JEE Main 2022 July 27 Shift 1 Question Paper with Solution PDF- Download Here

Let R₁ and R₂ be two relations defined on ℝ by a R₁b ⇔ ab ≥ 0 and aR₂b ⇔ a ≥ b. Then,

• (1) R₁ is an equivalence relation but not R₂
• (2) R₂ is an equivalence relation but not R₁
• (3) Both R₁ and R₂ are equivalence relations
• (4) Neither R₁ nor R₂ is an equivalence relation

Let
f,g:N = {1} → N be functions defined by
f(a) = α, where α is the maximum of the powers of those primes p such that p^α divides a, and g(a) = a + 1, for all a ∈ N – {1}. Then, the function f + g is

• (1) One-one but not onto
• (2) Onto but not one-one
• (3) Both one-one and onto
• (4) Neither one-one nor onto

• (1) 1000
• (2) 1024
• (3) 1105
• (4) 1196

Let
A = \(\begin{pmatrix}1 & 2\\ -2 & -5 \end{pmatrix}\)
Let \( \alpha, \beta \in \mathbb{R} \) be such that \( \alpha A^2 + \beta A = 2I \). Then \( \alpha + \beta \) is equal to 

• (1) –10
• (2) –6
• (3) 6
• (4) 10

The remainder when (2021)²⁰²² + (2022)²⁰²¹ is divided by 7 is

• (1) 0
• (2) 1
• (3) 2
• (4) 6

Suppose a₁, a₂, … a_n, … be an arithmetic progression of natural numbers. If the ration of the sum of first five terms to the sum of first nine terms of the progression is 5 : 17 and 110 < a₁₅ < 120, then the sum of the first ten terms of the progression is equal to

• (1) 290
• (2) 380
• (3) 460
• (4) 510

• (1) -1
• (2) -2
• (3) 1
• (4) 2

Let
\(I = ∫^{\frac{π}{3}}_{\frac{π}{4}}(\frac{8sinx-sin2x}{x})dx\)
Then

• (1) \(\frac{π}{2}<I<\frac{3π}{4}\)
• (2) \(\frac{π}{5}<I<\frac{5π}{12}\)
• (3) \(\frac{5π}{12}<I<\frac{\sqrt3}{3}π\)
• (4) \(\frac{3π}{4}<I<π\)

• (1) \(\frac{1}{3}(2-12√3+8π)\)
• (2) \(\frac{1}{3}(2-12√3+6π)\)
• (3) \(\frac{1}{3}(4-12√3+8π)\)
• (4) \(\frac{1}{3}(4-12√3+6π)\)

• (1) 0
• (2) 1
• (3) 2
• (4) 3

\(\begin{array}{l}\text{Let}~\vec{a} = \alpha \hat{i} + \hat{j} + \beta \hat{k}~\text{and}~ \vec{b} = 3 \hat{i} + 5\hat{j} + 4 \hat{k}~ \text{be two vectors, such that }\vec{a} \times \vec{b} = -\hat{i} + 9\hat{j} + 12 \hat{k}.\end{array}\)
\(\begin{array}{l}~\text{Then the projection of } \vec{b}-2\vec{a} ~\text{on}~ \vec{b}+ \vec{a}~\text {is equal to}\end{array}\)

• (1) 2
• (2) \(\frac{39}{5}\)
• (3) 9
• (4) \(\frac{46}{5}\)

Let S be the sample space of all five digit numbers. It p is the probability that a randomly selected number from S, is multiple of 7 but not divisible by 5, then 9p is equal to

• (1) 1.0146
• (2) 1.2085
• (3) 1.0285
• (4) 1.1521

Let\( A(1, 1), B(-4, 3) \)and \(C(-2, -5)\) be vertices of a triangle ABC, P be a point on side BC, and \(Δ1\) and \(Δ2\) be the areas of triangles APB and ABC, respectively. If \(Δ1 : Δ2 = 4 : 7\), then the area enclosed by the lines AP, AC and the x-axis is

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

• (1) √11
• (2) 4
• (3) 3
• (4) 2√23

Let a function f: ℝ → ℝ be defined as :
\(\begin{array}{l}f(x) = \left\{\begin{matrix}\int_{0}^{x}(5-|t-3|)dt, & x>4 \\x^2 + bx, & x \le4 \\\end{matrix}\right.\end{array}\)
where b ∈ ℝ. If f is continuous at x = 4 then which of the following statements is NOT true?

