JEE Main 2024 Apr 8 Shift 1 — Question Paper

Let $[t]$ be the greatest integer less than or equal to $t$. Let $A$ be the set of all prime factors of 2310 and $f : A \rightarrow \mathbb{Z}$ be the function $f(x)=\left[\log_2\left(x^2+\left[\frac{x^3}{5}\right]\right)\right]$. The number of one-to-one functions from $A$ to the range of $f$ is

Let $z$ be a complex number such that $|z+2|=1$ and $\mathrm{Im}\left(\frac{z+1}{z+2}\right)=\frac{1}{5}$. Then the value of $\left|\mathrm{Re}\left(\overline{z+2}\right)\right|$ is

The sum of all the solutions of the equation $(8)^{2x}-16\cdot(8)^{x}+48=0$ is :

Let $A=\begin{bmatrix} 2 & a & 0 \\ 1 & 3 & 1 \\ 0 & 5 & b \end{bmatrix}$. If $A^3=4A^2-A-21I$, where $I$ is the identity matrix of order $3\times 3$, then $2a+3b$ is equal to

The equations of two sides AB and AC of a triangle ABC are $4x+y=14$ and $3x-2y=5$, respectively. The point $\left(2,-\frac{4}{3}\right)$ divides the third side BC internally in the ratio 2:1. the equation of the side BC is

If the set $R=\{(a,b): a+5b=42, a,b\in\mathbb{N}\}$ has $m$ elements and $\sum_{n=1}^{m}\left(1-i^{n!}\right)=x+iy$, where $i=\sqrt{-1}$, then the value of $m+x+y$ is

For the function $f(x)=(\cos x)-x+1$, $x\in\mathbb{R}$, between the following two statements

(S1) $f(x)=0$ for only one value of $x$ in $[0,\pi]$.

(S2) $f(x)$ is decreasing in $\left[0,\frac{\pi}{2}\right]$ and increasing in $\left[\frac{\pi}{2},\pi\right]$.

The number of critical points of the function $f(x)=(x-2)^{2/3}(2x+1)$ is

Let $f(x)=4\cos^3 x+3\sqrt{3}\cos^2 x-10$. The number of points of local maxima of $f$ in interval $(0, 2\pi)$ is

Let $I(x)=\int \frac{6}{\sin^2 x\,(1-\cot x)^2}\,dx$. If $I(0)=3$, then $I\left(\frac{\pi}{12}\right)$ is equal to

The value of $k\in\mathbb{N}$ for which the integral $I_n=\int_0^1\left(1-x^k\right)^n dx$, $n\in\mathbb{N}$, satisfies $147\, I_{20}=148\, I_{21}$ is

Let $f(x)$ be a positive function such that the area bounded by $y=f(x)$, $y=0$ from $x=0$ to $x=a>0$ is $e^{-a}+4a^2+a-1$. Then the differential equation, whose general solution is $y=c_1 f(x)+c_2$, where $c_1$ and $c_2$ are arbitrary constants, is

Let $y=y(x)$ be the solution of the differential equation $(1+y^2)e^{\tan x}\,dx+\cos^2 x\,(1+e^{2\tan x})\,dy=0$, $y(0)=1$. Then $y\left(\frac{\pi}{4}\right)$ is equal to

If the shortest distance between the lines $$L_1 : \vec{r}=(2+\lambda)\hat{i}+(1-3\lambda)\hat{j}+(3+4\lambda)\hat{k}, \quad \lambda\in\mathbb{R}$$ $$L_2 : \vec{r}=2(1+\mu)\hat{i}+3(1+\mu)\hat{j}+(5+\mu)\hat{k}, \quad \mu\in\mathbb{R}$$ is $\frac{m}{\sqrt{n}}$, where $\gcd(m,n)=1$, then the value of $m+n$ equals

Let the circles $C_1 : (x-\alpha)^2+(y-\beta)^2=r_1^2$ and $C_2 : (x-8)^2+\left(y-\frac{15}{2}\right)^2=r_2^2$ touch each other externally at the point (6, 6). If the point (6, 6) divides the line segment joining the centres of the circles $C_1$ and $C_2$ internally in the ratio 2:1, then $(\alpha+\beta)+4\left(r_1^2+r_2^2\right)$ equals

Let $H : \frac{-x^2}{a^2}+\frac{y^2}{b^2}=1$ be the hyperbola, whose eccentricity is $\sqrt{3}$ and the length of the latus rectum is $4\sqrt{3}$. Suppose the point $(\alpha, 6)$, $\alpha>0$ lies on $H$. If $\beta$ is the product of the focal distances of the point $(\alpha, 6)$, then $\alpha^2+\beta$ is equal to

