JEE Main 2023 April 10 Shift 2 Question Paper with Solution PDF- Download Here

Let s={\(z=x+ry:\frac{2z-3i}{4z+2i}\) is a real number}. Then which of the following is not correct?

• (1) x=0
• (2) \((x,y)=(0,-\frac{1}{2})\)
• (3) \(y+x^2+y^2 ≠-\frac{1}{4}\)
• (4) \(y∈(-∞,-\frac{1}{2})∪(-\frac{1}{2},-∞)\)

Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways in which they can be transported is:

• (1) 1120
  
• (2) 560
  
• (3) 1680
• (4) 3360
  

Let the number  \((22)^{2022}\) + \((2022)^{22}\)  leave the remainder \( \alpha \) when divided by 3 and \( \beta \) when divided by 7. Then \( (\alpha^2 + \beta^2) \) is equal to:

• (1) 5
• (2) 20
  
• (3) 10
  
• (4) 13
  

Let g(x) = f(x) + f(1 - x) and f''(x) > 0, x ∈ (0,1). If g is decreasing in the interval (0, α) and increasing in the interval (α, 1), then tan-1 (2α) + tan^-1 (\(\frac{1}{α}\)) + tan^-1\((\frac{α+1}{α})\) is equal to

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

If the coefficients of \( x \) and \( x^2 \) in \( (1 + x)^p(1 - x)^q \) are 4 and -5 respectively, then \( 2p + 3q \) is equal to:

• (1) 60
  
• (2) 63
  
• (3) 66
  
• (4) 69

Let f be a continuous function satisfying \(∫^{t ^2}_ 0 ( f ( x ) + x ^2 ) d x = \frac{4}{3} t^3 , ∀ t > 0.\) Then \(f(\frac{π^2}{4})\) is equal to 

• (1) \(-\pi^2(1+\frac{\pi^2}{16})\)
• (2) \(\pi^2(1-\frac{\pi^2}{16})\)
• (3) \(-\pi(1+\frac{\pi^3}{16})\)
• (4) \(\pi(1-\frac{\pi^3}{16})\)

For, α, β, γ, δ ∈ \(\mathbb{N},\) if \(∫\left((\frac{x}{e})^{2x}+(\frac{e}{x})^{2x}\right)log_e\,xdx=\) \(\frac{1}{\alpha}(\frac{x}{e})^{βx}-\frac{1}{γ}(\frac{e}{x})^{δx}+c,\) Where \(e=\displaystyle\sum_{n=10}^{∞}\frac{1}{n!}\) and C is constant of integration, then α + 2β + 3γ - 4δ is equal to

• (1) -8
• (2) -4
• (3) 1
• (4) 4

Let m be the mean and σ be the standard deviation of the distribution

where ∑f_i = 62. if [x] denotes the greatest integer ≤ x, then [μ² + σ²] is equal

• (1) 6
• (2) 7
• (3) 8
• (4) 9

Let \(\overrightarrow{a}=2\^i+7\^j−\^k ,\overrightarrow{b} =3\^i+5 \^k\) and \(\overrightarrow{c}=\^i=\^j+2\^k\) . Let \(\overrightarrow{d}\) be a vector which is perpendicular to both \(\overrightarrow{a}\) and \(\overrightarrow{b}\) , and \(\overrightarrow{c}.\overrightarrow{d}=12\). Then \((-\^i+\^j=\^k).(\overrightarrow{c}\times\overrightarrow{d})\) is equal to

• (1) 24
• (2) 42
• (3) 44
• (4) 48

the points P and Q are respectively the circumcentre and the orthocentre of a ΔABC, then \( \overrightarrow{PA}+ \overrightarrow{PB}+ \overrightarrow{PC}\)  is 

• (1) \(\overrightarrow{2QP}\)
• (2) \(\overrightarrow{QP}\)
• (3) \(\overrightarrow{PQ}\)
• (4) \(\overrightarrow{2PQ}\)

Let A be the point (1, 2) and B be any point on the curve \( x^2 + y^2 = 16 \). If the centre of the locus of the point P, which divides the line segment AB in the ratio 3:2 is the point C (\( \alpha, \beta \)), then the length of the line segment AC is:

• (1) \( \frac{6 \sqrt{5}}{5} \)
  
• (2) \( \frac{2 \sqrt{5}}{5} \)
  
• (3) \( \frac{3 \sqrt{5}}{5} \)
  
• (4) \( \frac{4 \sqrt{5}}{5} \)

Let A = {2, 3, 4} and B = {8, 9, 12}. Then the number of elements in the relation R = {((a₁, b₁), (a₂, b₂)) ∈ (A × B, A × B) : a₁ divides b₂ and a₂ divides b₁} is

• (1) 12
• (2) 18
• (3) 24
• (4) 36

The statement ~[p v (~(p ∧ q))] is equivalent to

• (1) (~(р ∧ q)) ∧ q
• (2) ~ (р ∧ q)
• (3) (р ∧ q) ∧ (~р)
• (4) ~(p v q)

If \( S_n = 4 + 11 + 21 + 34 + 50 + \dots \) to \( n \) terms, then \( \frac{1}{60} (S_{29} - S_9) \) is equal to:

Let a die be rolled \( n \) times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is \( \frac{k}{2^{15}} \), then \( k \) is equal to:

• (1) 58
• (2) 60
• (3) 48
• (4) 65

Let the image of the point P(1, 2, 6) in the plane passing through the points A(1, 2, 0), B(1, 4, 1) and C(0, 5, 1) be Q (α, β, γ). Then (α² + β² + γ²) is equal to

• (1) 62
• (2) 65
• (3) 70
• (4) 76

Let the line \(\frac{x}{1}=\frac{6−y}{2}=\frac{z+8}{5}\)  intersect the lines  \(\frac{x-5}{1}=\frac{y-7}{3}=\frac{z+2}{1}\) and \(\frac{x+3}{6}=\frac{3−y}{3}=\frac{z-6}{1}\) at the points A and B respectively. Then the distance of the mid-point of the line segment AB from the plane 2x – 2y + z = 14 is 

• (1) \(\frac{10}{3}\)
• (2) \(\frac{11}{3}\)
• (3) 4
• (4) 3

Let S = {\( x∈(−\frac{ π}{ 2} , \frac{π}{2} )\) : 9^1−tan2 x + 9^tan2 x=10 } and \(β=∑_{ x∈s} t a n ^2 (\frac{ x}{ 3} )\) , then \(\frac{1}{6}\) ( β − 14 )²  is equal to

• (1) 8
• (2) 16
• (3) 32
• (4) 34

Let a circle of radius 4 be concentric to the ellipse \( 15x^2 + 19y^2 = 285 \). Then the common tangents are inclined to the minor axis of the ellipse at the angle:

• (1) \(\frac{\Pi}{3}\)
• (2) \(\frac{\Pi}{2}\)
• (3) \(\frac{\Pi}{6}\)
• (4) \(\frac{\Pi}{4}\)

if A=\(\frac{1}{5! 6! 7!}\begin{bmatrix} 5! & 6! & 7!\\ 6! & 7! & 8! \\ 7! & 8! & 9! \end{bmatrix}\), then |adj(adj(2A))| is equal t

• (1) \(2^{20}\)
• (2) \(2^{16}\)
• (3) \(2^{12}\)
• (4) \(2^{8}\)

Let the tangent at any point P on a curve passing through the points (1, 1) and (\(\frac{1}{10}\),100), intersect positive x-axis and y-axis at the points A and B respectively. If PA : PB = 1 : k and y = y(x) is the solution of the differential equation  \(\frac{dy}{e^{dx}}Kx+\frac{K}{2}\) , y(0) = k, then 4y(1) – 5log_e3 is equal to ______ .

If area bounded by region \({x, y)| |x^{2}-2| ≤ y ≤ x}\) is A, then 6A + 16\(\sqrt{2}\) is?

The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is equal to ______.

Let S be the set of values of λ, for which the system of equations  
6λx – 3y + 3z = 4λ2 ,  
2x + 6ly + 4z = 1, 
3x + 2y + 3λz = l has no solution. Then  12\( ∑ _{λ ∈ S}\) | λ | 12 ∑ λ ∈ | λ |  is equal to ________ .

