JEE Main 2024 30Jan Shift 2 Question Paper (Available)- Download Solution PDF with Answer Key

Let \( f : \mathbb{R} \rightarrow \mathbb{R} \) be a function defined by
\[ f(x) = \frac{x}{(1 + x^4)^{1/4}} \]
and \( g(x) = f(f(f(x))) \). Then
\[ 18 \int_{\sqrt[3]{\frac{8}{3}}}^{\sqrt[3]{\frac{4}{3}}} x^3 g(x) \, dx \]
equals: 

• (1) 33
• (2) 36
• (3) 42
• (4) 39

Let \( a \) and \( b \) be two distinct positive real numbers. Let the 11^th term of a GP, whose first term is \( a \) and third term is \( b \), be equal to the \( p \)-th term of another GP, whose first term is \( a \) and fifth term is \( b \). Then \( p \) is equal to

• (1) 24
• (2) 25
• (3) 21
• (4) 18

Let \( y = f(x) \) be a thrice differentiable function in \( (-5, 5) \). Let the tangents to the curve \( y = f(x) \) at \( (1, f(1)) \) and \( (3, f(3)) \) make angles \( \frac{\pi}{6} \) and \( \frac{\pi}{4} \), respectively, with the positive x-axis. If \(2 \int_{\frac{1}{\sqrt{3}}}^{1} \left( \left( f'(t) \right)^2 + 1 \right) f''(t) \, dt = \alpha + \beta \sqrt{3}\) where \( \alpha \), \( \beta \) are integers, then the value of \( \alpha + \beta \) equals

• (1) -14
• (2) 26
• (3) -16
• (4) 36

For \( \alpha, \beta \in \left( 0, \frac{\pi}{2} \right) \), let \( 3 \sin(\alpha + \beta) = 2 \sin(\alpha - \beta) \) and a real number \( k \) be such that \( \tan \alpha = k \tan \beta \). Then the value of \( k \) is equal to:

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

If \( z \) is a complex number, then the number of common roots of the equation \( z^{1985} + z^{100} + 1 = 0 \) and \( z^3 + 2z^2 + 2z + 1 = 0 \), is equal to:

• (1) 1
• (2) 0
• (3) 3
• (4) 4

Let \( f : \mathbb{R} - \{0\} \rightarrow \mathbb{R} \) be a function satisfying\[f\left( \frac{x}{y} \right) = \frac{f(x)}{f(y)}\]for all \( x, y \), \( f(y) \neq 0 \). If \( f'(1) = 2024 \),then

• (1) \( x f'(x) - 2024 f(x) = 0 \)
• (2) \( x f'(x) + 2024 f(x) = 0 \)
• (3) \( x f'(x) + f(x) = 2024 \)
• (4) \( x f'(x) - 2023 f(x) = 0 \)

Let \(R=\begin{pmatrix}x&0&0\\0&y&0\\0&0&z\end{pmatrix}\) be a non-zero \(3\times3\) matrix, where \(x\sin\theta=y\sin\left(\theta+\dfrac{2\pi}{3}\right)=z\sin\left(\theta+\dfrac{4\pi}{3}\right)\ne0,\ \theta\in(0,2\pi)\). For a square matrix \(M\), let trace \((M)\) denote the sum of all the diagonal entries of \(M\). Then, among the statements:
(I) Trace \((R)=0\)
(II) If trace \((\operatorname{adj}(\operatorname{adj}(R)))=0\), then \(R\) has exactly one non-zero entry.

• (1) Only (I) is true
• (2) Only (II) is true
• (3) Both (I) and (II) are true
• (4) Neither (I) nor (II) is true

If \(x^2-y^2+2hxy+2gx+2fy+c=0\) is the locus of points such that it is equidistant from the lines \(x+2y-8=0\) and \(2x+y+7=0\), then value of \(g+c+h-f\) is

• (1) 29
• (2) 6
• (3) 14
• (4) 8

Let \( a \) and \( b \) be real constants such that the function \( f \) defined by \[f(x) = \begin{cases} x^2 + 3x + a, & x \leq 1 \\ bx + 2, & x>1 \end{cases}\]be differentiable on \( \mathbb{R} \). Then, the value of \( \int_{-2}^{2} f(x) \, dx \) equals

