JEE Main 2023 Question Paper Jan 29 Shift 1: Download Paper with Solution PDF Here

Let \(λ ≠ 0\) be a real number. Let α, β be the roots of the equation \(14x^2 – 31x + 3λ = 0\) and α, γ be the roots of the equation \(35x^2 – 53x + 4λ = 0\). Then \(\frac{3\alpha}{\beta}\) and \(\frac{4\alpha}{\lambda}\) are the roots of the equation

• (1) 7x2 + 245x – 250 = 0
• (2) 49x2 + 245x + 250 = 0
• (3) 7x2 – 245x + 250 = 0
• (4) 49x2 – 245x + 250 = 0

Let B and C be the two points on the line \(y + x = 0\) such that B and C are symmetric with respect to the origin. Suppose A is a point on \(y – 2x = 2\) such that \(\Delta ABC\) is an equilateral triangle. Then, the area of the \(\Delta ABC\) is

• (1) 3√3
• (2) 2√3
• (3) 10/√3
• (4) 8/√3

Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X denote the number of rotten apples. If μ and σ² represent mean and variance of X, respectively, then 10(μ²+σ²) is equal to

• (1) 25
• (2) 250
• (3) 30
• (4) 20

Let \(f(\theta)=3[sin^4(\frac{3\pi}{2}-\theta)+sin^4(3\pi+θ)]-2(1-sin^22\theta)\) and \(S=\{\theta∈[0,\pi]:f'(\theta)=-\frac{\sqrt3}{2}\}\). If \(4\beta \sum_{\theta∈S}\theta\), then \(f(\beta)\) is equal to

• (1) 9/8
• (2) 3/2
• (3) 5/4
• (4) 11/8

Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is

• (1) 1/6
• (2) 5/36
• (3) 2/15
• (4) 5/24

Let the tangents at the points A(4, –11) and B(8, –5) on the circle \(x^2+y^2-3x+10y-15=0\), intersect at the point C. Then the radius of the circle, whose centre is C and the line joining A and B is its tangent, is equal to

• (1) √13
• (2) \( \frac{3 \sqrt{3}}{3}\)
• (3) \( \frac{2 \sqrt{13}}{3}\)
• (4) 2√13

Let \(f(x)=x+\frac{a}{\pi^2-4} sinx+\frac{b}{\pi^2-4} cos x\), \(x∈R\) be a function which satisfies \(f(x)=x+∫_0^{\frac{\pi}{2}} sin(x+y) f(y)dy\). Then (a+b) equal to

• (1) -π(π+2)
• (2) -π(π-2)
• (3) -2π(π+2)
• (4) -2π(π-2)

Let α and β be real numbers. Consider a \(3 \times 3\) matrix A such that \(A^2 = 3A + \alpha I\). If \(A^4 = 21A + \beta I\), then

• (1) α = 1
• (2) α=4
• (3) β=8
• (4) β=-8

A light ray emits from the origin making an angle \(30\degree\) with the positive x-axis. After getting reflected by the line \(x + y = 1\), if this ray intersects x-axis at Q, then the abscissa of Q is

• (1) 2/3-√3
• (2) 2/3+√3
• (3) √3/2(√3+1)
• (4) 2/(√3-1)

For two non-zero complex numbers z₁ and z₂, if Re(z₁z₂) = 0 and Re(z₁ + z₂), then which of the following are possible?
A. Im(z₁) > 0 and Im(z₂) > 0 |
B. Im(z₁) < 0 and Im(z₂) > 0 
C. Im(z₁) > 0 and Im(z₂) < 0 
D. Im(z₁) < 0 and Im(z₂) < 0 
Choose the correct answer from the options given below

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

Let \(y = f(x)\) be the solution of the differential equation \(y(x + 1)dx - x^2dy = 0\), \(y(1) = e\). Then \(lim_{x→0^-} f (x)\) is equal to

• (1) 1/e
• (2) 0
• (3) 1/e2
• (4) e2

Let \(\Delta\) be the area of the region \(\{(x,y)∈R^2:x^2+y^2≤21,y^2≤4x,x≥1\}\). Then \(\frac{1}{2}(\Delta-21\text{ sin}^{-1} (\frac{2}{\sqrt7}))\) is equal to