Let $P(x, y, z)$ be a point in the first octant, whose projection in the $xy$-plane is the point $Q$. Let $OP=\gamma$; the angle between $OQ$ and the positive $x$-axis be $\theta$; and the angle between $OP$ and the positive $z$-axis be $\phi$, where $O$ is the origin. Then the distance of $P$ from the $x$-axis is

The set of all $\alpha$, for which the vectors $\vec{a}=\alpha t\,\hat{i}+6\hat{j}-3\hat{k}$ and $\vec{b}=t\,\hat{i}-2\hat{j}-2\alpha t\,\hat{k}$ are inclined at an obtuse angle for all $t\in\mathbb{R}$, is

Let the sum of two positive integers be 24. If the probability, that their product is not less than $\frac{3}{4}$ times their greatest possible product, is $\frac{m}{n}$, where $\gcd(m,n)=1$, then $n-m$ equals

If $\sin x=-\frac{3}{5}$, where $\pi<x<\frac{3\pi}{2}$, then $80(\tan^2 x-\cos x)$ is equal to

If the range of $f(\theta)=\frac{\sin^4\theta+3\cos^2\theta}{\sin^4\theta+\cos^2\theta}$, $\theta\in\mathbb{R}$ is $[\alpha, \beta]$, then the sum of the infinite G.P., whose first term is 64 and the common ratio is $\frac{\alpha}{\beta}$, is equal to __________.

Let $A=\begin{bmatrix} 2 & -1 \\ 1 & 1 \end{bmatrix}$. If the sum of the diagonal elements of $A^{13}$ is $3^n$, then $n$ is equal to __________.

The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3, is equal to __________.

Let $\alpha=\sum_{r=0}^{n}\left(4r^2+2r+1\right){}^{n}C_r$ and $\beta=\left(\sum_{r=0}^{n}\frac{{}^{n}C_r}{r+1}\right)+\frac{1}{n+1}$. If $140<\frac{2\alpha}{\beta}<281$, then the value of $n$ is __________.

Let the positive integers be written in the form :

[Figure: triangular arrangement of positive integers — row 1: 1; row 2: 2, 3; row 3: 4, 5, 6; row 4: 7, 8, 9, 10; and so on]

If the $k^{\text{th}}$ row contains exactly $k$ numbers for every natural number $k$, then the row in which the number 5310 will be, is __________.

The value of $\lim_{x\to 0} 2\left(\frac{1-\cos x\sqrt{\cos 2x}\,\sqrt[3]{\cos 3x}\,......\,\sqrt[10]{\cos 10x}}{x^2}\right)$ is __________.

Let the area of the region enclosed by the curve $y=\min\{\sin x, \cos x\}$ and the $x$-axis between $x=-\pi$ to $x=\pi$ be $A$. Then $A^2$ is equal to __________.

Let $\vec{a}=9\hat{i}-13\hat{j}+25\hat{k}$, $\vec{b}=3\hat{i}+7\hat{j}-13\hat{k}$ and $\vec{c}=17\hat{i}-2\hat{j}+\hat{k}$ be three given vectors. If $\vec{r}$ is a vector such that $\vec{r}\times\vec{a}=(\vec{b}+\vec{c})\times\vec{a}$ and $\vec{r}\cdot(\vec{b}-\vec{c})=0$, then $\frac{|593\vec{r}+67\vec{a}|^2}{(593)^2}$ is equal to _____.

If the orthocentre of the triangle formed by the lines $2x+3y-1=0$, $x+2y-1=0$ and $ax+by-1=0$, is the centroid of another triangle, whose circumcentre and orthocentre respectively are (3, 4) and (−6, −8), then the value of $|a-b|$ is __________.

Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables $X$ and $Y$ respectively denote the number of blue and yellow balls. If $\bar{X}$ and $\bar{Y}$ are the means of $X$ and $Y$ respectively, then $7\bar{X}+4\bar{Y}$ is equal to __________.

