JEE Main 2024 — 1 Feb Shift 2 (Previous Year Paper)

Let α and β be the roots of the equation $px^2+qx-r=0$, where $p\ne0$. If p, q and r be the consecutive terms of a non constant G.P. and $\frac1\alpha+\frac1\beta=\frac34$, then the value of $(\alpha-\beta)^2$ is:

1. A.$\frac{80}{9}$✓
2. B.$\frac{20}{3}$
3. C.9
4. D.8

Correct answer: A

If the mirror image of the point P(3, 4, 9) in the line $\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-2}{1}$ is $(\alpha,\beta,\gamma)$, then $14(\alpha+\beta+\gamma)$ is:

1. A.138
2. B.132
3. C.102
4. D.108✓

Correct answer: D

Let Ajay will not appear in JEE exam with probability $p=\frac27$, while both Ajay and Vijay will appear in the exam with probability $q=\frac15$. Then the probability, that Ajay will appear in the exam and Vijay will not appear is:

1. A.$\frac{18}{35}$✓
2. B.$\frac9{35}$
3. C.$\frac3{35}$
4. D.$\frac{24}{35}$

Correct answer: A

The number of solutions of the equation $4\sin^2x-4\cos^3x+9-4\cos x=0$; $x\in[-2\pi,2\pi]$ is:

1. A.0✓
2. B.1
3. C.3
4. D.2

Correct answer: A

Let P and Q be the points on the line $\frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2}$ which are at a distance of 6 units from the point R (1, 2, 3). If the centroid of the tringle PQR is $(\alpha,\beta,\gamma)$, then $\alpha^2+\beta^2+\gamma^2$ is:

1. A.24
2. B.36
3. C.26✓
4. D.18

Correct answer: C

Consider 10 observations $x_1,x_2,\ldots,x_{10}$ such that $\sum_{i=1}^{10}(x_i-\alpha)=2$ and $\sum_{i=1}^{10}(x_i-\beta)^2=40$, where α, β are positive integers. Let the mean and the variance of the observations be $\frac65$ and $\frac{84}{25}$ respectively. Then $\frac\beta\alpha$ is equal to:

1. A.$\frac32$
2. B.2✓
3. C.$\frac52$
4. D.1

Correct answer: B

Consider the relations $R_1$ and $R_2$ defined as $aR_1b\Leftrightarrow a^2+b^2=1$ for all $a,b\in\mathbb{R}$ and $(a,b)R_2(c,d)\Leftrightarrow a+d=b+c$ for all $(a,b),(c,d)\in\mathbb{N}\times\mathbb{N}$. Then:

1. A.Neither $R_1$ nor $R_2$ is an equivalence relation
2. B.Only $R_2$ is an equivalence relation✓
3. C.Only $R_1$ is an equivalence relation
4. D.$R_1$ and $R_2$ both are equivalence relations

Correct answer: B

Let m and n be the coefficients of seventh and thirteenth terms respectively in the expansion of $\left(\frac13x^{\frac13}+\frac{1}{2x^{\frac23}}\right)^{18}$. Then $\left(\frac nm\right)^{\frac13}$ is:

1. A.$\frac94$✓
2. B.$\frac49$
3. C.$\frac14$
4. D.$\frac19$

Correct answer: A

Let the system of equations $x+2y+3z=5$, $2x+3y+z=9$, $4x+3y+\lambda z=\mu$ have infinite number of solutions. Then $\lambda+2\mu$ is equal to:

1. A.28
2. B.17✓
3. C.22
4. D.15

Correct answer: B

The value of $\int_0^1(2x^3-3x^2-x+1)^{\frac13}dx$ is equal to:

1. A.−1
2. B.2
3. C.0✓
4. D.1

Correct answer: C

Let the locus of the midpoints of the chords of the circle $x^2+(y-1)^2=1$ drawn from the origin intersect the line $x+y=1$ at P and Q. Then, the length of PQ is:

1. A.1
2. B.$\frac1{\sqrt2}$✓
3. C.$\frac12$
4. D.$\sqrt2$

Correct answer: B

Let $f(x)=\begin{cases}x-1, & x\text{ is even,}\\ 2x, & x\text{ is odd,}\end{cases}$ $x\in\mathbb{N}$. If for some $a\in\mathbb{N}$, $f(f(f(a)))=21$, then $\lim_{x\to a^-}\left\{\frac{|x|^3}{a}-\left[\frac xa\right]\right\}$, where [t] denotes the greatest integer less than or equal to t, is equal to:

1. A.225
2. B.121
3. C.169
4. D.144✓

Correct answer: D

Let $f(x)=\left|2x^2+5|x|-3\right|$, $x\in\mathbb{R}$. If m and n denote the number of points where f is not continuous and not differentiable respectively, then m + n is equal to:

1. A.5
2. B.2
3. C.0
4. D.3✓

Correct answer: D

If the domain of the function $f(x)=\frac{\sqrt{x^2-25}}{(4-x^2)}+\log_{10}(x^2+2x-15)$ is $(-\infty,\alpha)\cup[\beta,\infty)$, then $\alpha^2+\beta^3$ is equal to:

1. A.150✓
2. B.175
3. C.125
4. D.140

Correct answer: A

If $\int_0^{\pi/3}\cos^4x\,dx=a\pi+b\sqrt3$, where a and b are rational numbers, then 9a + 8b is equal to:

1. A.2✓
2. B.1
3. C.$\frac32$
4. D.3

Correct answer: A

Let $S_n$ denote the sum of the first n terms of an arithmetic progression. If $S_{10}=390$ and the ratio of the tenth and the fifth terms is 15 : 7, then $S_{15}-S_5$ is equal to:

1. A.790✓
2. B.690
3. C.800
4. D.890

Correct answer: A

Let P be a point on the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$. Let the line passing through P and parallel to y-axis meet the circle $x^2+y^2=9$ at point Q such that P and Q are on the same side of the x-axis. Then, the eccentricity of the locus of the point R on PQ such that PR : RQ = 4 : 3 as P moves on the ellipse, is:

1. A.$\frac{13}{21}$
2. B.$\frac{\sqrt{139}}{23}$
3. C.$\frac{\sqrt{13}}{7}$✓
4. D.$\frac{11}{19}$

Correct answer: C

Consider a ΔABC where A(1, 3, 2), B(–2, 8, 0) and C(3, 6, 7). If the angle bisector of ∠BAC meets the line BC at D, then the length of the project of the vector $\vec{AD}$ on the vector $\vec{AC}$ is:

1. A.$\frac{\sqrt{38}}{2}$
2. B.$\sqrt{19}$
3. C.$\frac{39}{2\sqrt{38}}$
4. D.$\frac{37}{2\sqrt{38}}$✓

Correct answer: D

The lines $L_1,L_2,\ldots,L_{20}$ are distinct. For n = 1, 2, 3, ...., 10 all the lines $L_{2n-1}$ are parallel to each other and all the lines $L_{2n}$ pass through a given P. The maximum number of points of intersection of pairs of lines form the set $\{L_1,L_2,\ldots,L_{20}\}$ is equal to ______.

Correct answer: 101

Let $\vec a=\hat i+\hat j+\hat k$, $\vec b=-\hat i-8\hat j+2\hat k$ and $\vec c=4\hat i+c_2\hat j+c_3\hat k$ be three vectors such that $\vec b\times\vec a=\vec c\times\vec a$. If the angle between vector $\vec c$ and the vector $3\hat i+4\hat j+\hat k$ is θ, then the greatest integer less than or equal to $\tan^2\theta$ is ______.

Correct answer: 38

If $\frac{dx}{dy}=\frac{1+x-y^2}{y}$, $x(1)=1$, then $5x(2)$ is equal to ______.

Correct answer: 5

Let $f:(0,\infty)\to\mathbb{R}$ and $F(x)=\int_0^xtf(t)dt$. If $F(x^2)=x^4+x^5$, then $\sum_{r=1}^{12}f(r^2)$ is equal to ______.

Correct answer: 219

Three points O(0, 0), P(a, a²), Q(–b, b²), a > 0, b > 0, are on the parabola $y=x^2$. Let $S_1$ be the area of the region bounded by the line PQ and the parabola, and $S_2$ be the area of the triangle OPQ. If the minimum value of $\frac{S_1}{S_2}$ is $\frac mn$, gcd(m, n) = 1, then m + n is equal to ______.