• (1) \( \frac{15}{6} \)
• (2) \( \frac{19}{6} \)
• (3) 21
• (4) 17

Let \( f : \mathbb{R} \rightarrow \mathbb{R} \) be defined \( f(x) = ae^{2x} + be^x + cx \). If \( f(0) = -1 \), \( f'(\log_e 2) = 21 \) and
\[\int_{0}^{\log_e 4} (f(x) - cx) \, dx = \frac{39}{2}\]
then the value of \( |a + b + c| \) equals:

• (1) 16
• (2) 10
• (3) 12
• (4) 8

Let \( L_1 : \vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \lambda (\hat{i} - \hat{j} + 2\hat{k}) \), \( \lambda \in \mathbb{R} \)
\( L_2 : \vec{r} = (\hat{j} - \hat{k}) + \mu (3\hat{i} + \hat{j} + p\hat{k}) \), \( \mu \in \mathbb{R} \) and
\( L_3 : \vec{r} = \delta (\ell \hat{i} + m \hat{j} + n \hat{k}) \), \( \delta \in \mathbb{R} \)
Be three lines such that \( L_1 \) is perpendicular to \( L_2 \) and \( L_3 \) is perpendicular to both \( L_1 \) and \( L_2 \). Then the point which lies on \( L_3 \) is

• (1) \((-1, 7, 4)\)
• (2) \((-1, -7, 4)\)
• (3) \((1, 7, -4)\)
• (4) \((1, -7, 4)\)

Let \( \vec{a} = \hat{i} + \alpha \hat{j} + \beta \hat{k} \), \( \alpha, \beta \in \mathbb{R} \). Let a vector \( \vec{b} \) be such that the angle between \( \vec{a} \) and \( \vec{b} \) is \( \frac{\pi}{4} \) and \( |\vec{b}|^2 = 6 \),
If \( \vec{a} \times\vec{b} = 3\sqrt{2} \), then the value of \( \left( \alpha^2 + \beta^2 \right) | \vec{a} \times \vec{b} |^2 \) is equal to

• (1) 90
• (2) 75
• (3) 95
• (4) 85

Let \( P \) be a point on the hyperbola \( H: \frac{x^2}{9} - \frac{y^2}{4} = 1 \), in the first quadrant such that the area of the triangle formed by \( P \) and the two foci of \( H \) is \( 2 \sqrt{13} \). Then, the square of the distance of \( P \) from the origin is

• (1) 18
• (2) 26
• (3) 22
• (4) 20

Let \( f(x) = (x + 3)^2 (x - 2)^3 \), \( x \in [-4, 4] \). If \( M \) and \( m \) are the maximum and minimum values of \( f \), respectively in \([-4, 4]\), then the value of \( M - m \) is:

• (1) 600
• (2) 392
• (3) 608
• (4) 108

Suppose \( 2 - p \), \( p \), \( 2 - \alpha \), \( \alpha \) are the coefficients of four consecutive terms in the expansion of \( (1 + x)^n \). Then the value of \( p^2 - \alpha^2 + 6\alpha + 2p \) equals

• (1) 4
• (2) 10
• (3) 8
• (4) 6

Consider the system of linear equations
x + y + z = 5,
x + 2y + λ²z = 9,
x + 3y + λz = μ,
where λ, μ ∈ ℝ.Then, which of the following statement is NOT correct?

