of the incident light.
Choose the correct answer from the options given below:

• (1) A and B only
• (2) B and C only
• (3) A and C only
• (4) A and E only

A bullet of mass 0.1 kg moving horizontally with speed 400 ms^-1 hits a wooden block of mass 3.9 kg kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20m before coming to rest. The coefficient of friction between the block and the surface is ______.
(Given g = 10 m/s²)

• (1) 0.25
• (2) 0.50
• (3) 0.65
• (4) 0.90

Given below are two statements:
Statement I: Area under velocity- time graph gives the distance travelled by the body in a given time.
Statement II: Area under acceleration-time graph is equal to the change in velocity- in the given time.
In the light of given statements, choose the correct answer from the options given below.

• (1) Statement I is incorrect but Statement II is True.
• (2) Both Statement I and Statement II are False.
• (3) Statement I is correct but Statement II is false.
• (4) Both Statement I and Statement II are true.

Which of the following expressions give the value of acceleration due to gravity (g') at the altitude h above the surface of Earth.
(R = radius of Earth, g = acceleration due to gravity at surface of Earth)

• (1) \( g' = g \left( 1 - \frac{h^2}{2R^2} \right) \)
  
• (2) \( g' = g \left( 1 - \frac{2h}{R} \right) \)
• (3) \( g' = g \left( 1 - \frac{h}{2R} \right) \)
  
• (4) \( g' = g \left( 1 - \frac{2h^2}{R^2} \right) \)
  

The equivalent resistance between \( A \) and \( B \) as shown in the figure is:

• (1) 5 Ω
• (2) 10 Ω
• (3) 20 Ω
• (4) 40 Ω

The waves emitted when a metal target is bombarded with high-energy electrons are:

• (1) X-ray
• (2) Infrared
• (3) Microwaves
• (4) Radiowave

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Electromagnets are made of soft iron.
Reason R : Soft iron has high permeability and low retentivity.
In the light of above, statements, choose the most appropriate answer from the options given below.

• (1) A is not correct but R is correct
• (2) Both A and R are correct and R is the correct explanation of A
• (3) A is correct but R is not correct
• (4) Both A and R are correct but R is NOT the correct explanation of A

Electric potential at a point \( P \) due to a point charge of \( 5 \times 10^{-9} \, \text{C} \) is \( 50 \, \text{V} \). The distance of \( P \) from the point charge is:

• (1) 90 cm
• (2) 70 cm
• (3) 60 cm
• (4) 50 cm

The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be

• (1) 3L
• (2) 4L
• (3) 8L
• (4) 9L

The temperature at which the kinetic energy of oxygen molecules becomes double than its value at 27°C is

• (1) 327°C
• (2) 627°C
• (3) 927°C
• (4) 1227°C

The trajectory of projectile, projected from the ground is given by y=x-x²/20. Where x and y are measured in meter. The maximum height attained by the projectile will be

• (1) 5m
• (2) 10√2m
• (3) 10m
• (4) 200m

The width of fringe is 2 mm on the screen in a double slits experiment for the light of wavelength of 400 nm. The width of the fringe for the light of wavelength 600 nm will be:

• (1) 2mm
• (2) 3mm
• (3) 4mm
• (4) 1.33mm

• (1) A-II, B-I, C-IV, D-III
• (2) A-II, B-IV, C-I, D-III
• (3) A-IV, B-II, C-III, D-I
• (4) A-III, B-IV, C-I, D-II

For a given transistor amplifier circuit in CE configuration V_CC = 1 V, R_c = 1 kΩ, R_b = 100 kΩ and β = 100. Value of base current I_b is

• (1) I_b = 0.1 μΑ
• (2) I_b = 10 μΑ
• (3) I_b = 1.0 μΑ
• (4) I_b = 100 μΑ

A radio active material is reduced to 1/8 of its original amount in 3 days.
If 8×10^-3 kg of the material is left after 5 days the initial amount of the material is

• (1) 32g
• (2) 40g
• (3) 256g
• (4) 64g

The power radiated from a linear antenna of length \( l \) is proportional to: (Given, \( \lambda \) = Wavelength of wave):

• (1) \(\frac{l}{λ}\)
• (2) \(\frac{l}{λ^2}\)
• (3) \(\left(\frac{l}{λ}\right)^2\)
• (4) \(\frac{l^2}{λ}\)

A Carnot engine working between 27°C and 127°C performs 2 kJ of work. The amount of heat rejected is equal to:

• (1) 4 kJ
• (2) 8 kJ
• (3) 6 kJ
• (4) 12 kJ

The number density of free electrons in copper is nearly 8 × 10²⁸ m^-3. A copper wire has its area of cross section = 2 × 10^-6 m² and is carrying a current of 3.2 A. The drift speed of the electrons is _____ ×10^-6 ms^-1

Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature 30 cm. The centre of curvature of surface is towards denser medium and a point object is placed on the principle axis in rarer medium at a distance of 15 cm from the pole of the surface. The distance of image from the pole of the surface is _____ cm.