• (1) f is not differentiable at x = 4
• (2) \(f'(3)+f'(5) = \frac{35}{4}\)
• (3) f is increasing in (-∞, \(\frac{1}{8}\))∪(8,∞)
• (4) f has local minima at x = \(\frac{1}{8}\)

Let P(a, b) be a point on the parabola y² = 8x such that the tangent at P passes through the centre of the circle x² + y² – 10x – 14y + 65 = 0. Let A be the product of all possible values of a and B be the product of all possible values of b. Then the value of A + B is equal to

• (1) 0
• (2) 25
• (3) 40
• (4) 65

Let α→ = \(2\^{i}-\^{j}+5\^{k} and b→= α\^{i}+β\^{j}+2\^{k}. If ((α→×b→)×\^{i}).\^{k} \)=\(\frac{ 23}{2}\),then \(|b→×2\^{j}\| \)is equal to

• (1) 4
• (2) 5
• (3) √21
• (4) √17

• (1) √5-2
• (2) √3-1
• (3) √7-2
• (4) √7-√3

\((p\wedge r)\Leftrightarrow(p\wedge(\sim q))\) is equivalent to \((\sim p)\) when \(r\) is

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

If the plane P passes through the intersection of two mutually perpendicular planes 2x + ky – 5z = 1 and 3kx – ky + z = 5, k < 3 and intercepts a unit length on positive x-axis, then the intercept made by the plane P on the y-axis is

• (1) \(\frac{1}{11}\)
• (2) \(\frac{5}{11}\)
• (3) 6
• (4) 7

For k ∈ R, let the solution of the equation
\(\cos\left(\sin^{-1}\left(x \cot\left(\tan^{-1}\left(\cos\left(\sin^{-1}\right)\right)\right)\right)\right) = k, \quad 0 < |x| < \frac{1}{\sqrt{2}}\)
Inverse trigonometric functions take only principal values. If the solutions of the equation x² – bx – 5 = 0 are
\(\frac{1}{α^2}+\frac{1}{β^2} \)and \(\frac{α}{β}\)
, then b/k2 is equal to_____.

The mean and variance of 10 observation were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is ________.

An ellipse
\(E:\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\)
passes through the vertices of the hyperbola
\(H:\frac{x^2}{49} - \frac{y^2}{64} = -1\)
Let the major and minor axes of the ellipse E coincide with the transverse and conjugate axes of the hyperbola H, respectively. Let the product of the eccentricities of E and H be 1/2. If the length of the latus rectum of the ellipse E, then the value of 113l is equal to _____.

Let y = y(x) be the solution curve of the differential equation
\(\sin(2x^2) \log_e(\tan(x^2)) \,dy + (4xy - 4\sqrt{2}x\sin(x^2 - \frac{\pi}{4})) \,dx = 0, \quad 0 < x < \sqrt{\frac{\pi}{2}}\)
which passes through the point \((\sqrt{\frac{π}{6}},1)\). Then \(|y(\sqrt{\frac{π}{3}})|\)
is equal to _______.

Let
\(f(x) = 2x^2 - x - 1\ and\ S = \{ n \in \mathbb{Z} : |f(n)| \leq 800 \}\)
Then, the value of ∑_n∈S f(n) is equal to ________.

Let S be the set containing all 3 × 3 matrices with entries from {-1, 0, 1}. The total number of matrices A ∈ S such that the sum of all the diagonal elements of A^T A is 6 is ________.

If the length of the latus rectum of the ellipse x² + 4y² + 2x + 8y – λ = 0 is 4, and l is the length of its major axis, then λ + l is equal to ________.

Let
\(S = \left\{z∈C : z^2+\overline{z} = 0 \right\}\). Then \(∑_{z∈S}(Re(z)+Im(z))\)
is equal to____.

Let the line
\(\frac{x - 3}{7} = \frac{y - 2}{-1} = \frac{z - 3}{-4}\)
intersect the plane containing the lines
\(\frac{x - 4}{1} = \frac{y + 1}{-2} = \frac{z}{1}\) and \(4ax-y+5z-7a = 0 = 2x-5y-z-3, a∈R\)
at the point P(α, β, γ). Then the value of α + β + γ equals _____.

Let M and N be the number of points on the curve y⁵ – 9xy + 2x = 0, where the tangents to the curve are parallel to x-axis and y-axis, respectively. Then the value of M + N equals ________.