Correct answer: 7

Let $A=I_2-2MM^T$ where M is a real matrix of order 2 × 1 such that the relation $M^TM=I_1$ holds. If λ is a real number such that the relation $AX=\lambda X$ holds for some non-zero real matrix X of order 2 × 1, then the sum of squares of all possible values of λ is equal to ______.

Correct answer: 2

The sum of squares of all possible values of k, for which area of the region bounded by the parabolas $2y^2=kx$ and $ky^2=2(y-x)$ is maximum, is equal to ______.

Correct answer: 8

If three successive terms of G.P. with common ration r (r > 1) are the lengths of the sides of a triangle and [r] denotes the greatest integer less than or equal to r, then 3[r] + [–r] is equal to ______.

Correct answer: 1

If $y=\frac{(\sqrt x+1)(x^2-\sqrt x)}{x\sqrt x+x+\sqrt x}+\frac1{15}(3\cos^2x-5)\cos^3x$, then $96y'\left(\frac\pi6\right)$ is equal to ______.

Correct answer: 105

Let ABC be an isosceles triangle in which A is at (–1, 0), $\angle A=\frac{2\pi}{3}$, AB = AC and B is on the positive x-axis. If $BC=4\sqrt3$ and the line BC intersects the line $y=x+3$ at $(\alpha,\beta)$ then $\frac{\beta^4}{\alpha^2}$ is ______.

Correct answer: 36

Conductivity of a photodiode starts changing only if the wavelength of incident light is less than 660 nm. The band gap of photodiode is found to be $\left(\frac X8\right)$ eV. The value of X is: (Given, h = $6.6\times10^{-34}$ J s, e = $1.6\times10^{-19}$ C)

1. A.11
2. B.13
3. C.21
4. D.15✓

Correct answer: D

A diatomic gas (γ = 1.4) does 200 J of work when it is expanded isobarically. The heat given to the gas in the process is:

1. A.700 J✓
2. B.600 J
3. C.800 J
4. D.850 J

Correct answer: A

In an ammeter, 5% of the main current passes through the galvanometer. If resistance of the galvanometer is G, the resistance of ammeter will be:

1. A.$\frac{G}{20}$✓
2. B.$\frac{G}{199}$
3. C.$199G$
4. D.$200G$

Correct answer: A

A galvanometer (G) of 2Ω resistance is connected in the given circuit. The ratio of charge stored in $C_1$ and $C_2$ is:

1. A.1
2. B.$\frac12$✓
3. C.$\frac32$
4. D.$\frac23$

Correct answer: B

From the statements given below: (A) The angular momentum of an electron in $n^{th}$ orbit is an integral multiple of ħ. (B) Nuclear forces do not obey inverse square law. (C) Nuclear forces are spin dependent. (D) Nuclear forces are central and charge independent. (E) Stability of nucleus is inversely proportional to the value of packing fraction. Choose the correct answer from the options given below:

1. A.(A), (C), (D), (E) only
2. B.(A), (B), (C), (E) only✓
3. C.(A), (B), (C), (D) only
4. D.(B), (C), (D), (E) only

Correct answer: B

A body of mass 4 kg experiences two forces $\vec F_1=5\hat i+8\hat j+7\hat k$ and $\vec F_2=3\hat i-4\hat j-3\hat k$. The acceleration acting on the body is:

1. A.$4\hat i+2\hat j+2\hat k$
2. B.$2\hat i+\hat j+\hat k$✓
3. C.$2\hat i+3\hat j+3\hat k$
4. D.$-2\hat i-\hat j-\hat k$

Correct answer: B

A disc of radius R and mass M is rolling horizontally without slipping with speed v. It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is:

1. A.$\frac34\frac{v^2}{g}$
2. B.$\frac{v^2}{g}$
3. C.$\frac12\frac{v^2}{g}$✓
4. D.$\frac23\frac{v^2}{g}$

Correct answer: C

In a metre-bridge when a resistance in the left gap is 2Ω and unknown resistance in the right gap, the balance length is found to be 40 cm. On shunting the unknown resistance with 2Ω, the balance length changes by:

1. A.22.5 cm✓
2. B.62.5 cm
3. C.65 cm
4. D.20 cm

Correct answer: A

A cricket player catches a ball of mass 120 g moving with 25 m/s speed. If the catching process is completed in 0.1 s then the magnitude of force exerted by the ball on the hand of player will be: (in SI unit):

1. A.12
2. B.30✓
3. C.25
4. D.24

Correct answer: B

If frequency of electromagnetic wave is 60 MHz and it travels in air along z direction then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other and the wavelength of the wave (in m) is:

1. A.10
2. B.2.5
3. C.5✓
4. D.2

Correct answer: C

$C_1$ and $C_2$ are two hollow concentric cubes enclosing charges 2Q and 3Q respectively as shown in figure. The ratio of electric flux passing through $C_1$ and $C_2$ is:

1. A.2 : 5✓
2. B.3 : 2
3. C.2 : 3
4. D.5 : 2

Correct answer: A

Train A is moving along two parallel rail tracks towards north with speed 72 km/h and train B is moving towards south with speed 108 km/h. Velocity of train B with respect to A and velocity of ground with respect to B are (in m s$^{-1}$):

1. A.−50 and −30
2. B.−50 and 30✓
3. C.50 and −30
4. D.−30 and 50

Correct answer: B

A microwave of wavelength 2.0 cm falls normally on a slit of width 4.0 cm. The angular spread of the central maxima of the diffraction pattern obtained on a screen 1.5 m away from the slit, will be:

1. A.45°
2. B.60°✓
3. C.30°
4. D.15°

Correct answer: B

A light planet is revolving around a massive star in a circular orbit of radius R with a period of revolution T. If the force of attraction between planet and star is proportional to $R^{-3/2}$ then chose the correct option:

1. A.$T^2\propto R^{7/2}$
2. B.$T^2\propto R^{5/2}$✓
3. C.$T^2\propto R^3$
4. D.$T^2\propto R^{3/2}$

Correct answer: B

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is 2 km/s, the root mean square velocity of oxygen at the same condition in km/s is:

1. A.0.5✓
2. B.1.0
3. C.1.5
4. D.2.0

Correct answer: A

A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become:

1. A.100 times
2. B.$\frac1{100}$th
3. C.10 times
4. D.$\frac1{10}$th✓

Correct answer: D

To measure the temperature coefficient of resistivity α of a semiconductor, an electrical arrangement shown in the figure is prepared. The arm BC is made up of the semiconductor. The experiment is being conducted at 25° and resistance of the semiconductor arm is 3 mΩ. Arm BC is cooled at a constant rate of 2°C/s. If the galvanometer G shows no deflection after 10 s. then α is:

1. A.$-1.5\times10^{-2}$ °C$^{-1}$
2. B.$-2\times10^{-2}$ °C$^{-1}$
3. C.$-1\times10^{-2}$ °C$^{-1}$✓
4. D.$-2.5\times10^{-2}$ °C$^{-1}$

Correct answer: C

Match List-I with List-II. List-I (Number): (A) 1001; (B) 010.1; (C) 100.100; (D) 0.0010010 List-II (Significant figure): (I) 3; (II) 4; (III) 5; (IV) 6 Choose the correct answer from the options given below:

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

Correct answer: C

Monochromatic light of frequency $6\times10^{14}$ Hz is produced by a laser. The power emitted is $2\times10^{-3}$ W. How many photons per second on an average, are emitted by the source?

1. A.$7\times10^{16}$
2. B.$9\times10^{18}$
3. C.$6\times10^{15}$
4. D.$5\times10^{15}$✓

Correct answer: D

A transformer has an efficiency of 80% and works at 10 V and 4 kW. If the secondary voltage is 240 V, then the current in the secondary coil is:

1. A.1.59 A
2. B.13.33 A✓
3. C.1.33 A
4. D.15.1 A

Correct answer: B

In an electrical circuit drawn below the amount of charge stored in the capacitor is ______ μC.

Correct answer: 60

A particle initially at rest starts moving from reference point x = 0 along x-axis, with velocity v that varies as $v=4\sqrt x$ m/s. The acceleration of the particle is ______ m s$^{-2}$.