If the domain of the function \( f(x) = \sec^{-1} \left( \frac{2x}{5x + 3} \right) \)  is \( [\alpha, \beta] \cup (\gamma, \delta) \), then \( |3\alpha + 10(\beta + \gamma) + 21\delta| \) is equal to:

Let the equations of two adjacent sides of a parallelogram ABCD be 2x – 3y = –23 and 5x + 4y = 23. If the equation of its one diagonal AC is 3x + 7y = 23 and the distance of A from the other diagonal is d, then 50 d2 is equal to____.

Let the foot of perpendicular from the point A(4, 3, 1) on the plane P : x - y + 2z + 3 = 0 be N. If B(5,α,β) ∈ Z   is a point on plane P such that the area of the triangle ABN in 3√2 . then α² + β² + αβ is equal to ____ .

Suppose a₁, a₂, 2, a₃, a4 be in an arithmeticogeometric progression. If the common ratio of the corresponding geometric progression is 2 and the sum of all 5 terms of the arithmetico-geometric progression is \(\frac{49}{2}\) , then a4 is equal to ________ .

Let the quadratic curve passing through the point \( (-1, 0) \) and touching the line \( y = x \) at \( (1, 1) \) be \( y = f(x) \). Then the x-intercept of the normal to the curve at the point \( (\alpha, \alpha + 1) \) in the first quadrant is:

In the figure, θ₁ + θ₂ = \(\frac{π}{2}\) and √3 (BE) = 4 (AB). If the area of ΔCAB is 2√3 - 3 unit2 , when \(\frac{θ_2}{θ_1}\) is the largest, then the perimeter (in unit) of ΔCED is equal to ________.

A person travels x distance with velocity v₁ and then x distance with velocity v₂ in the same direction. The average velocity of the person is v, then the relation between v, v₁ and v₂ will be

• (1) \(v=\frac{v_1+v_2}{2}\)
• (2) V=V₁+V₂
• (3) \(\frac{1}{v}=\frac{1}{v_1}+\frac{1}{v_2}\)<
• (4) \(\frac{2}{v}=\frac{1}{v_1}+\frac{1}{v_2}\)

If each diode has a forward bias resistance of 25Ω in the below circuit, Which of the following options is correct:

• (1) \(\frac{I_1}{I_2}=1\)
• (2) \(\frac{I_2}{I_3}=1\)
• (3) \(\frac{I_3}{I_4}=1\)
• (4) \(\frac{I_1}{I_2}=2\)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: An electric fan continues to rotate for some time after the current is switched off.
Reason R: Fan continuous to rotate due to inertia of motion.
In the light of above statements, choose the most appropriate answer from the options given below.

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

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor

• (1) drift from higher potential to lower potential.
• (2) move in the straight line paths in the same direction
• (3) move with the uniform velocity throughout from lower potential to higher potential
• (4) move in the curved paths from lower potential to higher potential

A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,

• (1) 11 RT
• (2) 4 RT
• (3) 8 RT
• (4) 16 RT

A bar magnet is released from rest along the axis of a very long, vertical aluminum tube. After sometime the magnet will :

• (1) move down with an acceleration equal to g
• (2) move down with an acceleration grater than g
• (3) will move with almost constant speed
• (4) oscillate inside the tube

Two projectiles are projected at 30° and 60° with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is :

• (1) \(1:\sqrt 3\)
• (2) 1:3
• (3) \(2:\sqrt 3\)
• (4) \(\sqrt 3:1\)

A gas is compressed adiabatically, which one of the follwing statement is NOT true.

