JEE Main 2024 27 Jan Shift 1 Question Paper (Available)- Download Solution PDF With Answer Keys

Evaluate the integral  \(\int_{0}^{1} \frac{1}{\sqrt{3+x} + \sqrt{1+x}} \, dx\) Given that the integral can be expressed in the form \(a + b\sqrt{2} + c\sqrt{3}\), where \(a, b, c\) are rational numbers, find the value of \(2a + 3b - 4c\).

• (1) \( 4 \)
• (2) \( 10 \)
• (3) \( 7 \)
• (4) \( 8 \)

If \(S = \{z \in C : |z – i| = |z + i| = |z–1|\}\), then, n(S) is:

• (1) 1
• (2) 0
• (3) 3
• (4) 4

Let \( S = \{ 1, 2, 3, \ldots, 10 \} \). Suppose \( M \) is the set of all the subsets of \( S \), then the relation \( R = \{ (A, B): A \cap B \neq \phi; A, B \in M \} \) is:

• (1) symmetric and reflexive only
• (2) reflexive only
• (3) symmetric and transitive only
• (4) symmetric only

If the shortest distance of the parabola \(y^{2}=4x\) from the centre of the circle \(x² + y² - 4x - 16y + 64 = 0\) is d, then d² is equal to:

• (1) 16
• (2) 24
• (3) 36
• (4) 20

If \( (a, b) \) be the orthocenter of the triangle whose vertices are \( (1, 2) \), \( (2, 3) \), and \( (3, 1) \), and \( I_1 = \int_a^b x \sin(4x - x^2) dx \), \( I_2 = \int_a^b \sin(4x - x^2) dx \), then \( 36 \frac{I_1}{I_2} \) is equal to:

• (1) 80
• (2) 88
• (3) 66
• (4) 72

Let \( x = x(t) \) and \( y = y(t) \) be solutions of the differential equations \( \frac{dx}{dt} + ax = 0 \) and \( \frac{dy}{dt} + by = 0 \) respectively, \( a, b \in \mathbb{R} \). Given \( x(0) = 2 \), \( y(0) = 1 \), and \( 3y(1) = 2x(1) \), the value of t for which \( x(t) = y(t) \), is:

• (1) \( \log_{ \frac{2}{3}}2 \)
• (2) \( \log_{4} 3 \)
• (3) \( \log_{3} 4 \)
• (4) \(\log_4{{\frac{2}{3}}} \)

The distance of the point \( (7, -2, 11) \) from the line \( \frac{x - 6}{1} = \frac{y - 4}{0} = \frac{z - 8}{3} \) along the line \( \frac{x - 5}{2} = \frac{y - 1}{-3} = \frac{z - 5}{6} \), is:

• (1) 12
• (2) 14
• (3) 18
• (4) 21

The length of the chord of the ellipse \(\frac{x^2}{25} + \frac{y^2}{16} = 1\), whose mid-point is \(\left(1, \frac{2}{5}\right)\), is equal to:

• (1) \(\frac{\sqrt{1691}}{5}\)
• (2) \(\frac{\sqrt{2009}}{5}\)
• (3) \(\frac{\sqrt{1741}}{5}\)
• (4) \(\frac{\sqrt{1541}}{5}\)

Consider the function.\(f(x) = \begin{cases}  \frac{a(7x - 12 - x^2)}{b(x^2 - 7x + 12)} & , \quad x < 3 \\[8pt] \frac{\sin(x - 3)}{2^{x - \lfloor x \rfloor}} & , \quad x > 3 \\[8pt] b & , \quad x = 3  \end{cases}\)Where \(\lfloor x \rfloor\)denotes the greatest integer less than or equal to \(x\). If \(S\) denotes the set of all ordered pairs \((a, b)\) such that \(f(x)\) is continuous at \(x = 3\), then the number of elements in \(S\) is:

• (1) 2
• (2) Infinitely many
• (3) 4
• (4) 1

If \( a = \lim_{{x \to 0}} \frac{\sqrt{1 + \sqrt{1 + x^4}} - \sqrt{2}}{x^4} \) and \( b = \lim_{{x \to 0}} \frac{\sin^2 x}{\sqrt{2} - \sqrt{1 + \cos x}} \), then the value of \( ab^3 \) is:

• (1) 36
• (2) 32
• (3) 25
• (4) 30

Consider the matrix \( f(x) = \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix} \).
Given below are two statements:
Statement I: \( f(-x) \) is the inverse of the matrix \( f(x) \).
Statement II: \( f(x) f(y) = f(x + y) \).
In the light of the above statements, choose the correct answer from the options given below:"

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

Four distinct points \( (2k, 3k), (1, 0), (0, 1) \) and \( (0, 0) \) lie on a circle for \( k \) equal to:

• (1) \(\frac{2}{13}\)
• (2) \(\frac{5}{13}\)
• (3) \(\frac{1}{13}\)
• (4) \(\frac{2}{13}\)

If the shortest distance between the lines \(\frac{x - 4}{1} = \frac{y + 1}{2} = \frac{z}{-3} and \frac{x - \lambda}{2} = \frac{y + 1}{4} = \frac{z - 2}{-5}\) is \(\frac{6}{\sqrt{5}}\), then the sum of all possible values of \(\lambda\) is:

• (1) \( 5 \)
• (2) \( 8 \)
• (3) \( 7 \)
• (4) \( 10 \)

The portion of the line \( 4x + 5y = 20 \) in the first quadrant is trisected by the lines \( L_1 \) and \( L_2 \) passing through the origin. The tangent of an angle between the lines \( L_1 \) and \( L_2 \) is:

• (1) \(\frac{8}{5}\)
• (2) \(\frac{25}{41}\)
• (3) \(\frac{2}{5}\)
• (4) \(\frac{30}{41}\)

\(^{n-1}C_r = (k^2 - 8)  ^{n}C_{r+1}\) if and only if:

• (1) \( 2\sqrt{2} < k ≤ 3 \)
• (2) \( 2\sqrt{3} < k ≤ 3\sqrt{2} \)
• (3) \( 2\sqrt{3} < k <3 \sqrt{3} \)
• (4) \( 2\sqrt{2} < k < 2\sqrt{3} \)

The number of common terms in the progressions 4, 9, 14, 19, ...,up to 25th term and 3, 6, 9, 12, ..., up to 37th term is:

• (1) 9
• (2) 5
• (3) 7
• (4) 8

Let \( a_1, a_2, \ldots, a_{10} \) be 10 observations such that   \(\sum_{k=1}^{10} a_k = 50 \quad \text{and} \quad \sum_{1 \leq k < j \leq 10} a_k \cdot a_j = 1100\). Then the standard deviation of \( a_1, a_2, \ldots, a_{10} \) is equal to:

• (1) \( 5 \)
• (2) \( \sqrt{5} \)
• (3) \( 10 \)
• (4) \( \sqrt{15} \)

Let \(\vec{a} = \hat{i} + 2\hat{j} + \hat{k}\), \(\vec{b} = 3(\hat{i} - \hat{j} + \hat{k})\). Let \(\vec{c}\) be the vector such that \(\vec{a} \times \vec{c} = \vec{b}\) and \(\vec{a} \cdot \vec{c} = 3\). Then \(\vec{a} \cdot ((\vec{c} \times \vec{b}) - \vec{b} \cdot \vec{c})\) is equal to:

• (1) 32
• (2) 24
• (3) 20
• (4) 36

If \( A \) denotes the sum of all the coefficients in the expansion of \( (1 - 3x + 10x^2)^n \) and \( B \) denotes the sum of all the coefficients in the expansion of \( (1 + x^2)^n \), then:

• (1) \( A = B^3 \)
• (2) \( 3A = B \)
• (3) \( B = A^3 \)
• (4) \( A = 3B \)

The function \( f : \mathbb{N} - \{1\} \to \mathbb{N} \); defined by \( f(n) \) = the highest prime factor of \( n \), is:

• (1) both one-one and onto
• (2) one-one only
• (3) onto only
• (4) neither one-one nor onto

If \( 8 = 3 + \frac{1}{4}(3 + p) + \frac{1}{4^2}(3 + 2p) + \frac{1}{4^3}(3 + 3p) + \ldots \infty \), then the value of \( p \) is ______.

If the solution of the differential equation \((2x + 3y - 2) \, dx + (4x + 6y - 7) \, dy = 0, \quad y(0) = 3,\) is  \(\alpha x + \beta y + 3 \log_e |2x + 3y - \gamma| = 6,\) then \(\alpha + 2\beta + 3\gamma\) is equal to ____.