Correct answer: 8

A mass m is suspended from a spring of negligible mass and the system oscillates with a frequency $f_1$. The frequency of oscillations if a mass 9 m is suspended from the same spring is $f_2$. The value of $\frac{f_1}{f_2}$ is ______.

Correct answer: 3

One end of a metal wire is fixed to a ceiling and a load of 2 kg hands from the other end. A similar wire is attached to the bottom of the load and anther load of 1 kg hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be ______. [Area of cross section of wire = 0.005 cm²; Y = $2\times10^{11}$ N m$^{-2}$ and g = 10 m s$^{-2}$]

Correct answer: 3

A coil of 200 turns and area 0.20 m² is rotated at half a revolution per second and is placed in uniform magnetic field of 0.01 T perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is $\frac{2\pi}{\beta}$ volt. The value of β is ______.

Correct answer: 5

A moving coil galvanometer has 100 turns and each has an area of 2.0 cm². The magnetic field produced by the magnet is 0.01 T and the deflection in the coil is 0.05 radian when a current of 10 mA is passed through it. The torsional constant of the suspension wire is $x\times10^{-5}$ N-m/rad. The value of x is ______.

Correct answer: 4

A uniform rod AB of mass 2 kg and length 30 cm at rest on a smooth horizontal surface. An impulse of force 0.2 Ns is applied to end B. The time taken by the rod to turn through at right angles will be $\frac\pi x$ s, where x = ______.

Correct answer: 4

A particular hydrogen - like ion emits the radiation of frequency $3\times10^{15}$ Hz when it makes transition from n = 2 to n = 1. The frequency of radiation emitted in transition from n = 3 to n = 1 is $\frac x9\times10^{15}$ Hz, when x = ______.

Correct answer: 32

In Yong's double slit experiment, monochromatic light of wavelength 5000 Å is used. The slits are 1.0 mm apart and screen is placed at 1.0 m away from slits. The distance from the centre of the screen where intensity becomes half of the maximum intensity for the first time is ______ $\times10^{-6}$ m.

Correct answer: 125

Suppose a uniformly charged wall provides a uniform electric field of $2\times10^4$ N/C normally. A charged particle of mass 2 g being suspended through a silk thread of length 20 cm and remain stayed at a distance of 10 cm from the wall. Then the charge on the particle will be $\frac1{\sqrt x}$ μC where x = ______. [use g = 10 m/s²]

Correct answer: 3

Given below are two statements: Statement (I): Both metals and non-metals exist in p and d-block elements. Statement (II): Non-metals have higher ionization enthalpy and higher electronegativity than the metals. In the light of the above statements, choose the most appropriate answer from the options given below:

1. A.Statements I is true but Statement II is false
2. B.Statement I is false but Statement II is true✓
3. C.Both Statement I and Statement II are true
4. D.Both Statement I and Statement II are false

Correct answer: B

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): In aqueous solutions $\text{Cr}^{2+}$ is reducing while $\text{Mn}^{3+}$ is oxidizing in nature. Reason (R): Extra stability to half filled electronic configuration is observed than incompletely filled electronic configuration. In the light of the above statements, choose the most appropriate answer from the options given below:

1. A.(A) is true but (R) is false
2. B.(A) is false but (R) is true
3. C.Both (A) and (R) are true and (R) is the correct explanation of (A)✓
4. D.Both (A) and (R) are true but (R) is not the correct explanation of (A)

Correct answer: C

Given below are two statements: Statement (I): $\text{SiO}_2$ and $\text{GeO}_2$ are acidic while SnO and PbO are amphoteric in nature. Statement (II): Allotropic forms of carbon are due to property of catenation and pπ-dπ bond formation. In the light of the above statements, choose the most appropriate answer from the options given below:

1. A.Statements I is true but Statement II is false✓
2. B.Both Statement I and Statement II are false
3. C.Statement I is false but Statement II is true
4. D.Both Statement I and Statement II are true

Correct answer: A

The number of radial node/s for 3p orbital is:

1. A.4
2. B.3
3. C.2
4. D.1✓

Correct answer: D

Solubility of calcium phosphate (molecular mass, M) in water is $W_g$ per 100 mL at 25 °C. Its solubility product at 25 °C will be approximately.