In an expression $a \times 10^{b}$:

A clock has 75 cm, 60 cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel $x$ distance more than the tip of minute hand. The value of $x$ in meter is nearly (Take $\pi = 3.14$) :

A stationary particle breaks into two parts of masses $m_A$ and $m_B$ which move with velocities $v_A$ and $v_B$ respectively. The ratio of their kinetic energies $(K_B : K_A)$ is :

A player caught a cricket ball of mass 150 g moving at a speed of 20 m/s. If the catching process is completed in 0.1 s, the magnitude of force exerted by the ball on the hand of the player is:

Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is :

Correct Bernoulli's equation is (symbols have their usual meaning) :

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $\frac{V_a}{V_d}$ and the ratio $\frac{V_b}{V_c}$ is:

[Figure: P-V diagram with two adiabatic curves a-d and b-c intersecting two isothermal curves; volumes marked $V_a$, $V_d$, $V_b$, $V_c$ on the V-axis]

Two planets A and B having masses $\mathrm{m_1}$ and $\mathrm{m_2}$ move around the sun in circular orbits of $\mathrm{r_1}$ and $\mathrm{r_2}$ radii respectively. If angular momentum of A is L and that of B is 3L, the ratio of time period $\left(\frac{T_A}{T_B}\right)$ is:

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature (27°C). The ratio of specific heat of gases at constant volume respectively is:

In the given circuit, the terminal potential difference of the cell is :

[Figure: circuit with a 3 V cell of internal resistance 1 Ω connected across two parallel 4 Ω resistors]

Paramagnetic substances:

A. align themselves along the directions of external magnetic field. B. attract strongly towards external magnetic field. C. has susceptibility little more than zero. D. move from a region of strong magnetic field to weak magnetic field.

Choose the most appropriate answer from the options given below:

Average force exerted on a non-reflecting surface at normal incidence is $2.4 \times 10^{-4}$ N. If $360\ \mathrm{W/cm^2}$ is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is:

Critical angle of incidence for a pair of optical media is 45°. The refractive indices of first and second media are in the ratio:

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is:

(Assume $h = 6.63 \times 10^{-34}$ J s, $\mathrm{m_e} = 9.0 \times 10^{-31}$ kg and $\mathrm{m_p} = 1836$ times $\mathrm{m_e}$)

Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

Binding energy of a certain nucleus is $18 \times 10^{8}$ J. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

The output Y of following circuit for given inputs is :

[Figure: logic circuit — inputs A and B; A and NOT(B) feed an OR gate; B and NOT(A) feed an AND gate; outputs of the OR and AND gates feed a final AND gate giving Y]

Young's modulus is determined by the equation given by $Y = 49000\,\frac{m}{l}\ \frac{\text{dyne}}{\text{cm}^2}$ where $M$ is the mass and $l$ is the extension of wire used in the experiment. Now error in Young modules $(Y)$ is estimated by taking data from $M$-$l$ plot in graph paper. The smallest scale divisions are 5 g and 0.02 cm along load axis and extension axis respectively. If the value of $M$ and $l$ are 500 g and 2 cm respectively then percentage error of $Y$ is :

The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to 1 mm. The main scale reading is 2 cm and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 g, the density of the sphere is:

A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

Three vectors $\vec{OP}, \vec{OQ}$ and $\vec{OR}$ each of magnitude A are acting as shown in figure. The resultant of the three vectors is $A\sqrt{x}$. The value of $x$ is ________.

[Figure: circle centred at O with three radial vectors — OP along the positive x-axis, OQ at 90° from OP (vertically up), and OR at 45° below OP]

A uniform thin metal plate of mass 10 kg with dimensions is shown. The ratio of x and y coordinates of center of mass of plate in $\frac{n}{9}$. The value of $n$ is ______.

[Figure: plate occupying the region from (0,0) to (3,2) with a rectangular notch cut from the top between (1,1), (1,2), (2,2) and (2,1)]

A liquid column of height 0.04 cm balances excess pressure of a soap bubble of certain radius. If density of liquid is $8 \times 10^{3}\ \mathrm{kg\ m^{-3}}$ and surface tension of soap solution is $0.28\ \mathrm{Nm^{-1}}$, then diameter of the soap bubble is________ cm. (if $g = 10\ \mathrm{m\ s^{-2}}$)

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $\left(\frac{a-1}{a}\right)$ then the value of a is _______.

An electric field, $\vec{E} = \frac{2\hat{i} + 6\hat{j} + 8\hat{k}}{\sqrt{6}}$ passes through the surface of $4\ \mathrm{m^2}$ area having unit vector $\hat{n} = \left(\frac{2\hat{i} + \hat{j} + \hat{k}}{\sqrt{6}}\right)$. The electric flux for that surface is ______ V m.