• (1) 15%
• (2) 25%
• (3) 75%
• (4) 5%

• (1)

• (2)

• (3)

• (4)

Sand is being dropped from a stationary dropper at a rate of 0.5 kgs^–1 on a conveyor belt moving with a velocity of 5 ms^–l. The power needed to keep the belt moving with the same velocity will be

• (1) 1.25 W
• (2) 2.5 W
• (3) 6.25 W
• (4) 12.5 W

• (1) 2 m
• (2) 0.5 m
• (3) 3.2 m
• (4) 0.8 ms

Two cylindrical vessels of equal cross-sectional area 16 cm² contain water upto heights 100 cm and 150 cm respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Take, density of water = 10³ kg/m³ and g = 10 ms^–2]

• (1) 0.25 J
• (2) 1 J
• (3) 8 J
• (4) 12 J

Two satellites A and B, having masses in the ratio 4 : 3, are revolving in circular orbits of radii 3r and 4r respectively around the earth. The ratio of total mechanical energy of A to B is

• (1) 9 : 16
• (2) 16 : 9
• (3) 1 : 1
• (4) 4 : 3

• (1) 18°C
• (2) 14°C
• (3) 45°C
• (4) 150°C

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

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

Two identical positive charges Q each are fixed at a distance of 2a apart from each other. Another point charge q₀ with mass m is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge q₀ executes SHM. The time period of oscillation of charge q₀ will be

• (1) \(\sqrt{\frac{4\pi^3ε0rna^3}{q0Q}}\)
• (2) \(\sqrt{\frac{qoQ}{4\pi^3εrna^3}}\)
• (3) \(\sqrt{\frac{2\pi^2ε_0rna^3}{q0Q}}\)
• (4) \(\sqrt{\frac{8\pi^3ε_0rna^3}{q0Q}}\)

Two sources of equal emfs are connected in series. This combination is connected to an external resistance R. The internal resistances of the two sources are r₁ and r₂ (r₁ > r₂). If the potential difference across the source of internal resistance r₁ is zero, then the value of R will be :

• (1) \(r_1-r_2\)
• (2) \(\frac{r_1r_2}{r_1+r_2}\)
• (3) \(\frac{r_1+r_2}{2}\)
• (4) \(r_2-r_1\)

A direct current of 4 A and an alternating current of peak value 4 A flow through resistance of 3 Ω and 2 Ω respectively. The ratio of heat produced in the two resistances in same interval of time will be :

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

A beam of light travelling along X-axis is described by the electric field E_y = 900sin ω(t – x/c). The ratio of electric force to magnetic force on a charge q moving along Y-axis with a speed of 3 × 10⁷ ms^–1 will be :
(Given speed of light = 3 × 10⁸ ms^–1)

• (1) 1 : 1
• (2) 1 : 10
• (3) 10 : 1
• (4) 1 : 2

A microscope was initially placed in air (refractive index 1). It is then immersed in oil (refractive index 2). For a light whose wavelength in air is λ, calculate the change of microscope’s resolving power due to oil and choose the correct option.

• (1) Resolving power will be\( \frac{1}{4}\) in the oil than it was in the air.
• (2) Resolving power will be twice in the oil than it was in the air.
• (3) Resolving power will be four times in the oil than it was in the air.
• (4) Resolving power will be \(\frac{1}{2}\) in the oil than it was in the air.

An electron (mass m) with an initial velocity
\(\vec{v}=v_0\hat{i}(v_0>0)\)
is moving in an electric field
\(\vec{E}=E_0\hat{i}(E_0>0)\)
where E₀ is constant. If at t = 0 de Broglie wavelength is
\(λ_0=\frac{ℎ}{mv_0}\)
, then its de Broglie wavelength after time t is given by

• (1) \(λ_0\)
• (2) \(λ_0\left(1+\frac{eE_0t}{mv_0}\right)\)
• (3) \(λ_0t\)
• (4) \(\frac{λ_0}{\left(1+\frac{eE_0t}{mv_0}\right)}\)

A logic gate circuit has two inputs A and B and output Y. The voltage waveforms of A, B and Y are shown below.
 

The logic gate circuit is :

• (1) AND gate
• (2) OR gate
• (3) NOR gate
• (4) NAND gate

Two bar magnets oscillate in a horizontal plane in earth’s magnetic field with time periods of 3 s and 4 s respectively. If their moments of inertia are in the ratio of 3 : 2, then the ratio of their magnetic moments will be :

• (1) 2 : 1
• (2) 8 : 3
• (3) 1 : 3
• (4) 27 : 16

A magnet hung at 45° with magnetic meridian makes an angle of 60° with the horizontal. The actual value of the angle of dip is

• (1) \(\tan^{-1}\left(\sqrt{\frac{3}{2}}\right)\)
• (2) \(\tan^{-1}\left(\sqrt{6}\right)\)
• (3) \(\tan^{-1}\left(\sqrt{\frac{2}{3}}\right)\)
• (4) \(\tan^{-1}\left(\sqrt{\frac{1}{2}}\right)\)

What is the half-life period of a radioactive material if its activity drops to 1/16 th of its initial value in 30 years?