• (1) The change in the internal energy is equal to the work done on the gas
• (2) The temperature of the gas increases
• (3) There is no heat supplied to the system
• (4) There is no change in the internal energy

For a periodic motion represented by the equation y = sin ωt + cos ωt, the amplitude of the motion is

• (1) \(\sqrt 2\)
• (2) 1
• (3) 2
• (4) 0.5

The amplitude of magnetic field in an electromagnetic wave propagating along y-axis is 6.0 × 10^-7 T. The maximum value of electric field in the electromagnetic wave is

• (1) 6.0 × 10^-7 Vm^-1
• (2) 180 Vm^-1
• (3) 2 × 10¹⁵ Vm^-1 
• (4) 5 × 10¹⁴ Vm^-1

The time period of a satellite revolving above earth's surface at a height equal to R will be
(given: \(g= \pi^2 \ m/s^2\), R= radius of earth)

• (1) \(\sqrt {4R}\)
• (2) \(\sqrt {2R}\)
• (3) \(\sqrt {8R}\)
• (4) \(\sqrt {32R}\)

Given below are two statements:  
Statement I: For diamagnetic substance -1 ≤ X < 0 , where X is the magnetic susceptibility.  
Statement II: Diamagnetic substances when placed in an external magnetic field, tend to move from stronger to weaker part of the field. 
In the light of the above statements, choose the correct answer from the options given below.  

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

The ratio of intensities at two points P and Q on the screen in a Young’s double slit experiment where phase difference between two wave of same amplitude are \(\frac{π}{3}\) and \(\frac{π}{2}\), respectively are 

• (1) 3:2
• (2) 2:3
• (3) 1:3
• (4) 3:1

Young's moduli of the material of wires A and B are in the ratio of 1:4, while its area of cross section are in the ratio of 1:3. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires A and B will in the ratio of
[Assume length of wires A and B are same]

• (1) 36: 1
• (2) 1:36
• (3) 1:12
• (4) 12:1

The variation of stopping potential (V0) as a function of the frequency (v) of the incident light for a metal is shown in figure. The work function of the surface is

• (1) 1.36 eV
• (2) 2.98 eV
• (3) 2.07 eV
• (4) 18.6 eV

Given below are two statement:
statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g).
statement II : The effect of rotation of the earth on the value of 'g' at the equator is minimum and that at the pole is maximum.
In the light of the above statements , choose the correct answer from the options given below

• (1) Both statement I and statement II are false
• (2) statement I is true but statement II is false
• (3) Both statement I and statement II are true
• (4) statement I is false but statement II is true

In an experiment with Vernier callipers of least count 0.1 mm, when two jaws are joined together the zero of Vernier scale lies right to the zero of the main scale and 6th division of Vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between 3.2 cm and 3.3 cm marks, and 4th division of vernier scale coincides with the main scale division. The diameter of bob is measured as

• (1) 3.26 cm
• (2) 3.25 cm
• (3) 3.22 cm
• (4) 3.18 cm

The distance between two plates of a capacitor is \(d\) and its capacitance is \(C_1\), when air is the medium between the plates. If a metal sheet of thickness \(\frac {2d}{3}\) and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes \(C_2\). The ratio \(\frac {C_2}{C_1}\) is

• (1) 4:1
• (2) 2:1
• (3) 3:1
• (4) 1:1

The half-life of a radioactive substance is 30 min. The time for disintegration \(\frac{7}{8}\)^th part of its original mass will be:

• (1) T
• (2) 2T
• (3) 3T
• (4) 8T

A message signal of frequency 3kHz is used to modulate a carrier signal of frequency 1.5 MHz. The bandwidth of the amplitude modulated wave is

• (1) 6 MHz
• (2) 3 MHz
• (3) 3 kHz
• (4) 6 kHz

A force of \(-P\hat k \) acts on the origin of the coordinate system. The torque about the point \((2, -3)\) is \(P(a\hat i+b\hat j)\), The ratio of \(\frac ab\) is \(\frac x2\). The value of x is -

A straight wire carrying of 14 A is bent into a semi-circular arc of radius 2.2 cm as shown in the figure. The magnetic field produced by the current at the centre (O) of the arc is ____ × 10^–4 T.

A rectangular block of mass 5 kg attached to an horizontal spiral spring executes simple harmonic motion of amplitude 1 m and time period 3.14s. The maximum force exerted by spring on block is _____N.