• (1) System has infinite number of solutions if λ = 1 and μ = 13
• (2) System is inconsistent if λ = 1 and μ ≠ 13
• (3) System is consistent if λ ≠ 1 and μ = 13
• (4) System has a unique solution if λ ≠ 1 and μ ≠ 13

Let \( \vec{a} \) and \( \vec{b} \) be two vectors such that \( |\vec{b}| = 1 \) and \( |\vec{b} \times \vec{a}| = 2 \). Then \( \left| (\vec{b} \times \vec{a}) - \vec{b} \right|^2 \) is equal to

• (1) 3
• (2) 5
• (3) 1
• (4) 4

If the domain of the function \( f(x) = \log_e \left( \frac{2x + 3}{4x^2 + x - 3} \right) + \cos^{-1} \left( \frac{2x - 1}{x + 2} \right) \) is \( (\alpha, \beta] \), then the value of \( 5\beta - 4\alpha \) is equal to

• (1) 12
• (2) 10
• (3) 11
• (4) 9

Bag A contains 3 white, 7 red balls and bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from bag A, if the ball drawn is white, is:

• (1) \( \frac{1}{4} \)
• (2) \( \frac{1}{9} \)
• (3) \( \frac{1}{3} \)
• (4) \( \frac{3}{10} \)

Let \( A(10, 0) \) and \( B(0, \beta) \) be the points on the line \( 5x + 7y = 50 \). Let the point \( P \) divide the line segment \( AB \) internally in the ratio \( 7 : 3 \). Let \( 3x - 25 = 0 \) be a directrix of the ellipse \( E : \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) and the corresponding focus be \( S \). If from \( S \), the perpendicular on the x-axis passes through \( P \), then the length of the latus rectum of \( E \) is equal to

• (1) \( \frac{25}{3} \)
• (2) \( \frac{32}{9} \)
• (3) \( \frac{32}{5} \)
• (4) \( \frac{25}{9} \)

In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : A, B and C . A student is required to attempt total 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions and section C has 6 questions, then the total number of ways a student can select 15 questions is _______ .

Let \( Y = Y(X) \) be a curve lying in the first quadrant such that the area enclosed by the line \( Y - y = Y'(x) (X - x) \) and the coordinate axes, where \( (x, y) \) is any point on the curve, is always\[\frac{-y^2}{2Y'(x)} + 1, \quad Y'(x) \neq 0.\]If \( Y(1) = 1 \), then \( 12Y(2) \) equals ______.

The number of real solutions of the equation\[x \left( x^2 + 3|x| + 5|x - 1| + 6|x - 2| \right) = 0\]is ______.

Consider two circles \( C_1 : x^2 + y^2 = 25 \) and \( C_2 : (x - \alpha)^2 + y^2 = 16 \), where \( \alpha \in (5, 9) \). Let the angle between the two radii (one to each circle) drawn from one of the intersection points of \( C_1 \) and \( C_2 \) be\[\sin^{-1} \left( \frac{\sqrt{63}}{8} \right).\]If the length of the common chord of \( C_1 \) and \( C_2 \) is \( \beta \), then the value of \( (\alpha \beta)^2 \) equals ____.

Let a line passing through the point \((-1, 2, 3)\) intersect the lines\( L_1 : \frac{x - 1}{3} = \frac{y - 2}{2} = \frac{z + 1}{-2} \) at \( M(\alpha, \beta, \gamma) \) and\( L_2 : \frac{x + 2}{-3} = \frac{y - 2}{-2} = \frac{z - 1}{4} \) at \( N(a, b, c) \).Then the value of \( \frac{(\alpha + \beta + \gamma)^2}{(a + b + c)^2} \) equals ____.

The variance \(\sigma^2\) of the data

The area of the region enclosed by the parabola \((y - 2)^2 = x - 1\), the line \(x - 2y + 4 = 0\) and the positive coordinate axes is ______.

The number of symmetric relations defined on the set {1, 2, 3, 4} which are not reflexive is _____.

Let \( \alpha = \sum_{k=0}^{n} \left( \frac{\binom{n}{k}}{k+1} \right)^2 \) and \( \beta = \sum_{k=0}^{n-1} \left( \frac{\binom{n}{k} \binom{n}{k+1}}{k+2} \right) \).
If \( 5\alpha = 6\beta \), then \( n \) equals __________.

Let \( S_n \) be the sum to \( n \)-terms of an arithmetic progression \( 3, 7, 11, \ldots \).
If \( 40 < \left( \frac{6}{n(n+1)} \sum_{k=1}^{n} S_k \right) <42 \), then \( n \) equals ___.