Let \( f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3) \), \( x \in \mathbb{R} \). Then \( f'(10) \) is equal to ______.

Let the set of all \( a \in \mathbb{R} \) such that the equation \(\cos 2x + a \sin x = 2a - 7\) has a solution be \([p, q]\) and \( r = \tan 9^\circ - \tan 27^\circ - \frac{1}{\cot 63^\circ + \tan 81^\circ} \), then \( pqr \) is equal to ______.

Let for a differentiable function \(f : (0, \infty) \rightarrow \mathbb{R}\), \(f(x) - f(y) \geq \log_e \left( \frac{x}{y} \right) + x - y, \quad \forall \; x, y \in (0, \infty).\) 
Then \(\sum_{n=1}^{20} f'\left(\frac{1}{n^2}\right)\) is equal to ____.

Let the area of the region \(\{(x, y) : x - 2y + 4 \geq 0, x + 2y^2 \geq 0, x + 4y^2 \leq 8, y \geq 0\}\) be \(\frac{m}{n}\), where \( m \) and \( n \) are coprime numbers. Then \( m + n \) is equal to ______.

Let \( A = \begin{bmatrix} 2 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1 \end{bmatrix} \), \( B = [B_1, B_2, B_3] \), where \( B_1, B_2, B_3 \) are column matrices, and \( AB_1 = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} \), \( AB_2 = \begin{bmatrix} 2 \\ 3 \\ 0 \end{bmatrix} \), \( AB_3 = \begin{bmatrix} 3 \\ 2 \\ 1 \end{bmatrix} \).
If \(\alpha = |B|\) and \(\beta\) is the sum of all the diagonal elements of B, then \(\alpha^3 + \beta^3\) is equal to _____.

The least positive integral value of \( \alpha \), for which the angle between the vectors \( \alpha \hat{i} - 2\hat{j} + 2\hat{k} \) and \( \alpha \hat{i} + 2\alpha \hat{j} - 2\hat{k} \) is acute, is ______.

If \(\alpha\) satisfies the equation \(x^2 + x + 1 = 0\) and \((1 + \alpha)^7 = A + B \alpha + C \alpha^2\), \(A, B, C \geq 0\), then \(5(3A - 2B - C)\) is equal to ______.

A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required and let \(a=P(X=3), b=P(X≥3)\), and \(( c = P(X \geq 6|X>3).\) Then \(\frac{b+c}{a}\) is equals to ____.

Position of an ant \( S \) (in meters) moving in the Y-Z plane is given by \( S = 2t \hat{j} + 5t \hat{k} \) (where \( t \) is in seconds). The magnitude and direction of velocity of the ant at \( t = 1 \, s \) will be:

• (1) 16 m/s in y-direction
• (2) 4 m/s in x-direction
• (3) 9 m/s in z-direction
• (4) 4 m/s in y-direction

Given below are two statements:
Statement (I): Viscosity of gases is greater than that of liquids. 
Statement (II): Surface tension of a liquid decreases due to the presence of insoluble impurities. 
In the light of the above statements, choose the most appropriate answer from the options given below:

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

If the refractive index of the material of a prism is \(cot\bigg(\frac{A}{2}\bigg)\), where A is the angle of the prism, then the angle of minimum deviation will be:

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

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If \( \vec{E} \) and \( \vec{B} \) represent the electric and magnetic fields respectively, then the region of space may have:
(A) \( \vec{E} = 0, \vec{B} = 0 \) 
(B) \( \vec{E} = 0, \vec{B} \neq 0 \) 
(C) \( \vec{E} \neq 0, \vec{B} = 0 \) 
(D) \( \vec{E} \neq 0, \vec{B} \neq 0 \) 
Choose the most appropriate answer from the options given below:

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

The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be:

• (1) g/4
• (2) 4g
• (3) g/2
• (4) 2g

A train is moving with a speed of 12 m/s on rails which are 1.5 m apart. To negotiate a curve radius of 400 m, the height by which the outer rail should be raised with respect to the inner rail is (Given, \( g = 10 \, \text{m/s}^2 \)):

• (1) 6.0 cm
• (2) 5.4 cm
• (3) 4.8 cm
• (4) 4.2 cm

Which of the following circuits is reverse-biased?