• (1) √3-4/3
• (2) 2√3-1/3
• (3) √3-2/3
• (4) 2√3-2/3

The domain of \(f(x)=\frac{log_{x+1}(x-2)}{e^{2logx}-(2x+3)}\), \(x∈R\) is

• (1) R-{-1,3}
• (2) (-1,∞)-{3}
• (3) R-{3}
• (4) (2,∞)-{3}

Let f: R→R be a function such that \(f(x)=\frac{x^2+2x+1}{x^2+1}\). Then

• (1) f(x) is many-one in (–∞,–1)
• (2) f(x) is one-one in [1, ∞) but not in (–∞, ∞)
• (3) f(x) is many-one in (1, ∞)
• (4) f(x) is one-one in (–∞, ∞)

Let [x] denote the greatest integer ≤ x. Consider the function \(f(x)=max \{x^2,1+[x] \}\). Then the value of the integral \(∫_0^2 f(x)dx\) is

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

Let
\(A=\{(x,y) ∈R^2:y≥0,2x≤y≤\sqrt{4-(x-1)^2} \}\)
and
\(B=\{(x,y) ∈R\times R:0≤y≤min \{2x,\sqrt{4-(x-1)^2}\}\}\)
Then the ratio of the area of A to the area of B is

• (1) π/π-1
• (2) π+1/π-1
• (3) π-1/π+1
• (4) π/π+1

Consider the following system of equations
\(\alpha x + 2y + z = 1\)
\(2\alpha x + 3y + z = 1\)
\(3x + \alpha y + 2z = b\)
For some \(\alpha,\beta∈R\) then which of the following is NOT correct?

• (1) It has no solution if α = – 1 and β≠2
• (2) It has no solution if α ≠– 1 and β=2
• (3) It has no solution if α =3 and for all β≠2
• (4) It has no solution if α =– 1 and for all β ∈ R

If the vectors \(\overrightarrow{a} =\lambda \hat{i}+\mu\hat{j}+4\hat{k}\), \(\overrightarrow{b}=-2\hat{i}+4\hat{j}-2\hat{k}\) and \(\overrightarrow{c}=2\hat{i}+3\hat{j}+\hat{k}\) are coplanar and the projection of \(\overrightarrow{a}\) on the vector \(\overrightarrow{b}\) is \(\sqrt{54}\) units, then the sum of all possible values of \(\lambda + \mu\) is equal to

• (1) 24
• (2) 6
• (3) 0
• (4) 18

Let \(x = 2\) be a root of the equation \(x^2 + px + q = 0\) and \(f(x)=\begin{cases}\frac{1-cos(x^2-4px+q^2+8q+16)}{(x-2p)^4} & x≠2p\\0 & x=2p\end{cases}\).
Then \(lim_{x \rightarrow 2p}[f(x)]\), where [·] denotes greatest integer function, is

• (1) 1
• (2) 2
• (3) 0
• (4) -1

If p, q and r are three propositions, then which of the following combination of truth values of p, q and r makes the logical expression \({(p∨q)∧((∼p)∨r)}🡢((∼q)∨r)\) false?

• (1) p = F, q = T, r = F
• (2) p = T, q = F, r = T
• (3) p = T, q = T, r = F
• (4) p = T, q = F, r = F

Let a₁, a₂, a₃, … be a G.P of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and seventh terms is 24, then a₁ a₉+a₂ a₄ a₉+a₅+a₇ is equal to __________.

Suppose f is a function satisfying \(f(x + y) + f(x) + f(y)\) for all \(x, y ∈N\) and \(f(1)=\frac{1}{5}\). If \(∑_{n=1}^{m} \frac{f(n)}{n(n+1)(n+2)}=\frac{1}{2}\), then m is equal to _______.

Let the coefficients of three consecutive terms in the binomial expansion of (1 + 2x)n be the ratio 2 : 5 : 8. Then the coefficient of the term, which is in the middle of these three terms, is _______.

If the co-efficient of x⁹ in \((αx^3+\frac{1}{βx})^{11}\) and the co-efficient of x^-9 in \((αx-\frac{1}{βx^3})^{11}\) are equal, then \((αβ)^2\) is equal to ________.

If all the six digit numbers x₁ x₂ x₃ x₄ x₅ x₆ with \(0<x_1<x_2<x_3<x_4<x_5<x_6\) are arranged in the increasing order, then the sum of the digits in the 72^th number is _____________.

Let \(f : R → R\) be a differentiable function that satisfies the relation \(f(x + y) = f(x) + f(y) – 1, ∀x, y ∈R\). If \(f'(0) = 2\), then \(|f(–2)|\) is equal to ___________.

Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with serial number. For example, the number 77777 has serial number 1. Then the serial number of 35337 is _________

Let the co-ordinates of one vertex of \(\Delta ABC\) be \(A(0, 2, \alpha)\) and the other two vertices lie on the line \(x+\frac{\alpha}{5}=y-\frac{1}{2}=z+\frac{4}{3}\) For \(\alpha∈Z\), if the area of \(\Delta ABC\) is 21 sq. units and the line segment BC has length \(2\sqrt{21}\) units, then α² is equal to ___________.

Let the equation of the plane P containing the line \(x+10=\frac{8-y}{2}=z\) be \(ax + by + 3z = 2(a + b)\) and the distance of the plane P from the point (1, 27, 7) be c. Then a²+b²+c² is equal to ____________.

Let a b, and c be three non-zero non-coplanar vectors. Let the position vectors of four points A, B, C and D be \(a-b+c\), \(λa-3b+4c\), \(-a+2b-3c\) and \(2a-4b+6c\) respectively. If AB AC , and AD are coplanar, then λ is equal to ____.

Two particles of equal mass ‘m’ move in a circle of radius ‘r’ under the action of their mutual gravitational attraction. The speed of each particle will be :

• (1) \( \sqrt{\frac{GM}{2r}} \)
• (2) \( \sqrt{\frac{GM}{4r}} \)
• (3) \( \sqrt{\frac{GM}{r}} \)
• (4) \( \sqrt{\frac{4GM}{r}} \)

Find the mutual inductance in the arrangement, when a small circular loop of radius R is placed inside a large square loop of side \(L\) (\(L \gg R\)). The loops are coplanar and their centers coincide:

• (1) \(M = \frac{\sqrt{2} \mu_0 R^2}{L}\)
• (2) \(M = \frac{2 \sqrt{2} \mu_0 R}{L^2}\)
• (3) \(M = \frac{2 \sqrt{2} \mu_0 R^2}{L}\)
• (4) \(M = \frac{\sqrt{2} \mu_0 R}{L^2}\)

In a cuboid of dimension \(2L \times 2L \times L\), a charge q is placed at the center of the surface ‘S’ having area of 4 L². The flux through the opposite surface to ‘S’ is:

• (1) \( \frac{q}{2\epsilon_0} \)
• (2) \( \frac{q}{6\epsilon_0} \)
• (3) \( \frac{q}{12\epsilon_0} \)
• (4) \( \frac{q}{3\epsilon_0} \)

The surface tension of a soap bubble is \(2 \times 10^{-2} \, \text{N/m}\). Work done to increase the radius of the bubble from 3.5 cm to 7 cm will be:

• (1) \(4.072 \times 10^{-3} \, \text{J}\)
• (2) \(5.76 \times 10^{-3} \, \text{J}\)
• (3) \(9.24 \times 10^{-3} \, \text{J}\)
• (4) \(1.848 \times 10^{-3} \, \text{J}\)

Assertion A: If \( dQ \) and \( dW \) represent the heat supplied to the system and the work done on the system respectively, then according to the first law of thermodynamics: \[ dQ = dU - dW. \]
Reason R: First law of thermodynamics is based on the law of conservation of energy.
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) A is correct but R is not correct
• (3) A is not correct but R is correct
• (4) Both A and R are correct but R is not the correct explanation of A

The magnitude of magnetic induction at the mid-point O due to the current arrangement shown in the figure is:

• (1) 0
• (2) \( \frac{\mu_0 I}{2 \pi a} \)
• (3) \( \frac{\mu_0 I}{\pi a} \)
• (4) \( \frac{\mu_0 I}{4 \pi a} \)

A stone is projected at an angle of \(30\degree\) to the horizontal. The ratio of kinetic energy at projection to its kinetic energy at the highest point is:

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

A block of mass m slides down the plane inclined at angle \(30\degree\) with an acceleration \(\frac{g}{4}\). The value of the coefficient of kinetic friction will be:

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

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

A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of the car will be, if the friction coefficient between tyres and road is 0.34. (Take g = 10 m/s²):

• (1) 13.4m/s
• (2) 13m/s
• (3) 22.4m/s
• (4) 17m/s

Which of the following are true?
A. Speed of light in vacuum is dependent on the direction of propagation. 
B. Speed of light in a medium is independent of the wavelength of light. 
C. The speed of light is independent of the motion of the source. 
D. The speed of light in a medium is independent of intensity.
Choose the correct answer from the options given below:

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

In a Young’s double slit experiment, two slits are illuminated with light of wavelength \(800 \, \text{nm}\). The first minimum is detected at \(P\). The value of slit separation \(a\) is:

• (1) 0.4 mm
• (2) 0.1 mm
• (3) 0.2 mm
• (4) 0.5 mm

A single current-carrying loop of wire carrying current I flows in the anticlockwise direction (seen from the +z direction) and lies in the xy plane. The plot of \(\hat{j}\) component of magnetic field (\(B_y\)) at a distance a (less than radius of the coil) and on the yz plane vs z coordinate looks like:

• (1)

• (2)

• (3)

• (4)

Which of the following statements is not correct in the case of light emitting diodes (LEDs)?
A. It is a heavily doped p-n junction. 
B. It emits light only when it is forward-biased. 
C. It emits light only when it is reverse-biased. 
D. The energy of the light emitted is equal to or slightly less then the energy gap of the semiconductor used.
Choose the correct answer from the options given below:

• (1) C and D
• (2) C
• (3) B
• (4) A

A bicycle tyre is filled with air having pressure of 270 kPa at \(27\degree  C\). The approximate pressure of the air in the tyre when the temperature increases to \(36\degree C\) is:

• (1) 270 kPa
• (2) 278 kPa
• (3) 360 kPa
• (4) 262 kPa

The threshold wavelength for photoelectric emission from a material is \(5500Å\). Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a 
A. 75 W infra-red lamp 
B. 10 W infra-red lamp 
C. 75 W ultra-violet lamp 
D. 10 W ultra-violet lamp 
Choose the correct answer from the options given below:

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

Ratio of thermal energy released in two resistors R and 3R connected in parallel in an electric circuit is:

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

If a radioactive element with a half-life of 30 min undergoes beta decay. The fraction of the radioactive element that remains undecayed after 90 min is:

• (1) \(\frac{1}{8}\)
• (2) \(\frac{1}{4}\)
• (3) \(\frac{1}{16}\)
• (4) \(\frac{1}{2}\)

A person observes two moving trains, ‘A’ reaching the station and ‘B’ leaving the station with equal speed of 30 m/s. If both trains emit sounds with frequency 300 Hz, (Speed of sound: 330 m/s) approximate difference of frequencies heard by the person will be:

• (1) 33 Hz
• (2) 10 Hz
• (3) 55 Hz
• (4) 80 Hz

If the height of transmitting and receiving antennas are 80 m each, the maximum line of sight distance will be:
Given: Earth’s radius = \(6.4 \times 106\text{ m}\)

• (1) 64 km
• (2) 36 km
• (3) 28 km
• (4) 32 km

Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is _____ degree.

A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be ____ ms^–1.

In a metre bridge experiment, the balance point is obtained if the gaps are closed by \(2 \Omega\) and \(3 \Omega\). A shunt of \(X \Omega\) is added to \(3 \Omega\) resistor to shift the balancing point by 22.5 cm. The value of X is _______ .

A point charge \(q_1 = 4q_0\) is placed at origin. Another point charge \(q_2 = –q_0\) is placed at \(x = 12\text{ cm}\). Charge of proton is q₀. The proton is placed on x axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the origin is _____ cm.

Three identical polaroids \(P_1\), \(P_2\), and \(P_3\) are placed one after another. The pass axis of \(P_2\) and \(P_3\) are inclined at angles of \(60^\circ\) and \(90^\circ\) with respect to the axis of \(P_1\). The source \(S\) has an intensity of \(\frac{256 \, \text{W}}{\text{m}^2}\). The intensity of light at point \(O\) is _____ \(\frac{\text{W}}{\text{m}^2}\).

A 0.4 kg mass takes 8 s to reach ground when dropped from a certain height ‘P’ above surface of earth. The loss of potential energy in the last second of fall is ____ J. (Take g = 10 m/s²)

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B = 0.8 T. When released the radius of the loop starts shrinking at a constant rate of 2 cm/s. The induced emf in the loop at an instant when the radius of the loop is 10 cm will be _____ mV.

A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact with the floor for 0.2 s. The average acceleration during contact is_____ m/s². (Given g =10 m/s²)

A body cools from \(60\degree C\) to \(40\degree C\) in 6 minutes. If, temperature of surroundings is \(10\degree C\). Then, after the next 6 minutes, its temperature will be ______\(\degree C\).