A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be _______ cm.

A body of mass \( 5 \, \text{kg} \) is moving with a momentum of \( 10 \, \text{kg} \cdot \text{ms}^{-1} \). Now a force of \( 2 \, \text{N} \) acts on the body in the direction of its motion for \( 5 \, \text{s} \). The increase in the kinetic energy of the body is _____ J.

The ratio of the wavelength of spectral lines \( H_\alpha \) and \( H_\beta \) in the Balmer series is \( \frac{x}{20} \). The value of \( x \) is _______.

A steel rod of length 1 m and cross sectional area 10^-4 m² is heated from 0°C to 200°C without being allowed to extend or bend. The compressive tension produced in the rod is______ ×10⁴N. (Given Young's modulus of steel = 2×10¹¹ Nm^-2, coefficient of linear expansion = 10^-5K^-1)

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity 3 m/s (as shown in figure). Maximum height with respect to the initial position covered by it will be_____ cm (take, g = 10 m/s²)

The ratio of magnetic field due to coil at centre and at distance of R from the centre on the axis passing through the centre and perpendicular to the plane of ring is : 1x (R is the radius of coil), find the value of x.

A 600 pF capacitor is charged by 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. Electrostatic energy lost in the process is _____ μ.J

A series combination of resistor of resistance 100 Ω, inductor of inductance 1 H and capacitor of capacitance 6.25 µF is connected to an ac source. The quality factor of the circuit will be ______

• (1) A-II, B-IV, C-I, D-III
• (2) A-III, B-IV, C-I, D-II
• (3) A-II, B-I, C-IV, D-III
• (4) A-IV, B-III, C-II, D-I

The correct IUPAC nomenclature for the following compound is.

• (1) 2 Methyl 5 oxohexanoic acid
• (2) 2 Formyl 5 methylhexan 6 oic acid
• (3) 5 Formyl 2 methylhexanoic acid
• (4) 5 Methyl 2 oxohexan 6 oic acid

Major product 'P' formed in the following reaction is:

• (1)

• (2)

• (3)

• (4)

A compound 'X' when treated with phthalic anhydride in presence of concentrated \(\mathrm{H_2SO_4}\) yields 'Y'. 'Y' is used as an acid/base indicator. 'X' and 'Y' are respectively

• (1) Toludine, Phenolphthalein
• (2) Carbolic acid, Phenolphthalein
• (3) Salicylaldehyde, Phenolphthalein
• (4) Anisole, methyl orange

Henry Moseley studied characteristic X-ray spectra of elements. The graph which represents his observation correctly is
Given v = frequency of X-ray emitted
Z = atomic number

• (1)

• (2)

• (3)

• (4)

Given below are two statements:
Statement I: In redox titration, the indicators used are sensitive to change in pH of the solution.
Statement II: In acid-base titration, the indicators used are sensitive to change in oxidation potential.
In the light of the above statements, choose the most appropriate answer from the options given below

• (1) Both Statement I and Statement II are correct
• (2) Both Statement I and Statement II are incorrect
• (3) Statement I is correct but Statement II is incorrect
• (4) Statement I is incorrect but Statement II is correct

In good quality cement ratio of lime total oxides of Si(SiO\(_2\)), Aluminium(Al\(_2\)O\(_3\)) and Iron(Fe\(_2\)O\(_3\)) should be as close as possible to _____ .

The correct order of reactivity of following haloarenes towards nucleophilic substitution with aqueous NaOH is 

Choose the correct answer from the options given below:

• (1) A>B>D>C
• (2) C>A>D>B
• (3) D>C>B>A
• (4) D>B>A>C

The correct reaction profile diagram for a positive catalyst reaction .

• (1)

• (2)

• (3)

• (4)

• (1) A-III, B-I, C-IV, D-II
• (2) A-III, B-IV, C-I, D-II
• (3) A-II, B-I, C-IV, D-III
• (4) A-IV, B-III, C-I, D-II

The product (P) formed from the following multistep reaction is:

• (1)

• (2)

• (3)

• (4)

The descending order of acidity for the following carboxylic acid is-
A. CH₃COOH
B. F₃C-COOH
C. CICH₂-COOH
D. FCH₂-COOH
E. BrCH₂-COOH
Choose the correct answer from the options given below:

• (1) E>D>B>A>C
• (2) B>C>D>E>A
• (3) D>B>A>E>C
• (4) B>D>C>E>A

Statement-1: Methyl orange is a weak acid 
Statement-2: Benzenoid form of methyl orange is deeply coloured than quinonoid form
Check out which of the above statement is true?