1. A.$10^7\left(\frac WM\right)^3$
2. B.$10^7\left(\frac WM\right)^5$✓
3. C.$10^3\left(\frac WM\right)^5$
4. D.$10^5\left(\frac WM\right)^5$

Correct answer: B

Match List-I with List-II. List-I (Compound): (A) Carbon tetrachloride; (B) Methylene chloride; (C) DDT; (D) Freons List-II (Use): (I) Paint remover; (II) Refrigerators and air conditioners; (III) Fire extinguisher; (IV) Non Biodegradable insecticide Choose the correct answer from the options given below:

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

Correct answer: D

The functional group that shows negative resonance effect is:

1. A.–OR
2. B.–OH
3. C.–COOH✓
4. D.–NH$_2$

Correct answer: C

$[\text{Co(NH}_3)_6]^{3+}$ and $[\text{CoF}_6]^{3-}$ are respectively known as:

1. A.Inner orbital complex, Spin paired Complex
2. B.Spin paired Complex, Spin free Complex✓
3. C.Outer orbital Complex Inner orbital Complex
4. D.Spin free Complex, Spin paired Complex

Correct answer: B

Which of the following compounds show colour due to d-d transition?

1. A.$\text{K}_2\text{CrO}_4$
2. B.$\text{K}_2\text{Cr}_2\text{O}_7$
3. C.$\text{CuSO}_4\cdot5\text{H}_2\text{O}$✓
4. D.$\text{KMnO}_4$

Correct answer: C

Lassaigne's test is used for detection of :

1. A.Phosphorous and halogens only
2. B.Nitrogen, Sulphur and Phosphorous only
3. C.Nitrogen, Sulphur and halogens✓
4. D.Nitrogen and Sulphur only

Correct answer: C

Select the compound from the following that will show intramolecular hydrogen bonding.

1. A.$\text{C}_2\text{H}_5\text{OH}$
2. B.o-Nitrophenol✓
3. C.$\text{NH}_3$
4. D.$\text{H}_2\text{O}$

Correct answer: B

In the given reaction identify A and B $\text{H}_2+A\xrightarrow{\text{Pd/C}}$ cis-$\text{CH}_3\text{CH=CHC}_2\text{H}_5$ (cis-pent-2-ene) $\text{CH}_3\text{-C}\equiv\text{C-CH}_3+\text{H}_2\xrightarrow{\text{Na/Liquid NH}_3}$ "B"

1. A.A : 2 – Pentyne, B : Cis – 2 – butene
2. B.A : n – Pentane, B : Cis – 2 – butene
3. C.A : 2 – Pentyne, B : trans – 2 – butene✓
4. D.A : n – Pentane, B : trans – 2 – butene

Correct answer: C

The set of meta directing functional groups from the following sets is:

1. A.–NO$_2$, –CHO, –SO$_3$H, –COR✓
2. B.–CN, –NH$_2$, –NHR, –OCH$_3$
3. C.–CN, –CHO, –NHCOCH$_3$, –COOR
4. D.–NO$_2$, –NH$_2$, –COOH, –COOR

Correct answer: A

Which among the following has highest boiling point?

1. A.$\text{H}_5\text{C}_2\text{-O-C}_2\text{H}_5$
2. B.$\text{CH}_3\text{CH}_2\text{CH}_2\text{CH}_3$
3. C.$\text{CH}_3\text{CH}_2\text{CH}_2\text{CHO}$
4. D.$\text{CH}_3\text{CH}_2\text{CH}_2\text{CH}_2\text{-OH}$✓

Correct answer: D

Given below are two statements: Statement (I): A π bonding MO has lower electron density above and below the inter-nuclear axis. Statement (II): The π* antibonding MO has a node between the nuclei. In the light of the above statements, choose the most appropriate answer from the options given below:

1. A.Both Statement I and Statement II are true
2. B.Statements I is true but Statement II is false
3. C.Statement I is false but Statement II is true✓
4. D.Both Statement I and Statement II are false

Correct answer: C

The transition metal having highest 3rd ionisation enthalpy is:

1. A.V
2. B.Fe
3. C.Mn✓
4. D.Cr

Correct answer: C

$\text{C}_2\text{H}_5\text{Br}\xrightarrow{\text{alc. KOH}}A\xrightarrow{\text{Br}_2/\text{CCl}_4}B\xrightarrow{\text{KCN (Excess)}}C\xrightarrow{\text{H}_3\text{O}^+\text{ (Excess)}}D$. Acid D formed in above reaction is:

1. A.Succinic acid✓
2. B.Oxalic acid
3. C.Gluconic acid
4. D.Malonic acid

Correct answer: A

Given below are two statements: Statement (I): Dimethyl glyoxime forms a six-membered covalent chelate when treated with $\text{NiCl}_2$ solution in presence of $\text{NH}_4\text{OH}$. Statement (II): Prussian blue precipitate contains ion both in (+2) and (+3) oxidation states. In the light of the above statements, choose the most appropriate answer from the options given below:

1. A.Statements I is true but Statement II is false
2. B.Both Statement I and Statement II are false
3. C.Both Statement I and Statement II are true
4. D.Statement I is false but Statement II is true✓

Correct answer: D

The strongest reducing agent among the following is:

1. A.$\text{PH}_3$
2. B.$\text{NH}_3$
3. C.$\text{BiH}_3$✓
4. D.$\text{SbH}_3$

Correct answer: C

Match List-I with List-II. List-I (Reactants): (A) Phenol, Zn/Δ; (B) Phenol, $\text{CHCl}_3$, NaOH, HCl; (C) Phenol, $\text{CO}_2$, NaOH, HCl; (D) Phenol, Conc. $\text{HNO}_3$ List-II (Product): (I) Salicylaldehyde; (II) Salicylic acid; (III) Benzene; (IV) Picric acid Choose the correct answer from the options given below:

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

Correct answer: D

Total number of isomeric compounds (including stereoisomers) formed by monochlorination of 2-methylbutane is ______.

Correct answer: 6

Mass of ethylene glycol (antifreeze) to be added to 18.6 kg of water to protect the freezing point at –24°C is ______ kg (Molar mass in g mol$^{-1}$ for ethylene glycol 62, $K_f$ of water = 1.86 K kg mol$^{-1}$)

Correct answer: 15

For a certain reaction at 300 K, K = 10, then ΔG° for the same reaction is ______ $\times10^{-1}$ kJ mol$^{-1}$. (Given R = 8.314 J K$^{-1}$ mol$^{-1}$)

Correct answer: 57

The number of tripeptides formed by three different amino acids using each amino acid once is ______.

Correct answer: 6

10 mL of gaseous hydrocarbon on combustion gives 40 mL of $\text{CO}_2$(g) and 50 mL of water vapour. Total number of carbon and hydrogen atoms in the hydrocarbon is ______.

Correct answer: 14

The amount of electricity in Columb required for the oxidation of 1 mol of $\text{H}_2\text{O}$ to $\text{O}_2$ is ______ $\times10^5$ C.

Correct answer: 2

Number of compounds which give reaction with Hinsberg's reagent is ______.

Correct answer: 5

Following Kjeldahl's method, 1g of organic compound released ammonia, that neutralised 10 mL of 2M $\text{H}_2\text{SO}_4$. The percentage of nitrogen in the compound is ______ %.

Correct answer: 56

Consider the following redox reaction: $\text{MnO}_4^-+\text{H}^++\text{H}_2\text{C}_2\text{O}_4\rightleftharpoons\text{Mn}^{2+}+\text{H}_2\text{O}+\text{CO}_2$. The standard reduction potentials are given as below: $E^\circ_{\text{MnO}_4^-/\text{Mn}^{2+}}=+1.51$ V; $E^\circ_{\text{CO}_2/\text{H}_2\text{C}_2\text{O}_4}=-0.49$ V. If the equilibrium constant of the above reaction is given as $K_{eq}=10^x$, then the value of x = ______. (nearest Integer)

Correct answer: 338

The following data were obtained during the first order thermal decomposition of a gas A at constant volume: $A(g)\to2B(g)+C(g)$ | S. No. | Time/s | Total pressure/(atm) | | 1. | 0 | 0.1 | | 2. | 115 | 0.28 | The rate constant of the reaction is ______ $\times10^{-2}$ s$^{-1}$ (nearest integer)

Correct answer: 2