• (1) 0.01 mm
• (2) 0.1 mm
• (3) 0.1 cm
• (4) 0.01 cm

• (1) 2
• (2) 1
• (3) 3
• (4) 0

In the given circuit, the voltage across load resistance (\( R_L \)) is:

• (1) 8.75 V
• (2) 9.00 V
• (3) 8.50 V
• (4) 14.00 V

An alternating voltage \( V(t) = 220 \sin 100 \pi t \) volt is applied to a purely resistive load of 50 \( \Omega \). The time taken for the current to rise from half of the peak value to the peak value is:

• (1) 5 ms
• (2) 3.3 ms
• (3) 7.2 ms
• (4) 2.2 ms

Choose the correct statement for processes A & B shown in figure.

• (1) \( PV^n = k \) for process B and \( PV = k \) for process A.
• (2) \( PV = k \) for process B and A.
• (3) \( P^{n-1} = k \) for process B and \( T^n = k \) for process A.
• (4) \( T^n P^{n-1} = k \) for process A and \( PV = k \) for process B.

A block of mass m is placed on a surface having vertical cross section given by \(y=\frac{x^2}{4}\). If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is:

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

Ice at temperature –10°C is converted to steam at 100°C, the curve plotted between temperature (T) and time (t) when it is being heated by constant power source is

• (1)

• (2)

• (3)

• (4)

When a potential difference V is applied across a wire of resistance R, it dissipates energy at a rate W. If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the same supply, the energy dissipation rate will become:

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

Match List I with List II

Choose the correct answer from the options given below:

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

• (1) \( c \sqrt{\frac{c \Delta M}{M}} \)
• (2) \( c \sqrt{\frac{2 \Delta M}{M}} \)
• (3) \( \frac{\Delta M c^2}{3} \)
• (4) \( \sqrt{\frac{2c \Delta M}{M}} \)

For the photoelectric effect, the maximum kinetic energy \( E_k \) of the photoelectrons is plotted against the frequency \( \nu \) of the incident photons as shown in figure. The slope of the graph gives

• (1) Planck’s constant
• (2) Charge of electron
• (3) Work function of the metal
• (4) Ratio of Planck’s constant to electric charge

• (1) \(\frac{I_0}{2}\)
• (2) \(\frac{I_0}{2\sqrt2}\)
• (3) \(\frac{I_0}{4}\)
• (4) \(\frac{I_0}{8}\)

\(\text{If three moles of monoatomic gas } \left( \gamma = \frac{5}{3} \right) \text{ is mixed with two moles of a diatomic gas } \left( \gamma = \frac{7}{5} \right),\)\(\text{the value of adiabatic exponent } \gamma \text{ for the mixture is:}\)

• (1) 1.75
• (2) 1.4
• (3) 1.52
• (4) 1.35

Three blocks A, B and C are pulled on a horizontal smooth surface by a force of 80 N as shown in figure

The tensions T1 and T2 in the string are respectively:

• (1) 40N, 64N
• (2) 60N, 80N
• (3) 88N, 96N
• (4) 80N, 100N

• (1) \( T = 2\pi r \sqrt{\frac{m}{2kq}} \)
• (2) \( T^2 = \frac{4\pi m r^3}{2kq} \)
• (3) \( T = \frac{1}{2\pi r} \sqrt{\frac{m}{2kq}} \)
• (4) \( T = \frac{2kq}{m} \)

• (1) 11.2 km/s
• (2) 8.4 km/s
• (3) 4.2 km/s
• (4) 7.9 km/s

Projectiles A and B are thrown at angles of \(45^{\circ}\) and \(60^{\circ}\) with vertical respectively from top of a \(400\ m\) high tower. If their ranges and times of flight are same, the ratio of their speeds of projection \(v_A:v_B\) is :
[Take \(g=10\ ms^{-2}\)]

• (1) \(1:2\)
• (2) \(\sqrt2:1\)
• (3) \(1:\sqrt2\)
• (4) \(1:\sqrt3\)

If the total energy transferred to a surface in time \( t \) is \( 6.48 \times 10^5 \, \text{J} \), then the magnitude of the total momentum delivered to this surface for complete absorption will be :