• (1) Statement-1 is correct and Statement-2 is wrong
• (2) Both the Statements-1 and Statement-2 are correct
• (3) Statement-1 is wrong and Statement-2 is correct
• (4) None of them

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Sodium is about 30 times as abundant as potassium in the oceans.
Reason R : Potassium is bigger in size than sodium.
In the light of the above statements, choose the correct answer from the options given below

• (1) Both A and R are true and R is the correct explanation of A
• (2) Both A and R are true and R is NOT the correct explanation of A
• (3) A is true but R is false
• (4) A is false but R is true

Which of the following have same number of significant figures?
A. 0.00253
B. 1.0003
C. 15.0
D. 163
Choose the correct answer from the options given below

• (1) B and C only
• (2) C and D only
• (3) A, B and C only
• (4) A, C and D only

Arrange the following gases in increasing order of van der Waals constant 'a'
A. Ar
B. CH4
C. H₂O
D. C6H6
Choose the correct option from the following.

• (1) A, B, C and D
• (2) D, C, B and A
• (3) B, C, D and A
• (4) C, D, B and A

Which of these reactions is not a part of breakdown of ozone in stratosphere?

• (1) \(CF_2Cl_2(g)\xrightarrow{uv}\dot{C}l(g)+\dot{C}F_2Cl(g)\)
• (2) \(C\dot{l}(g)+O_3(g)\rightarrow Cl\dot{O}(g)+O_2(g)\)
• (3) \(Cl\dot{O}(g)+O(g)\rightarrow C\dot{l}(g)+O_2(g)\)
• (4) \(2Cl\dot{O}\rightarrow ClO_2(g)+C\dot{l}(g)\)

The statement/s which are true about antagonists from the following is/are:
A. They bind to the receptor site.
B. Get transferred inside the cell for their action.
C. Inhibit the natural communication of the body.
D. Mimic the natural messenger.
Choose the correct answer from the options given below:

• (1) A and B
• (2) A, C and D
• (3) B only
• (4) A and C

In Hall - Heroult process, the following is used for reducing Al₂O₃ :-

• (1) Na₃AlF₆
• (2) Graphite
• (3) Magnesium
• (4) CaF₂

Which of the following acts as a stabilizer in the decomposition of H₂O₂?

• (1) Urea
• (2) Alkali
• (3) Glass
• (4) Dust

The number of species from the following carrying a single lone pair on central atom Xenon is ______ .
XeF₅⁺, XeO₃, XeO₂F₂, XeF₅^-, XeO₃F₂, XeOF₄, XeF₄

Total spin only magnetic moment of the ion [Mn(SCN)₆]^x– is 5.92 B.M. Find out the value of x.

• (1) 5
• (2) 3
• (3) 2
• (4) 4

The solubility product of BaSO₄ is \(1 \times 10^{-10}\) at 298 K. The solubility of BaSO₄ in 0.1 M K₂SO₄(aq) is \(x \times 10^{-9}\) g L⁻¹. Calculate the value of \(x\).

If the boiling points of two solvents X and Y (having same molecular weights) are in the ratio 2:1 and their enthalpy of vaporizations are in the ratio 1:2, then the boiling point elevation constant of X is m times the boiling point elevation constant of Y. The value of m is ______ (nearest integer).

For complete combustion of ethene,
\(C_2H_4(g) + 3O_2(g) \longrightarrow 2CO_2(g) + 2H_2O (l)\)
the amount of heat produced as measured in bomb calorimeter is 1406 kJ mol^-1 at 300K. The minimum value of \(T\Delta S\) needed to reach equilibrium is (-) _____ . kJ.(Nearest integer)
Given: R = 8.3 J K^-1 mol^-1

The number of atomic orbitals from the following having 5 radial nodes is ___________.
\(7s,\ 7p,\ 6s,\ 8p,\ 8d\)

Find out the oxidation number of the central metal atom of fe(CO)₅ , VO₂⁺, and WO₃. Then calculate the sum of their oxidation state.

The number of incorrect statements from the following is _____
A. The electrical work that a reaction can perform at constant pressure and temperature is equal to the reaction Gibbs energy.
B. E°_cell is dependent on the pressure.
C. dE^θ cell/dT = Δ_rS^θ/nF
D. A cell is operating reversibly if the cell potential is exactly balanced by an opposing source of potential difference.

What is the ratio of σ and pi bonds in pyrophosphoric acid ?

Coagulating value of the electrolytes AlCl₃ and NaCl for As₂S₃ are 0.09 and 50.04 respectively. The coagulating power of AlCl₃ is x times the coagulating power of NaCl. The value of x is ______ .