JEE Main 2024 1 Feb Shift 2 Question Paper (Available)- Download Solution PDF with Answer Key

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) 140
• (2) 175
• (3) 150
• (4) 125

If \(z\) is a complex number such that \(|z| \geq 1\), then the minimum value of \[\left| z + \frac{1}{2}(3 + 4i) \right|\]is:

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

Consider a \(\triangle ABC\) where \(A(1, 2, 3)\), \(B(-2, 8, 0)\), and \(C(3, 6, 7)\). If the angle bisector of \(\angle BAC\) meets the line \(BC\) at \(D\), then the length of the projection of the vector \(\overrightarrow{AD}\) on the vector \(\overrightarrow{AC}\) is:

• (1) \(\frac{37}{2\sqrt{38}}\)
• (2) \(\frac{\sqrt{38}}{2}\)
• (3) \(\frac{39}{2\sqrt{38}}\)
• (4) \(\sqrt{19}\)

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

• (1) Only R1 is an equivalence relation
• (2) Only R2 is an equivalence relation
• (3) R1 and R2 both are equivalence relations
• (4) Neither R1 nor R2 is an equivalence relation

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

• (1) 28
• (2) 17
• (3) 22
• (4) 15

If \[\int_{0}^{\frac{\pi}{3}} \cos^4 x \, dx = a\pi + b\sqrt{3},\]where \(a\) and \(b\) are rational numbers, then \(9a + 8b\) is equal to:

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

Let \(\alpha\) and \(\beta\) be the roots of the equation \(px^2 + qx - r = 0\), where \(p \neq 0\). If \(p, q,\) and \(r\) be the consecutive terms of a non-constant G.P. and \[\frac{1}{\alpha} + \frac{1}{\beta} = \frac{3}{4},\] then the value of \((\alpha - \beta)^2\) is:

• (1) \(\frac{80}{9}\)
• (2) 9
• (3) \(\frac{20}{3}\)
• (4) 8

Let Ajay will not appear in JEE exam with probability \(p = \frac{2}{7}\), while both Ajay and Vijay will appear in the exam with probability \(q = \frac{1}{5}\). Then the probability that Ajay will appear in the exam and Vijay will not appear is:

• (1) \(\frac{9}{35}\)
• (2) \(\frac{18}{35}\)
• (3) \(\frac{24}{35}\)
• (4) \(\frac{3}{35}\)

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 the \(y\)-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) \(\frac{11}{19}\)
• (2) \(\frac{13}{21}\)
• (3) \(\frac{\sqrt{139}}{23}\)
• (4) \(\frac{\sqrt{13}}{7}\)

Consider 10 observations \(x_1, x_2, \ldots, x_{10}\) such that \[\sum_{i=1}^{10} (x_i - \alpha) = 2 \quad \text{and} \quad \sum_{i=1}^{10} (x_i - \beta)^2 = 40,\]where \(\alpha, \beta\) are positive integers. Let the mean and the variance of the observations be \(\frac{6}{5}\) and \(\frac{84}{25}\), respectively. The value of \(\frac{\beta}{\alpha}\) is equal to:

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

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

• (1) 5
• (2) 2
• (3) 0
• (4) 3

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

• (1) 1
• (2) 3
• (3) 2
• (4) 0

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

Let \(\alpha\) be a non-zero real number. Suppose \(f : \mathbb{R} \to \mathbb{R}\) is a differentiable function such that \(f(0) = 2\) and \[\lim_{x \to \infty} f(x) = 1.\]If \(f'(x) = \alpha f(x) + 3\), for all \(x \in \mathbb{R}\), then \(f(-\log 2)\) is equal to ________ .

• (1) 3
• (2) 5
• (3) 9
• (4) 7

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 triangle \(PQR\) is \((\alpha, \beta, \gamma)\), then \(\alpha^2 + \beta^2 + \gamma^2\) is:

• (1) 26
• (2) 36
• (3) 18
• (4) 24

The value of \[\int_{0}^{1} \left(2x^3 - 3x^2 - x + 1\right)^{\frac{1}{3}} \, dx\]is equal to:

• (1) 0
• (2) 1
• (3) 2
• (4) -1

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) 102
• (2) 138
• (3) 108
• (4) 132

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) 800
• (2) 890
• (3) 790
• (4)
  690