A radioactive element \({}^{242}_{92}X\) emits two \(\alpha\)-particles, one electron, and two positrons. The product nucleus is represented by \({}^{234}_{P}Y.\) The value of \(P\) is _______.

The major product ‘P’ for the following sequence of reactions is :

• (1)
• (2)
• (3)
• (4)

The magnetic behavior of Li₂O, Na₂O₂ and KO₂, respectively, are

• (1) Paramagnetic, paramagnetic and diamagnetic
• (2) Diamagnetic, diamagnetic and paramagnetic
• (3) Paramagnetic, diamagnetic and paramagnetic
• (4) Diamagnetic, paramagnetic and diamagnetic

Compound that will give positive Lassaigne’s test for both nitrogen and halogen is

• (1) CH₃NH₂.HCl
• (2) NH₂OH .HCl
• (3) NH₄Cl
• (4) N₂H₄ . HCl

Identify the correct order for the given property for following compounds. 

Choose the correct answer from the option given below :

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

The bond dissociation energy is highest for

• (1) Cl₂
• (2) I₂
• (3) F₂
• (4) Br₂

Number of cyclic tripeptides formed with 2 amino acids A and B is:

• (1) 3
• (2) 4
• (3) 2
• (4) 5

The shortest wavelength of hydrogen atom in Lyman series is λ. The longest wavelength in Balmer series of He⁺ is

• (1) 5/9λ
• (2) 5λ/9
• (3) 36λ/5
• (4) 9λ/5

Match List I with List II

Choose the correct answer from the option given below:

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

The increasing order of pKa for the following phenols is 
(A) 2,4-Dinitrophenol 
(B) 4-Nitrophenol 
(C) 2,4,5-Trimethylphenol 
(D) Phenol 
(E) 3-Chlorophenol 
Choose the correct answer from the option given below :

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

Chiral complex from the following is 

 

• (1) trans – [Co(NH₃)₄Cl₂] ⁺ 
• (2) cis – [PtCl₂(en)₂] ²⁺
• (3) cis – [PtCl₂(NH₃)₂] 
• (4) trans – [PtCl₂(en)₂] ²⁺

The standard electrode potential \((\frac{M^{3+}}{M^{2+}})\) for V, Cr, Mn & Co are –0.26 V, –0.41 V, +1.57 V and +1.97 V, respectively. The metal ions which can liberate H₂ from a dilute acid are

• (1) V²⁺ and Cr²⁺
• (2) V²⁺ and Mn²⁺
• (3) Cr²⁺ and Co²⁺
• (4) Mn²⁺ and Co²⁺

Match List I with List II.

Choose the correct answer from the options given below:

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

The correct order of hydration enthalpies is 
(A) K⁺ 
(B) Rb²⁺ 
(C) Mg²⁺ 
(D) Cs⁺ 
(E) Ca²⁺ 
Choose the correct answer from the options given below:

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

Correct statement about smog is

• (1) NO₂ is present in classical smog
• (2) Classical smog also has high concentration of oxidizing agents
• (3) Photochemical smog has high concentration of oxidizing agents
• (4) Both NO₂ and SO₂ are present in classical smog

During the borax bead test with CuSO₄, a blue-green colour of the bead was observed in oxidizing flame due to the formation of

• (1) CuO
• (2) \(Cu(BO_2)_2\)
• (3) \(Cu_3B_2\)
• (4) Cu

Which of the given compounds can enhance the efficiency of hydrogen storage tank?

• (1) \(Li/P_4\)
• (2) \(NaNi_5\)
• (3) \(SiH_4\)
• (4) Di-isobutylaluminium hydride

“A” obtained by Ostwald’s method involving air oxidation of\( NH_3\), upon further air oxidation produces “B”. “B” on hydration forms an oxoacid of Nitrogen along with evolution of “A”. The oxoacid also produces “A” and gives positive brown ring test. 

• (1) \(NO, NO_2\)
• (2) \(N_2O_3, NO_2\)
• (3) \(NO_2, N_2O_4\)
• (4) \(NO_2, N_2O_5\)

Which of the following salt solutions would coagulate the colloid solution formed when FeCl₃ is added to NaOH solution, at the fastest rate?