Resistance of a wire at 0 °C, 100 °C and t °C is found to be $10\ \Omega$, $10.2\ \Omega$ and $10.95\ \Omega$ respectively. The temperature t in Kelvin scale is ________.

An electron with kinetic energy 5 eV enters a region of uniform magnetic field of $3\ \mu\mathrm{T}$ perpendicular to its direction. An electric field E is applied perpendicular to the direction of velocity and magnetic field. The value of E, so that electron moves along the same path, is _____ $\mathrm{NC^{-1}}$.

(Given, mass of electron $= 9 \times 10^{-31}$ kg, electric charge $= 1.6 \times 10^{-19}$ C)

In an alpha particle scattering experiment distance of closest approach for the $\alpha$ particle is $4.5 \times 10^{-14}$ m. If target nucleus has atomic number 80, then maximum velocity of $\alpha$-particle is___________ $\times 10^{5}$ m/s approximately.

($\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}$ SI unit, mass of $\alpha$ particle $= 6.72 \times 10^{-27}$ kg)

A parallel beam of monochromatic light of wavelength 600 nm passes through single slit of 0.4 mm width. Angular divergence corresponding to second order minima would be _______ $\times 10^{-3}$ rad.

A square loop PQRS having 10 turns, area $3.6 \times 10^{-3}\ \mathrm{m^2}$ and resistance $100\ \Omega$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude B = 0.5 T as shown. Work done in pulling the loop out of the field in 1.0 s is ________ $\times 10^{-6}$ J.

[Figure: square loop PQRS inside a region of uniform magnetic field directed into the page (shown by crosses), being pulled out to the left with velocity $v$]

Combustion of glucose $\mathrm{(C_6H_{12}O_6)}$ produces $\mathrm{CO_2}$ and water. The amount of oxygen (in g) required for the complete combustion of 900 g of glucose is :

[Molar mass of glucose in $\mathrm{g\ mol^{-1}}$ = 180]

Match List I with List II

	LIST I (Molecule)		LIST II (Shape)
A.	$\mathrm{NH_3}$	I.	Square pyramid
B.	$\mathrm{BrF_5}$	II.	Tetrahedral
C.	$\mathrm{PCl_5}$	III.	Trigonal pyramidal
D.	$\mathrm{CH_4}$	IV.	Trigonal bipyramidal

Choose the correct answer from the options given below:

For the given hypothetical reactions, the equilibrium constants are as follows :

$\mathrm{X \rightleftharpoons Y;\ K_1 = 1.0}$

$\mathrm{Y \rightleftharpoons Z;\ K_2 = 2.0}$

$\mathrm{Z \rightleftharpoons W;\ K_3 = 4.0}$

The equilibrium constant for the reaction $\mathrm{X \rightleftharpoons W}$ is

Thiosulphate reacts differently with iodine and bromine in the reactions given below:

$$\mathrm{2S_2O_3^{2-} + I_2 \rightarrow S_4O_6^{2-} + 2I^-}$$

$$\mathrm{S_2O_3^{2-} + 5Br_2 + 5H_2O \rightarrow 2SO_4^{2-} + 4Br^- + 10H^+}$$

Which of the following statement justifies the above dual behaviour of thiosulphate?

Among the following halogens

$\mathrm{F_2,\ Cl_2,\ Br_2}$ and $\mathrm{I_2}$

Which can undergo disproportionation reactions?

Give below are two statements: One is labelled as Assertion A and the other is labelled as Reason R:

Assertion A: The stability order of +1 oxidation state of Ga, In and Tl is Ga < In < Tl.

Reason R: The inert pair effect stabilizes the lower oxidation state down the group.

In the light of the above statements, choose the correct answer from the options given below:

Given below are two statements:

Statement I: $\mathrm{N(CH_3)_3}$ and $\mathrm{P(CH_3)_3}$ can act as ligands to form transition metal complexes.

Statement II: As N and P are from same group, the nature of bonding of $\mathrm{N(CH_3)_3}$ and $\mathrm{P(CH_3)_3}$ is always same with transition metals.