Let \(m\) and \(n\) be the coefficients of the seventh and thirteenth terms respectively in the expansion of \[\left( \frac{1}{3}x^{\frac{1}{3}} + \frac{1}{2x^{\frac{2}{3}}} \right)^{18}.\]Then \[\left(\frac{n}{m}\right)^{\frac{1}{3}}\]is:

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

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

• (1) 121
• (2) 144
• (3) 169
• (4) 225

Three points \(O(0, 0)\), \(P(a, a^2)\), \(Q(-b, b^2)\), \(a>0, b>0\), 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 \(\frac{m}{n}\), \(\gcd(m, n) = 1\), then \(m + n\) is equal to:

The sum of squares of all possible values of \(k\), for which the area of the region bounded by the parabolas \[2y^2 = kx \quad \text{and} \quad ky^2 = 2(y - x)\]is maximum, is equal to:

If \[y = \frac{\left(\sqrt{x} + 1\right)\left(x^2 - \sqrt{x}\right)}{x\sqrt{x} + x + \sqrt{x}} + \frac{1}{15}(3\cos^2 x - 5)\cos^3 x,\]then \(96y'\left(\frac{\pi}{6}\right)\) is equal to:

If \[\frac{dx}{dy} = \frac{1 + x - y^2}{y}, \quad x(1) = 1,\]then \(5x(2)\) is equal to:

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

Let \(\triangle ABC\) 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 \(BC = 4\sqrt{3}\) and the line \(BC\) intersects the line \(y = x + 3\) at \((\alpha, \beta)\), then \(\frac{\beta^4}{\alpha^2}\) is:

Let \(A=I_2-2MM^T\), where \(M\) is a real matrix of order \(2\times1\) such that the relation \(M^TM=I_1\) holds. If \(\lambda\) is a real number such that the relation \(AX=\lambda X\) holds for some non-zero real matrix \(X\) of order \(2\times1\), then the sum of squares of all possible values of \(\lambda\) is equal to ____________ .

Let \[\vec{a} = \hat{i} + \hat{j} + \hat{k}, \quad \vec{b} = -\hat{i} - 8\hat{j} + 2\hat{k}, \quad \text{and} \quad \vec{c} = 4\hat{i} + c_2\hat{j} + c_3\hat{k} \]be three vectors such that \[\vec{b} \times \vec{a} = \vec{c} \times \vec{a}.\]If the angle between the vector \(\vec{c}\) and the vector \(3\hat{i} + 4\hat{j} + \hat{k}\) is \(\theta\), then the greatest integer less than or equal to \(\tan^2 \theta\) is:

If three successive terms of a G.P. with common ratio \(r \, (r>1)\) are the lengths of the sides of a triangle and \(\lfloor r \rfloor\) denotes the greatest integer less than or equal to \(r\), then \(3\lfloor r \rfloor + \lfloor -r \rfloor\) is equal to:

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

From the statements given below :
(A) The angular momentum of an electron in nth orbit is an integral multiple of h.
(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), (B), (C), (D) only
• (2) (A), (C), (D), (E) only
• (3) (A), (B), (C), (E) only
• (4) (B), (C), (D), (E) only

A body of mass \(4 \, \text{kg}\) experiences two forces \[\vec{F}_1 = 5\hat{i} + 8\hat{j} + 7\hat{k} \quad \text{and} \quad \vec{F}_2 = 3\hat{i} - 4\hat{j} - 3\hat{k}.\]The acceleration acting on the body is:

• (1) \(-2\hat{i} - \hat{j} - \hat{k}\)
• (2) \(4\hat{i} + 2\hat{j} + 2\hat{k}\)
• (3) \(2\hat{i} + \hat{j} + \hat{k}\)
• (4) \(2\hat{i} + 3\hat{j} + 3\hat{k}\)

Monochromatic light of frequency \(6 \times 10^{14}\) Hz is produced by a laser. The power emitted is \(2 \times 10^{-3}\) W. How many photons per second on average are emitted by the source.(Given \(h = 6.63 \times 10^{-34} \, \text{Js}\))

• (1) \(9 \times 10^{18}\)
• (2) \(6 \times 10^{15}\)
• (3) \(5 \times 10^{15}\)
• (4) \(7 \times 10^{16}\)

C1 and C2 are two hollow concentric cubes enclosing charges 2Q and 3Q respectively as shown in figure. The ratio of electric flux passing through C1 and C2 is :