• (1)
• (2)

• (3)

• (4)

Identify the physical quantity that cannot be measured using a spherometer:

• (1) Radius of curvature of concave surface
• (2) Specific rotation of liquids
• (3) Thickness of thin plates
• (4) Radius of curvature of convex surface

Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of the magnitude of their linear momentum is:

• (1) 3:5
• (2) 2:5
• (3) 5:4
• (4) 4:5

0.08 kg of air is heated at constant volume through 5°C. The specific heat of air at constant volume is 0.17 kcal/kg°C and \( J = 4.18 \) joule/cal. The change in its internal energy is approximately:

• (1) 318 J
• (2) 298 J
• (3) 284 J
• (4) 142 J

The radius of the third stationary orbit of an electron in Bohr's atom is \( R \). The radius of the fourth stationary orbit will be:

• (1) \(\frac{4}{3} R\)
• (2) \(\frac{16}{9} R\)
• (3) \(\frac{3}{4} R\)
• (4) \(\frac{9}{16} R\)

A rectangular loop of length 2.5 m and width 2 m is placed at 60° to a magnetic field of 4 T. The loop is removed from the field in 10 sec. The average emf induced in the loop during this time is:

• (1) -2V
• (2) \(+2V\)
• (3) \(+ 1V\)
• (4) – 1V

• (1) 0 V
• (2) \( \sqrt{6} \) V
• (3) \(\sqrt{3} \) V
• (4) 3 V

A convex lens of focal length 40 cm forms an image of an extended source of light on a photo-electric cell. A current \( I \) is produced. The lens is replaced by another convex lens having the same diameter but focal length 20 cm. The photoelectric current now is:

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

A body of mass 1000 kg is moving horizontally with a velocity of 6 m/s. If 200 kg extra mass is added, the final velocity (in m/s) is:

• (1) 5 m/s
• (2) 4 m/s
• (3) 2 m/s
• (4) 6 m/s

A plane electromagnetic wave propagating in x-direction is described by \( E_y = (200 \, \text{V/m}) \sin(1.5 \times 10^7 t - 0.05 x) \). The intensity of the wave is:

• (1) 35.4 W/m²
• (2) 53.1 W/m²
• (3) 26.6 W/m²
• (4) 106.2 W/m²

Given below are two statements: 
Statement (I): Planck's constant and angular momentum have the same dimensions. 
Statement (II): Linear momentum and moment of force have the same dimensions. 
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

A wire of length 10 cm and radius \( \sqrt{7} \times 10^{-4} \, m \) is connected across the right gap of a meter bridge. When a resistance of 4.5 \( \Omega \) is connected on the left gap by using a resistance box, the balance length is found to be at 60 cm from the left end. If the resistivity of the wire is \( R \times 10^{-7} \, \Omega \, m \), then the value of \( R \) is:

• (1) 63
• (2) 70
• (3) 66
• (4) 35

A wire of resistance \( R \) and length \( L \) is cut into 5 equal parts. If these parts are joined in parallel, then the resultant resistance will be:

• (1) 5 R
• (2) 25 R
• (3) \( \frac{R}{25} \)
• (4) \( \frac{R}{5} \)

The average kinetic energy of a monatomic molecule is 0.414 eV at temperature: (Use \( k_B = 1.38 \times 10^{-23} \, \text{J/mol-K} \))

• (1) 3000 K
• (2) 3200 K
• (3) 1600 K
• (4) 1500 K

A particle starts from origin at \( t = 0 \) with a velocity \( 5\hat{i} \, \text{m/s} \) and moves in the \( x\)-\( y \) plane under the action of a force that produces a constant acceleration of \( (3\hat{i} + 2\hat{j}) \, \text{m/s}^2 \). If the \( x \)-coordinate of the particle at that instant is 84 m, then the speed of the particle at this time is \( \sqrt{\alpha} \, \text{m/s} \). The value of \( \alpha \) is ______.

A thin metallic wire having a cross-sectional area of \( 10^{-4} \, \text{m}^2 \) is used to make a ring of radius 30 cm. A positive charge of \( 2\pi \, C \) is uniformly distributed over the ring, while another positive charge of 30 pC is kept at the center of the ring. The tension in the ring is ______ N; provided that the ring does not deform (neglect the influence of gravity).
(Given, \(\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{SI units}\))

Two coils have mutual inductance 0.002 H. The current changes in the first coil according to the relation \( i = i_0 \sin \omega t \), where \( i_0 = 5 \, \text{A} \) and \( \omega = 50\pi \, \text{rad/s} \). The maximum value of emf in the second coil is \( \frac{\pi}{\alpha} \). The value of \( \alpha \) is ______.