• (1) \( 2.16 \times 10^{-3} \, \text{kg m/s} \)
• (2) \( 2.46 \times 10^{-3} \, \text{kg m/s} \)
• (3) \( 1.58 \times 10^{-3} \, \text{kg m/s} \)
• (4) \( 4.32 \times 10^{-3} \, \text{kg m/s} \)

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

A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of 60° by a force of 10 N parallel to the inclined surface as shown in the figure. When the block is pushed up by 10 m along the inclined surface, the work done against frictional force is:

• (1) \( \sqrt{5} \, J \)
• (2) \( 5 \times 10^3 \, J \)
• (3) 5J
• (4) \( 10 \, J \)

A big drop is formed by coalescing 1000 small identical drops of water. If E₁ be the total surface energy of 1000 small drops of water and E₂ be the surface energy of single big drop of water, the E₁ : E₂ is x : 1 where x = ________.

A power transmission line feeds input power at 2.3 kV to a step down transformer with its primary winding having 3000 turns. The output power is delivered at 230 V by the transformer. The current in the primary of the transformer is 5A and its efficiency is 90%. The winding of transformer is made of copper. The output current of transformer is_____A.

The current of 5 A flows in a square loop of sides 1 m placed in air. The magnetic field at the center of the loop is \(X\sqrt{2} \times 10^{-7} \, T\). The value of X = _________.

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 37° with each other. When suspended in a liquid of density 0.7 g/cm³, the angle remains the same. If the density of the material of the sphere is 1.4 g/cm³, the dielectric constant of the liquid is ___________. (tan 37° =\( \frac{3}{4}\))

In an experiment to measure the focal length (f) of a convex lens, the magnitude of object distance (x) and the image distance (y) are measured with reference to the focal point of the lens. The y-x plot is shown in figure.
The focal length of the lens is_____cm.

The products A and B formed in the following reaction scheme are respectively

• (1)
• (2)

• (3)
• (4)

The correct stability order of carbocations is

• (1) \((\text{CH}_3)_3\text{C}^+ \gt \text{CH}_3 - \text{CH}_2 \gt (\text{CH}_3)_2\text{CH}^+ \gt \text{CH}_3\)
• (2)

• (3)
• (4)

Which among the following purification methods is based on the principle of “Solubility” in two different solvents?

• (1) Column Chromatography
• (2) Sublimation
• (3) Differential Extraction
• (4) Distillation

IUPAC name of following compound is

• (1) 2-Aminopentanitrile
• (2) 3-Aminobutanenitrile
• (3) 2-Aminobutanitrile
• (4) 3-Aminopropanenitrile

The solution from the following with highest depression in freezing point/lowest freezing point is

• (1) 180 g of benzoic acid dissolved in benzene
• (2) 180 g of acetic acid dissolved in benzene
• (3) 180 g of acetic acid dissolved in water
• (4) 180 g of glucose dissolved in water

Statement I: Since fluorine is more electronegative than nitrogen, the net dipole moment of NF₃ is greater than NH₃.
Statement II: In NH₃, the orbital dipole due to the lone pair and the dipole moment of NH bonds are in opposite directions, but in NF₃, the orbital dipole due to the lone pair and the dipole moments of N-F bonds are in the same direction.
In light of the above statements, choose the most appropriate from the options given below:

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

\(\text{A and B formed in the following reactions are:}\) \[ \text{CrO}_2\text{Cl}_2 + 4\text{NaOH} \rightarrow \text{A} + 2\text{NaCl} + 2\text{H}_2\text{O} \] \[ \text{A} + 2\text{HCl} + 2\text{H}_2\text{O}_2 \rightarrow \text{B} + 3\text{H}_2\text{O} \]

• (1) \(\text{A} = \text{Na}_2\text{CrO}_4, \, \text{B} = \text{CrO}_3\)
• (2) \(\text{A} = \text{Na}_2\text{Cr}_2\text{O}_4, \, \text{B} = \text{CrO}_4\)
• (3) \(\text{A} = \text{Na}_2\text{Cr}_2\text{O}_7, \, \text{B} = \text{CrO}_3\)
• (4) \(\text{A} = \text{Na}_2\text{Cr}_2\text{O}_7, \, \text{B} = \text{CrO}_5\)

• (1) \(\frac{n_C}{n_A + n_B + n_C}\)
• (2) \(\frac{n_C}{n_A \times n_B \times n_C}\)
• (3) \(\frac{n_C}{n_A - n_B - n_C}\)
• (4) \(\frac{n_B}{n_A + n_B}\)

Which of the following has a square pyramidal shape?