• (1) 10 mL of 0.1 mol dm^–3 Ca3(PO₄)₂
• (2) 10 mL of 0.2 mol dm^–3 AlCl₃
• (3) 10 mL of 0.1 mol dm^–3 Na₂SO₄
• (4) 10 mL of 0.15 mol dm^–3 CaCl₂

For 1 mol of gas, the plot of pV vs. p is shown below. p is the pressure and V is the volume of the gas. What is the value of compressibility factor at point A?

• (1) \(1-\frac{a}{RTV}\)
• (2) \(1+\frac{b}{V}\)
• (3) \(1-\frac{b}{V}\)
• (4) \(1+\frac{a}{RTV}\)

The reaction representing the Mond process for metal refining is _________.

• (1) \(2\text{K[Au(CN)}_2] + \text{Zn} \xrightarrow{\Delta} \text{K}_2[\text{Zn(CN)}_4] + 2\text{Au}\)
• (2) \(\text{Ni} + 4\text{CO} \xrightarrow{\Delta} \text{Ni(CO)}_4\)
• (3) \(\text{Zr} + 2\text{I}_2 \xrightarrow{\Delta} \text{ZrI}_4\)
• (4) \(\text{ZnO} + \text{C} \xrightarrow{\Delta} \text{Zn} + \text{CO}\)

Following chromatogram was developed by adsorption of compound 'A' on a 6 cm TLC glass plate. Retardation factor of the compound 'A' is_____ \(\times 10^{–1}\).

Millimoles of calcium hydroxide required to produce 100 mL of the aqueous solution of pH 12 is \(x \times 10^{-1}\). The value of \(x\) is — (Nearest integer).

For certain chemical reaction X 🡢 Y, the rate of formation of product is plotted against the time as shown in the figure. The number of correct statement/s from the following is______.
(A) Over all order of this reaction is one
(B) Order of this reaction can't be determined 
(C) In region I and III, the reaction is of first and zero order respectively 
(D) In region-II, the reaction is of first order 
(E) In region-II, the order of reaction is in the range of 0.1 to 0.9.

The number of molecules or ions from the following, which do not have odd number of electrons are ______.
(A) NO₂
(B) ICI₄^- 
(C) BrF₃ 
(D) CIO₂ 
(E) NO₂²⁺ 
(F) NO

Following figure shows dependence of molar conductance of two electrolytes on concentration. Λ^o _m is the limiting molar conductivity. The number of incorrect statement(s) from the following is ________ 

(A) \(\Lambda \text{o m}\) for electrolyte A is obtained by extrapolation. 
(B) For electrolyte B, \(\Lambda \text{m}\) vs \(\sqrt c\) graph is a straight line with intercept equal to o \(\Lambda \text{m}\)
(C) At infinite dilution, the value of degree of dissociation approaches zero for electrolyte B. 
(D) Λo m for any electrolyte A or B can be calculated using \(\lambda0\) for individual ions.

Solid Lead nitrate is dissolved in 1 litre of water. The solution was found to boil at \(100.15\degree C\). When 0.2 mol of NaCl is added to the resulting solution, it was observed that the solution froze at \(–0.8\degree C\). The solubility product of PbCl₂ formed is ________ \(\times 10^{–6}\) at 298 K. (Nearest integer) Given: \(Kb = 0.5 K \text{ kg mol}^{–1}\) and \(Kf = 1.8 K \text{ kg mol}^{–1}\).
Assume molality to be equal to molarity in all cases.

Water decomposes at 2300 K
\(H_2O(g)\longrightarrow H (g)+(\frac{1}{2})O_2(g)\)
The percent of water decomposing at 2300 K and 1 bar is ________ (Nearest integer). Equilibrium constant for the reaction is \(2 \times 10^{–3}\) at 2300 K.

Consider the following reaction approaching equilibrium at \(27\degree C\) and 1 atm pressure

The standard Gibb's energy change \((\Delta rG\degree)\) at \(27\degree C\) is (–)_____ kJ mol^–1 (Nearest integer).
(Given: R = 8.3 J K^–1 mol^–1 and In 10 = 2.3)

The sum of bridging carbonyls in W(CO)₆ and Mn₂(CO)₁₀ is_____.

17 mg of a hydrocarbon (M.F. C₁₀H₁₆) takes up 8.40 mL of the H₂ gas measured at \(0\degree C\) and 760 mm of Hg. Ozonolysis of the same hydrocarbon yields

The number of double bond/s present in the hydrocarbon is_______.