• (1) 9.5 years
• (2) 8.5 years
• (3) 7.5 years
• (4) 10.5 years

At a particular station, the TV transmission tower has a height of 100 m. To triple its coverage range, height of the tower should be increased to

• (1) 200 m
• (2) 300 m
• (3) 600 m
• (4) 900 m

In a meter bridge experiment, for measuring unknown resistance ‘S’, the null point is obtained at a distance 30 cm from the left side as shown at point D. If R is 5.6 kΩ, then the value of unknown resistance ‘S’ will be ___Ω.

The one division of main scale of Vernier callipers reads 1mm and 10 divisions of Vernier scale is equal to the 9 division on main scale. When the two jaws of the instrument touch each other, the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between 4.1 cm and 4.2 cm and 6^th Vernier division coincides with a main scale division. The diameter of the bob will be ___ × 10^–2 cm.

Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the two beams are π/2 and π/3 at points A and B, respectively. The difference between the resultant intensities at the two points is xI. The value of x will be ___.

To light, a W, 100 V lamp is connected, in series with a capacitor of capacitance 
\(\frac{50}{π\sqrt{x}}\mu F\) with \(200 V\), 50 Hz AC source.
The value of x will be ___.

A 1 m long copper wire carries a current of 1 A. If the cross section of the wire is 2.0 mm² and the resistivity of copper is 1.7 × 10^–8 Ω, the force experienced by moving electron in the wire is ___ × 10^–23N.
(Charge on electron = 1.6 × 10^–19C)

A mass 0.9 kg, attached a horizontal spring, executes SHM with an amplitude A₁. When this mass passes through its mean position, then a smaller mass of 124 g is placed over it and both masses move together with amplitude A₂. If the ratio A₁/A₂ is α/(α – 1), then the value of α will be _____.

A square aluminium (shear modulus is 25 × 10⁹ Nm^–2) slab of side 60 cm and thickness 15 cm is subjected to a shearing force (on its narrow face) of 18.0 × 10⁴ N. The lower edge is riveted to the floor. The displacement of the upper edge is ______μm.

A pulley of radius 1.5 m is rotated about its axis by a force F = (12t – 3t²) N applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of rotation is 4.5 kg m², the number of rotations made by the pulley before its direction of motion is reversed, will be K/π. The value of K is ________.

A ball of mass m is thrown vertically upward. Another ball of mass 2 m is thrown at an angle θ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is 1/x. The value of x is _______.

\(250\) \(g\) solution of \(D-glucose\) in water contains 10.8% of carbon by weight. The molality of the solution is nearest to (Given: Atomic Weights are, \(H, 1 u; C, 12 u; O, 16 u\))

• (1) 1.03
• (2) 2.06
• (3) 3.09
• (4) 5.40

Given below are two statements.
Statement I: \(O_2, Cu^{2+}, \;and\; Fe^{3+}\) are weakly attracted by magnetic field and are magnetized in the same direction as magnetic field.
Statement II: \(NaCl\) and \(H_2O\) are weakly magnetized in opposite directions to the magnetic field.
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.

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Energy of 2s orbital of hydrogen atom is greater than that of 2s orbital of lithium.
Reason R : Energies of the orbitals in the same subshell decrease with increase in the atomic number.
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 but R is NOT the correct explanation of A.
• (3) A is true but R is false.
• (4) A is false but R is true.

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Activated charcoal adsorbs \(SO_2\) more efficiently than \(CH_4\).
Reason R: Gases with lower critical temperatures are readily adsorbed by activated charcoal.
In the light of the above statements, choose the correct 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) A is correct but R is not correct.
• (4) A is not correct but R is correct.

Boiling point of a 2% aqueous solution of a non-volatile solute A is equal to the boiling point of 8% aqueous solution of a non-volatile solute B. The relation between molecular weights of A and B is

• (1) \(M_A = 4M_B\)
• (2) \(M_B = 4M_A\)
• (3) \(M_A = 8M_B\)
• (4) \(M_B = 8M_A\)

The incorrect statement is

• (1) The first ionization enthalpy of K is less than that of Na and Li.
• (2) Xe does not have the lowest first ionization enthalpy in its group.
• (3) The first ionization enthalpy of element with atomic number 37 is lower than that of the element with atomic number 38.
• (4) The first ionization enthalpy of Ga is higher than that of the d-block element with atomic number 30.