• (1) PCI₅
• (2) BrF₅
• (3) PF₅
• (4) [Ni(CN)₄]^2-

• (1) Both statements are true
• (2) Statement I is true, II is false
• (3) Both statements are false
• (4) Statement I is false, Statement II is true

\(\text{Choose the correct statements about the hydrides of group 15 elements.}\)
A. The stability of the hydrides decreases in the order \(\text{NH}_3 > \text{PH}_3 > \text{AsH}_3 > \text{SbH}_3 > \text{BiH}_3\)
B. The reducing ability of the hydrides increases in the order \(\text{NH}_3 < \text{PH}_3 < \text{AsH}_3 < \text{SbH}_3 < \text{BiH}_3\)
C. Among the hydrides, \(\text{NH}_3\) is a strong reducing agent while \(\text{BiH}_3\) is a mild reducing agent.
D. The basicity of the hydrides increases in the order \(\text{NH}_3 < \text{PH}_3 < \text{AsH}_3 < \text{SbH}_3 < \text{BiH}_3\)
Choose the most appropriate from the option given below:

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

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

• (1) Mn\(_2\)O\(_7\) and MnO\(_4^-\)
• (2) MnO\(_4^{2-}\) and MnO\(_4^-\)
• (3) Mn\(_2\)O\(_3\) and MnO\(_4^{2-}\)
• (4) MnO\(_4^{2-}\) and Mn\(_2\)O\(_7\)

Salicylaldehyde is synthesized from phenol, when reacted with

• (1) HCl, NaOH
• (2) CO₂ , NaOH
• (3) CCl₄ , NaOH
• (4)

m–chlorobenzaldehyde on treatment with 50\(\%\) KOH solution yields

• (1)

• (2)

• (3)

• (4)

Product A and B formed in the following set of reactions are:

• (1)

• (2)

• (3)

• (4)

\(\text{The orange colour of } \text{K}_2\text{Cr}_2\text{O}_7 \text{ and purple colour of KMnO}_4 \text{ is due to}\)

• (1) d\(\rightarrow\)d transition in K\(_2\)Cr\(_2\)O\(_7\) and charge transfer transitions in KMnO\(_4\).
• (2) d\(\rightarrow\)d transition in KMnO\(_4\) and charge transfer transitions in K\(_2\)Cr\(_2\)O\(_7\).
• (3) Charge transfer transition in both.
• (4) d\(\rightarrow\)d transition in both.

The coordination geometry around the manganese in decacarbonyldimanganese(0) is

• (1) Octahedral
• (2) Trigonal bipyramidal
• (3) Square pyramidal
• (4) Square planar

\(\text{Reduction potential of ions are given below:}\)
\[ \begin{array}{ccc} \text{ClO}_4^- & \text{IO}_4^- & \text{BrO}_4^- \\ E^\circ = 1.19 \, \text{V} & E^\circ = 1.65 \, \text{V} & E^\circ = 1.74 \, \text{V} \\ \end{array} \]
The correct order of their oxidising power is:

• (1) \(\text{ClO}_4^- \gt \text{IO}_4^- \gt \text{BrO}_4^-\)
• (2) \(\text{BrO}_4^- \gt \text{IO}_4^- \gt \text{ClO}_4^-\)
• (3) \(\text{BrO}_4^- \gt \text{ClO}_4^- \gt \text{IO}_4^-\)
• (4) \(\text{IO}_4^- \gt \text{BrO}_4^- \gt \text{ClO}_4^-\)

Statement I: Along the period, the chemical reactivity of the element gradually increases from group 1 to group 18.
Statement II: The nature of oxides formed by group 1 element is basic while that of group 17 elements is acidic.
In the light of the above statements, choose the most appropriate from the questions given below:

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

The total number of correct statements, regarding the nucleic acids is_________.
A. RNA is regarded as the reserve of genetic information.
B. DNA molecule self-duplicates during cell division.
C. DNA synthesizes proteins in the cell.
D. The message for the synthesis of particular proteins is present in DNA.
E. Identical DNA strands are transferred to daughter cells.