A square loop of side 2.0 cm is placed inside a long solenoid that has 50 turns per centimetre and carries as sinusoidally varying current of amplitude 2.5 A and angular frequency 700 rad s^–1. The central axes of the loop and selenoid coincide. The amplitude of the emf induced in the loop is x×10^–4 V . The value of x is ______ . (Take, \(\pi\) = 22/7)

If the maximum load carried by an elevator is 1400 kg (600 kg - Passengers + 800 kg- elevator), which is moving up with a uniform speed of 3 ms^-1 and the frictional force acting on it is 2000 N, then the maximum power used by the motor is ____ kW. (g=10 m/s²)

An electron revolves around an infinite cylindrical wire having uniform linear charge density \(2×10^{–8}\ Cm^{-1}\) in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is ____ \(\times 10^6 ms^{-1}\). Given mass of electron = \(9\times10^{-31}\) kg.

A rectangular parallelopiped is measured as 1 cm × 1 cm × 100 cm. If its specific resistance is 3 × 10^-7 Ωm, then the resistance between its two opposite rectangular faces will be _____ ×10^-7 Ω.

Figure below shows a liquid being pushed out of the tube by a piston having area of cross section 2.0 cm². The area of cross section at the oulet is 10 mm². If the piston is pushed at a speed of 4 cm s^-1, the speed of outgoing fluid is ______ cm s^-1.

A point object, 'O' is placed in front of two thin symmetrical coaxial convex lenses L₁ and L₂ with focal length 24 cm and 9 cm respectively. The distance between two lenses is 10 cm and the object is placed 6 cm away from lens L₁ as shown in the figure. The distance between the object and the image formed by the system of two lenses is _____ cm.

If 917 Å be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be _____ Å.

The major product P formed in the given reaction is:

• (1)
• (2)
• (3)
• (4)

The decreasing order of hydride affinity for following carbocations is:
Choose the correct answer from the options given below:

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

In the reaction given below :

The Product ‘X’ is:

• (1)
• (2)
• (3)
• (4)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R:
Assertion A: The energy required to form \(Mg^{2+}\) from Mg is much higher than that required to produce \(Mg^+\)
Reason R: \(Mg^{2+}\) is small ion and carry more charge than \(Mg^{+}\).
In the light of the above statements, choose the correct answer from the options given below.

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

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R:
Assertion A: 3.1500 g of hydrated oxalic acid dissolved in water to make 250.0 mL solution will result in 0.1 M oxalic acid solution.
Reason R: Molar mass of hydrated oxalic acid is 126 g mol^–1.
In the light of the above statements, choose the correct answer from the options given below.

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

The correct order of the number of unpaired electrons in the given complexes is
A. \([Fe(CN)_6]^{3–}\)
B. \([FeF_6]^{3–}\)
C. \([CoF_6]^{3–}\)
D. \([Cr(oxalate)_3]^{3–}\)
E. \([Ni(CO)_4]\)
Choose the correct answer from the options given below:

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

The correct order for acidity of the following hydroxyl compound is:

Choose the correct answer from the options given below:

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

Incorrect method of preparation for alcohols from the following is:

• (1) Hydroboration-oxidation of alkene.
• (2) Reaction of Ketone with RMgBr followed by hydrolysis.
• (3) Reaction of alkyl halide with aqueous NaOH.
• (4) Ozonolysis of alkene.

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

In Carius tube, an organic compound ‘X’ is treated with sodium peroxide to form a mineral acid ‘Y’. The solution of \(BaCl_2\), is added to ‘Y’ to form a precipitate ‘Z’. ‘Z’ is used for the quantitative estimation of an extra element. ‘X’ could be

• (1) A nucleotide
• (2) Chioroxylenol
• (3) Methionine
• (4) Cytosine

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

Gibbs energy vs T plot for the formation of oxides is given below.