Given below are two statements.
Statement I: Iron (III) catalyst, acidified \(K_2Cr_2O_7\) and neutral \(KMnO_4\) have the ability to oxidise \(I^–\) to \(I_2\) independently.
Statement II: Manganate ion is paramagnetic in nature and involves \(pπ – pπ\) bonding.
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 true but Statement II is false
• (4) Statement I is false but Statement II is true

The total number of \(Mn=O\) bonds in \(Mn_2O_7\) is ___.

• (1) 4
• (2) 5
• (3) 6
• (4) 3

Given below are two statements: one is labelled as Assertion A and, the other is labelled as Reason R.
Assertion A: [6] Annulene, [8] Annulene and cis-[10] Annulene, are respectively aromatic, not-aromatic and aromatic.
Reason R: Planarity is one, of the requirements of aromatic systems.
In the light of the 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) A is correct but R is not correct.
• (4) A is not correct but R is correct.

In the above reaction product ’P’ is

• (1)
• (2)
• (3)
• (4)

A sugar ‘X’ dehydrates very slowly under acidic conditions to give furfural which on further reaction with resorcinol gives the coloured product after some time. Sugar ‘X’ is

• (1) Aldopentose
• (2) Aldotetrose
• (3) Oxalic acid
• (4) Ketotetrose

In Carius method of estimation of halogen, 0.45 g of an organic compound gave 0.36 g of AgBr. Find out the percentage of bromine in the compound.
(Molar masses: AgBr = 188 g mol^–1; Br = 80 g mol^–1)

• (1) 34.04%
• (2) 40.04%
• (3) 36.03%
• (4) 38.04%

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

1. Liquation
2. Calcination
3. Electrolysis
4. Leaching
5. Distillation

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

Given below are two statements.
Statement I : Hydrogen peroxide can act as an oxidizing agent in both acidic and basic conditions.
Statement II : Density of hydrogen peroxide at 298 K is lower than that of \(D_2O\).
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 true but Statement II is false
• (4) Statement I is false but Statement II is true

Given below are two statements.
Statement I : The chlorides of Be and Al have Cl-bridged structure. Both are soluble in organic solvents and act as Lewis bases.
Statement II : Hydroxides of Be and Al dissolve in excess alkali to give beryllate and aluminate ions.
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 true but Statement II is false
• (4) Statement I is false but Statement II is true

Which oxoacid of phosphorous has the highest number of oxygen atoms present in its chemical formula?

• (1) Pyrophosphorus acid
• (2) Hypophosphoric acid
• (3) Phosphoric acid
• (4) Pyrophosphoric acid

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

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

Match the List I  with List II

List I		List II
A		I	Anti-depressant
B		II	550 times sweeter than cane sugar
C		III	Narcotic analgesic
D		IV	Antiseptic

Choose the correct answer from the options given below:

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

20 mL of 0.02 M K₂Cr₂O₇ solution is used for the titration of 10 mL of Fe²⁺ solution in the acidic medium. The molarity of Fe²⁺ solution is ______×10^–2 M. (Nearest integer)

2NO + 2H₂ → N₂ + 2H₂O
The above reaction has been studied at 800 °C. The related data is given in the table below.
The order of the reaction with respect to NO is ___.

Amongst the following, the number of oxide(s) which are paramagnetic in nature is
Na₂O, KO₂, NO₂, N₂O, ClO₂, NO, SO₂, Cl₂O

The molar heat capacity for an ideal gas at constant pressure is 20.785 J K^–1 mol^–1. The change in internal energy is 5000 J upon heating it from 300 K to 500 K. The number of moles of the gas at constant volume is _____. (Nearest integer)
(Given : R = 8.314 JK-1mol-1).

According to MO theory, number of species/ions from the following having identical bond order is ___.
CN-, NO+, O2, O+2, O2+2

At 310 K, the solubility of CaF₂ in water is 2.34 ×10^–3 g/100 mL. The solubility product of CaF₂ is _____ × 10^–8 (mol/L)³.
(Given molar mass : CaF₂ = 78 g mol^–1).

The conductivity of a solution of complex with formula CoCl₃(NH₃)₄ corresponds to 1 : 1 electrolyte, then the primary valency of central metal ion is ______.

In the titration of KMnO₄ and oxalic acid in acidic medium, the change in oxidation number of carbon at the end point is _____.

Optical activity of an enantiomeric mixture is +12.6° and the specific rotation of (+) isomer is +30°. The optical purity is _______%.

In the following reaction,
the % yield for reaction I is 60% and that of reaction II is 50%. The overall yield of the complete reaction is _______%. [Nearest integer].