In the light of the above statements, choose the most appropriate answer from the options given below:

Match List I with List II

	LIST I (Elements)		LIST II (Properties in their respective groups)
A.	Cl, S	I.	Elements with highest electronegativity
B.	Ge, As	II.	Elements with largest atomic size
C.	Fr, Ra	III.	Elements which show properties of both metals and non-metal
D.	F, O	IV.	Elements with highest negative electron gain enthalpy

Choose the correct answer from the options given below:

Iron (III) catalyses the reaction between iodide and persulphate ions, in which

A. $\mathrm{Fe^{3+}}$ oxidises the iodide ion

B. $\mathrm{Fe^{3+}}$ oxidises the persulphate ion

C. $\mathrm{Fe^{2+}}$ reduces the iodide ion

D. $\mathrm{Fe^{2+}}$ reduces the persulphate ion

Choose the most appropriate answer from the options given below:

An octahedral complex with the formula $\mathrm{CoCl_3 \cdot nNH_3}$ upon reaction with excess of $\mathrm{AgNO_3}$ solution gives 2 moles of AgCl. Consider the oxidation state of Co in the complex is 'x'. The value of "x + n" is _________.

Number of Complexes with even number of electrons in $\mathrm{t_{2g}}$ orbitals is -

$\mathrm{[Fe(H_2O)_6]^{2+}, [Co(H_2O)_6]^{2+}, [Co(H_2O)_6]^{3+}, [Cu(H_2O)_6]^{2+}, [Cr(H_2O)_6]^{2+}}$

Match List I with List II

	LIST I (Name of the test)		LIST II (Reaction sequence involved) [M is metal]
A.	Borax bead test	I.	$\mathrm{MCO_3 \rightarrow MO \xrightarrow{Co(NO_3)_2,\ +\Delta} CoO \cdot MO}$
B.	Charcoal cavity test	II.	$\mathrm{MCO_3 \rightarrow MCl_2 \rightarrow M^{2+}}$
C.	Cobalt nitrate test	III.	$\mathrm{MSO_4 \xrightarrow[\Delta]{Na_2B_4O_7} M(BO_2)_2 \rightarrow MBO_2 \rightarrow M}$
D.	Flame test	IV.	$\mathrm{MSO_4 \xrightarrow[\Delta]{Na_2CO_3} MCO_3 \rightarrow MO \rightarrow M}$

Choose the correct answer from the options given below:

Match List I with List II

	LIST I (Compound)		LIST II (Colour)
A.	$\mathrm{Fe_4[Fe(CN)_6]_3 \cdot xH_2O}$	I.	Violet
B.	$\mathrm{[Fe(CN)_5NOS]^{4-}}$	II.	Blood Red
C.	$\mathrm{[Fe(SCN)]^{2+}}$	III.	Prussian Blue
D.	$\mathrm{(NH_4)_3PO_4 \cdot 12MoO_3}$	IV.	Yellow

Choose the correct answer from the options given below:

Given below are two statements:

Statement I: [Figure: Compound A — benzene ring bearing Cl, with one NO2 group ortho to Cl and another NO2 group para to Cl (1-chloro-2,4-dinitrobenzene skeleton)] IUPAC name of Compound A is 4-chloro-1,3-dinitrobenzene.

Statement II: [Figure: Compound B — benzene ring bearing NH2, with a CH3 group ortho to NH2 and a C2H5 group para to NH2] IUPAC name of Compound B is 4-ethyl-2-methylaniline.

In the light of the above statements, choose the most appropriate answer from the options given below:

In the given compound, the number of 2° carbon atom/s is __________.

$$\mathrm{CH_3-\underset{\underset{\mathrm{H}}{|}}{C}(CH_3)-\underset{\underset{\mathrm{H}}{|}}{C}H-\underset{\underset{\mathrm{H}}{|}}{C}(CH_3)-CH_3}$$

Which of the following are aromatic?

A. [Figure: naphthalene — two fused six-membered rings, fully conjugated]

B. [Figure: styrene — benzene ring with a vinyl ($\mathrm{CH{=}CH_2}$) substituent]

C. [Figure: ten-membered monocyclic ring with five alternating double bonds ([10]annulene)]

D. [Figure: sixteen-membered monocyclic ring with eight alternating double bonds ([16]annulene)]

Which among the following compounds will undergo fastest $\mathrm{S_N2}$ reaction.

Identify the major products A and B respectively in the following set of reactions.

[Figure: 1-methylcyclohexan-1-ol (cyclohexane ring with CH3 and OH on the same carbon); with $\mathrm{Conc.\ H_2SO_4,\ \Delta}$ it gives A, and with $\mathrm{CH_3COCl}$/Pyridine it gives B]

Identify the product (P) in the following reaction:

[Figure: cyclopentane ring bearing COOH] $\xrightarrow{\text{i) } \mathrm{Br_2}/\text{Red P, ii) } \mathrm{H_2O}}$ (P)

[Figure: Fischer projection of an open-chain sugar — CHO at the top; C2: OH on the right; C3: OH on the left; C4: OH on the right; C5: OH on the right; CH2OH at the bottom (D-glucose)]

The incorrect statement regarding the given structure is

A hypothetical electromagnetic wave is show below.