Two immiscible liquids of refractive indices \( \frac{8}{5} \) and \( \frac{3}{2} \) respectively are put in a beaker as shown in the figure. The height of each column is 6 cm. A coin is placed at the bottom of the beaker. For near-normal vision, the apparent depth of the coin is \( \frac{\alpha}{4} \) cm. The value of \( \alpha \) is ______.

Four particles each of mass 1 kg are placed at four corners of a square of side 2 m. Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertices is _____ kgm².

A particle executes simple harmonic motion with an amplitude of 4 cm. At the mean position, the velocity of the particle is 10 cm/s. The distance of the particle from the mean position when its speed becomes 5 cm/s is \( \sqrt{\alpha} \) cm, where \(\alpha\) = ______

Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is 5.0 cm. The magnitude of the magnetic field at a point P midway between the wires is ____ μT
(Given: \(\mu_0 = 4\pi \times 10^{-7} \, \text{TmA}^{-1}\))

The charge accumulated on the capacitor connected in the following circuit is ____ µC
(Given \( C = 150 \, \mu \text{F} \))

If the average depth of an ocean is 4000 m and the bulk modulus of water is \( 2 \times 10^9 \, \text{N/m}^2 \), then the fractional compression \( \frac{\Delta V}{V} \) of water at the bottom of the ocean is \( \alpha \times 10^{-2} \). The value of \( \alpha \) is ______ (Given \( g = 10 \, \text{m/s}^2 \), \( p = 1000 \, \text{kg/m}^3 \)).

Two nucleotides are joined together by a linkage known as:

• (1) Disulphide linkage
• (2) Glycosidic linkage
• (3) Phosphodiester linkage
• (4) Peptide linkage

Highest enol content will be shown by:

• (1)

• (2)

• (3)

• (4)

Element not showing variable oxidation state is:

• (1) Chlorine
• (2) Fluorine
• (3) Bromine
• (4) Iodine

Which of the following is strongest Bronsted base?

• (1)

• (2)

• (3)

• (4)

Which of the following electronic configurations would be associated with the highest magnetic moment?

• (1) \([Ar] 3d^7\)
• (2) \([Ar] 3d^8\)
• (3) \([Ar] 3d^2\)
• (4) \([Ar] 3d^6\)

Which of the following has highly acidic hydrogen?

• (1)
• (2)
• (3)
• (4)

A solution of two miscible liquids showing negative deviation from Raoult's law will have:

• (1) Increased vapour pressure, increased boiling point
• (2) Increased vapour pressure, decreased boiling point
• (3) Decreased vapour pressure, decreased boiling point
• (4) Decreased vapour pressure, increased boiling point

Consider the following complex ions:
P = \([FeF_6]^{3-}\) 
Q = \([V(H_2O)_6]^{2+}\) 
R = \([Fe(H_2O)_6]^{2+}\) 
The correct order of the complex ions, according to their spin-only magnetic moment values (in B.M.) is:

• (1) R < Q < P
• (2) R < P < Q
• (3) Q < R < P
• (4) Q < P < R

Choose the polar molecule from the following:

• (1) \(CH_2=CH_2\)
• (2) \(CHCl_3\)
• (3) \(CCl_4\)
• (4) \(CO_2\)

Given below are two statements:
Statement (I): The 4f and 5f-series of elements are placed separately in the Periodic table to preserve the principle of classification.
Statement (II): s-block elements can be found in pure form in nature.
In the light of the above statements, choose the most appropriate answer from the options given below:

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

Given below are two statements: 
Statement (I): p-nitrophenol is more acidic than m-nitrophenol and o-nitrophenol. 
Statement (II): Ethanol will give immediate turbidity with Lucas reagent. 
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) Both Statement I and Statement II are true
• (3) Statement I is true but Statement II is false
• (4) Statement I is false but Statement II is true

The ascending order of acidity of –OH group in the following compounds is: 

Choose the correct answer from the options given below :

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

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Melting point of Boron (2453 K) is unusually high in group 13 elements.
Reason (R): Solid Boron has a very strong crystalline lattice. 
In the light of the above statements, choose the most appropriate answer from the options given below:

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

Cyclohexene is _________ type of an organic compound.