Number of metal ions characterized by flame test among the following is _______.
\(\text{Sr}^{2+}, \text{Ba}^{2+}, \text{Ca}^{2+}, \text{Cu}^{2+}, \text{Zn}^{2+}, \text{Co}^{2+}, \text{Fe}^{2+}\)

Number of spectral lines obtained in He⁺ spectra, when an electron makes transition from fifth excited state to first excited state will be __________.

Total number of species from the following which can undergo disproportionation reaction _______.
\(\text{H}_2\text{O}_2, \text{ClO}_3^-, \text{P}_4, \text{Cl}_2, \text{Ag}, \text{Cu}^{+1}, \text{F}_2, \text{NO}_2, \text{K}^+\)

Number of geometrical isomers possible for the given structure is/are ___________.

\(\text{The pH of an aqueous solution containing 1 M benzoic acid (} pK_a = 4.20 \text{) and 1 M sodium benzoate is 4.5.}\)
\(\text{The volume of benzoic acid solution in 300 mL of this buffer solution is \_\_\_\_\_\_ mL.}\)

\(\text{NO}_2 \text{ required for a reaction is produced by decomposition of } \text{N}_2\text{O}_5 \text{ in } \text{CCl}_4 \text{ as by equation}\)
\[ 2\text{N}_2\text{O}_{5(g)} \rightarrow 4\text{NO}_{2(g)} + \text{O}_{2(g)} \]
\(\text{The initial concentration of } \text{N}_2\text{O}_5 \text{ is } 3 \text{ mol L}^{-1} \text{ and it is } 2.75 \text{ mol L}^{-1} \text{ after 30 minutes.}\)
\(\text{The rate of formation of } \text{NO}_2 \text{ is } x \times 10^{-3} \text{ mol L}^{-1} \text{ min}^{-1} , \text{ value of } x \text{ is \_\_\_\_\_\_.}\)

\(\text{Number of complexes which show optical isomerism among the following is \_\_\_\_\_\_.}\)
\[ \text{cis}-[\text{Cr(ox)}_2\text{Cl}_2]^{3-}, \quad [\text{Co(en)}_3]^{3+}, \] \[ \text{cis}-[\text{Pt(en)}_2\text{Cl}_2]^{2+}, \quad \text{cis}-[\text{Co(en)}_2\text{Cl}_2]^{+}, \] \[ \text{trans}-[\text{Pt(en)}_2\text{Cl}_2]^{2+}, \quad \text{trans}-[\text{Cr(ox)}_2\text{Cl}_2]^{3-} \]

\(\text{2-chlorobutane} + \text{Cl}_2 \rightarrow \text{C}_4\text{H}_8\text{Cl}_2 \, (\text{isomers})\)
\(\text{Total number of optically active isomers shown by} \, \text{C}_4\text{H}_8\text{Cl}_2, \, \text{obtained in the above reaction is} \, \_\_\_\_\_\_.\)

\(\text{Two reactions are given below:}\) \[ 2\text{Fe}_{(s)} + \frac{3}{2}\text{O}_{2(g)} \rightarrow \text{Fe}_2\text{O}_{3(s)}, \Delta H^\circ = -822 \, \text{kJ/mol} \] \[ \text{C}_{(s)} + \frac{1}{2}\text{O}_{2(g)} \rightarrow \text{CO}_{(g)}, \Delta H^\circ = -110 \, \text{kJ/mol} \] \(\text{Then enthalpy change for the following reaction}\) \[ 3\text{C}_{(s)} + \text{Fe}_2\text{O}_{3(s)} \rightarrow 2\text{Fe}_{(s)} + 3\text{CO}_{(g)} \]