• (1) At 600°C, CO cannot reduce FeO
• (2) At 600°C, C can reduce FeO
• (3) At 600°C, C can reduce ZnO
• (4) At 600°C, CO can reduce ZnO

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Physical properties of isotopes of hydrogen are different.
Reason R: Mass difference between isotopes of hydrogen is very large.
In the light of the above statements, choose the correct answer from the options given below:

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

The correct order of metallic character is:

• (1) Be > Ca > K
• (2) Ca > K > Be
• (3) K > Ca > Be
• (4) K > Be > Ca

Buna-S can be represented as:

• (1)
• (2)
• (3)
• (4)

Ferric chloride is applied to stop bleeding because-

• (1) Fe³⁺ ions coagulate blood which is a negatively charged sol.
• (2) FeCl₃ reacts with the constituents of blood which is a positively charged sol.
• (3) Blood absorbs FeCl₃ and forms a complex.
• (4) Cl^– ions cause coagulation of blood.

The correct relationships between unit cell edge length ‘a’ and radius of sphere ‘r’ for face-centred and body-centred cubic structures respectively are:

• (1) \(2\sqrt 2r = a\) and \(4r = \sqrt 3 a\)
• (2) \(r = 2\sqrt 2a\) and \(\sqrt 3 r = 4a\)
• (3) \(r = 2\sqrt 2a\) and \( 4r = \sqrt 3a\)
• (4) \(r = 2\sqrt 2a\) and \( \sqrt 3r =4a\)

Number of water molecules in washing soda and soda ash respectively are :

• (1) 1 and 10
• (2) 1 and 0
• (3) 10 and 1
• (4) 10 and 0

The reaction used for preparation of soap from fat is :

• (1) reduction reaction
• (2) an addition reaction
• (3) alkaline hydrolysis reaction
• (4) an oxidation reaction

Delicate balance of \(CO_2\) and \(O_2\) is not disturbed by:

• (1) Deforestation
• (2) Respiration
• (3) Burning of coal
• (4) Burning of petroleum

An aqueous solution of volume 300 cm³ contains 0.63 g of protein. The osmotic pressure of the solution
at 300 K is 1.29 mbar. The molar mass of the protein is ____ g mol^–1.
Given: R = 0.083 L bar K^–1 mol^–1

The number of molecules from the following which contain only two lone pair of electrons is _____ .
\(H_2O, N_2, CO, XeF_4, NH_3, NO, CO_2, F_2\)

For a metal ion, the calculated magnetic moment is 4.90 BM. This metal ion has ______ number of unpaired electrons.

In alkaline medium, the reduction of permanganate anion involves a gain of _____ electrons.

The number of incorrect statement/s from the following is ____ .
A. The successive half lives of zero order reactions decreases with time.
B. A substance appearing as reactant in the chemical equation may not affect the rate of reaction.
C. Order and molecularity of a chemical reaction can be a fractional number.
D. The rate constant units of zero and second order reaction are mol L^–1s^–1 and mol^–1 Ls^–1 respectively.

The electron in the \(n^{th}\) orbit of \(Li^{2+}\) is excited to \((n + 1)\) orbit using the radiation of energy \(1.47 × 10^{–1}J \) (as shown in the diagrarn). The value of n is ______ .
Given: \(R_H = 2.18 × 10^{–18} J\).

The number of endothermic process/es from the following is _____ .
A. \(I_2 (g) → 2I (g)\)
B. \(HCl (g) → H(g) + Cl (g)\)
C. \(H_2O(l) → H_2O (g)\)
D. \(C(s) + O_2 (g) → CO_2 (g)\)
E. Dissolution of ammonium chloride in water.

\(A(g) ⇋ 2B(g) + C(g)\)
For the given reaction, if the initial pressure is 450 mm Hg and the pressure at time t is 720 mm Hg at a constant temperature T and constant volume V. The fraction of A(g) decomposed under these conditions is \(x × 10^{–1}\). The value of x is _____ . (nearest integer)

The specific conductance of 0.0025 M acetic acid is \(5 × 10^{–5} S\ cm^{–1}\) at a certain temperature. The dissociation constant of acetic acid is ___________ \(× 10^{–7}.\) (Nearest integer) Consider limiting molar conductivity of \(CH_3COOH\) as \(400\  S cm^2 mol^{–1}\).

The difference in the oxidation state of \(Xe\) between the oxidised product of \(Xe\) formed on complete hydrolysis of \(XeF_4\) and \(XeF_4\) is _____ .