• (1) Alicyclic
• (2) Acyclic
• (3) Benzenoid non-aromatic
• (4) Benzenoid aromatic

Yellow compound of lead chromate gets dissolved on treatment with hot NaOH solution. The product of lead formed is a:

• (1) Tetraanionic complex with coordination number six
• (2) Neutral complex with coordination number four
• (3) Dianionic complex with coordination number six
• (4) Dianionic complex with coordination number four

Given below are two statements:
Statement (I): Aqueous solution of ammonium carbonate is basic.
Statement (II): Acidic/basic nature of salt solution of a salt of weak acid and weak base depends on \( K_a \) and \( K_b \) value of acid and the base forming it.
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) Statement I is correct but Statement II is incorrect
• (3) Both Statement I and Statement II are incorrect
• (4) Statement I is incorrect but Statement II is correct

IUPAC name of the following compound (P) is:

• (1) 1-Ethyl-5, 5-dimethylcyclohexane
• (2) 3-Ethyl-1,1-dimethylcyclohexane
• (3) 1-Ethyl-3, 3-dimethylcyclohexane
• (4) 1,1-Dimethyl-3-ethylcyclohexane

NaCl reacts with conc. \( H_2SO_4 \) and \( K_2Cr_2O_7 \) to give reddish fumes (B), which react with NaOH to give yellow solution (C). (B) and (C) respectively are:

• (1) \(CrO_2Cl_2, Na_2CrO_4\)
• (2) \(Na_2CrO_4, CrO_2Cl_2\)
• (3) \(CrO_2Cl_2, KHSO_4\)
• (4) \(CrO_2Cl_2, Na_2Cr_2O_7\)

The correct statement regarding nucleophilic substitution reaction in a chiral alkyl halide is:

• (1) Retention occurs in \(SN_1\) reaction and inversion occurs in \( SN_2 \) reaction.
• (2) Racemisation occurs in \( SN_1 \) reaction and retention occurs in \( SN_2 \) reaction.
• (3) Racemisation occurs in both \( SN_1 \) and \( SN_2 \) reactions.
• (4) Racemisation occurs in \( S_N1 \) reaction and inversion occurs in \( S_N2 \) reaction.

The electronic configuration of Neodymium (60) Nd is

• (1) \([Xe] 4f^46s^2\)
• (2) \([Xe] 5f^1\)
• (3) \([Xe] 4f^26s^2\)
• (4) \([Xe] 5f^44d^1\)

The mass of silver (Molar mass of Ag : 108 gmol^–1 ) displaced by a quantity of electricity which displaces 5600 mL of O₂ at S.T.P. will be _____ g.

Consider the following data for the given reaction
 \(2\)\(\text{HI}_{(g)}\) \(\rightarrow\) \(\text{H}_2{(g)}\)\( + \)\(\text{I}_2{(g)}\)

The order of the reaction is __________.

Mass of methane required to produce 22 g of CO₂​ after complete combustion is ______ g.
(Given Molar mass in g mol⁻¹: C=12.0, H=1.0, O=16.0).

If three moles of an ideal gas at 300 K expand isothermally from 30 dm³ to 45 dm³ against a constant opposing pressure of 80 kPa, then the amount of heat transferred is ______ J.

3-Methylhex-2-ene on reaction with HBr in presence of peroxide forms an addition product (A). The number of possible stereoisomers for 'A' is ______.

Among the given organic compounds, the total number of aromatic compounds is

Among the following, total number of meta directing functional groups is (Integer based) \(−OCH_3​, −NO_2​, −CN, −CH_3​, −NHCOCH_3​, −COR, −OH, −COOH, −Cl\).

The number of electrons present in all the completely filled subshells having n=4 and s=+½​ is _____. (Where n = principal quantum number and s = spin quantum number).

Sum of bond order of CO and NO⁺ is _____.

From the given list, the number of compounds with +4 oxidation state of Sulphur_____.
\(SO_3​, H_2​SO_3​, SOCl_2​, SF_4​, BaSO_4​, H_2​S_2​O_7\)​.