[Figure: sinusoidal wave; a horizontal span of 1.5 pm is marked from the start of the wave up to the first crest]

The frequency of the wave is $x \times 10^{19}$ Hz.

x = _________ (nearest integer)

Number of molecules from the following which are exceptions to octet rule is _________.

$\mathrm{CO_2,\ NO_2,\ H_2SO_4,\ BF_3,\ CH_4,\ SiF_4,\ ClO_2,\ PCl_5,\ BeF_2,\ C_2H_6,\ CHCl_3,\ CBr_4}$

[Figure: vertical cylinder fitted with a piston; lower position A at 10 L and upper position B at 90 L]

Consider the figure provided.

1 mol of an ideal gas is kept in a cylinder, fitted with a piston, at the position A, at 18° C. If the piston is moved to position B, keeping the temperature unchanged, then 'x' L atm work is done in this reversible process.

x = __________ L atm. (nearest integer)

[Given : Absolute temperature = °C + 273.15, R = 0.08206 $\mathrm{L\ atm\ mol^{-1}\ K^{-1}}$]

A solution containing 10 g of an electrolyte $\mathrm{AB_2}$ in 100 g of water boils at 100.52°C. The degree of ionization of the electrolyte ($\alpha$) is _________ $\times 10^{-1}$. (nearest integer)

[Given : Molar mass of $\mathrm{AB_2}$ = 200 $\mathrm{g\ mol^{-1}}$, $K_b$ (molal boiling point elevation const. of water) = 0.52 $\mathrm{K\ kg\ mol^{-1}}$, boiling point of water = 100°C ; $\mathrm{AB_2}$ ionises as $\mathrm{AB_2 \rightarrow A^{2+} + 2B^-}$]

Consider the following reaction

$\mathrm{A + B \rightarrow C}$

The time taken for A to become $1/4^{th}$ of its initial concentration is twice the time taken to become 1/2 of the same. Also, when the change of concentration of B is plotted against time, the resulting graph gives a straight line with a negative slope and a positive intercept on the concentration axis.

The overall order of the reaction is __________.

The 'spin only' magnetic moment value of $\mathrm{MO_4^{2-}}$ is __________ BM. (Where M is a metal having least metallic radii. among Sc, Ti, V, Cr, Mn and Zn).

(Given atomic number: Sc = 21, Ti = 22, V = 23, Cr = 24, Mn = 25 and Zn = 30)

If 279 g of aniline is reacted with one equivalent of benzenediazonium chloride, the maximum amount of aniline yellow formed will be _______ g. (nearest integer)

(consider complete conversion).

The number of optical isomers in following compound is:_________

[Figure: three linearly fused six-membered rings (perhydroanthracene skeleton); Br on a ring-fusion carbon of the left ring and CH3 on a carbon of the right ring]

Major product B of the following reaction has ________ $\pi$-bond.

[Figure: ethylbenzene — benzene ring bearing a CH2CH3 group]

$$\mathrm{C_6H_5CH_2CH_3 \xrightarrow[\Delta]{KMnO_4-KOH} (A) \xrightarrow{HNO_3/H_2SO_4} (B)}$$

Number of amine compounds from the following giving solids which are soluble in NaOH upon reaction with Hinsberg's reagent is ________.

[Figure: eleven structures — (1) aniline $\mathrm{C_6H_5NH_2}$; (2) benzamide $\mathrm{C_6H_5CONH_2}$; (3) semicarbazide $\mathrm{H_2N{-}NH{-}CO{-}NH_2}$; (4) N-methylaniline $\mathrm{C_6H_5{-}NH{-}CH_3}$; (5) phenyl–NH– attached to a six-membered diene ring bearing NH2 (N-phenyl diamine structure); (6) urea $\mathrm{H_2N{-}CO{-}NH_2}$; (7) 2-methoxyaniline (benzene ring with NH2 and OCH3 on adjacent carbons); (8) propan-1-amine $\mathrm{CH_3CH_2CH_2NH_2}$; (9) triethylamine $\mathrm{(C_2H_5)_3N}$; (10) tertiary amine — N bearing ethyl, methyl and cyclohexylmethyl groups; (11) cyclohexylamine]