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

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

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

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

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

• (1) 100 times
• (2) 10 times
• (3) \(\frac{1}{100}th\)
• (4) \(\frac{1}{10}th\)

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) 24
• (2) 12
• (3) 25
• (4) 30

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

• (1) 22.5 cm
• (2) 20 cm
• (3) 62.5 cm
• (4) 65 cm

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

• (1) 850 J
• (2) 800 J
• (3) 600 J
• (4) 700 J

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) –30 and 50
• (2) –50 and –30
• (3) –50 and 30
• (4) 50 and –30

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 the planet and the star is proportional to \(R^{-\frac{3}{2}}\), then choose the correct option:

• (1) \(T^2 \propto R^{5/2}\)
• (2) \(T^2 \propto R^{7/2}\)
• (3) \(T^2 \propto R^{3/2}\)
• (4) \(T^2 \propto R^3\)

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) \(30\degree\)
• (2) \(15\degree\)
• (3) \(60\degree\)
• (4) \(45\degree\)

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) 2.0
• (2) 0.5
• (3) 1.5
• (4) 1.0

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) 2.5
• (2) 10
• (3) 5
• (4) 2

To measure the temperature coefficient of resistivity \(\alpha\) 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 \(25^\circ \text{C}\) and the resistance of the semiconductor arm is \(3 \, \text{m}\Omega\). Arm BC is cooled at a constant rate of \(2^\circ \text{C/s}\). If the galvanometer G shows no deflection after 10 s, then \(\alpha\) is:

• (1) \(-2 \times 10^{-2} \, \degree \text{C}^{-1}\)
• (2) \(-1.5 \times 10^{-2} \, \degree \text{C}^{-1}\)
• (3) \(-1 \times 10^{-2} \, \degree \text{C}^{-1}\)
• (4) \(-2.5 \times 10^{-2} \, \degree \text{C}^{-1}\)

Conductivity of a photodiode starts changing only if the wavelength of incident light is less than 660 nm. The band gap of the photodiode is found to be \[\frac{X}{8} \, \text{eV}.\]The value of \(X\) is:(Given, \(h = 6.6 \times 10^{-34} \, \text{Js}\), \(e = 1.6 \times 10^{-19} \, \text{C}\))

• (1) 15
• (2) 11
• (3) 13
• (4) 21

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

• (1) 1.59 A
• (2) 13.33 A
• (3) 1.33 A
• (4) 15.1 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) \(\frac{G}{200}\)
• (2) \(\frac{G}{199}\)
• (3) 199 G
• (4) 200 G
• (5) None of these

A disc of radius R and mass M is rolling horizontally without slipping with speed . 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) \(\frac{v^2}{g}\)
• (2) \(\frac{3v^2}{4g}\)
• (3) \(\frac{v^2}{2g}\)
• (4) \(\frac{2v^2}{3g}\)

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 \(9m\) is suspended from the same spring is \(f_2\). The value of \(\frac{f_1}{f_2}\) is ___.

In an electrical circuit drawn below, the amount of charge stored in the capacitor is ______ \(\mu C\).

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

Suppose a uniformly charged wall provides a uniform electric field of \(2 \times 10^4 \, \text{N/C}\) normally. A charged particle of mass \(2 \, \text{g}\) is suspended through a silk thread of length 20 cm and remains stayed at a distance of 10 cm from the wall. Then the charge on the particle will be \[\frac{1}{\sqrt{x}} \, \mu\text{C}, \, \text{where} \, x = \_.\]

A moving coil galvanometer has 100 turns and each turn has an area of \(2.0 \, \text{cm}^2\). The magnetic field produced by the magnet is \(0.01 \, \text{T}\) and the deflection in the coil is \(0.05\) radians when a current of \(10 \, \text{mA}\) is passed through it. The torsional constant of the suspension wire is \(x \times 10^{-5} \, \text{N} \cdot \text{m/rad}\). The value of \(x\) is:

One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1 kg hangs from this lower wire. Then the ratio of longitudinal strain of the upper wire to that of the lower wire will be:\[\text{[Area of cross section of wire = 0.005 cm}^2, \, Y = 2 \times 10^{11} \, \text{N/m}^2, \, g = 10 \, \text{m/s}^2\text{]}\]

In Young's double slit experiment, monochromatic light of wavelength 5000 \, Å is used. The slits are 1.0 mm apart and the screen is placed 1.0 m away from the slits. The distance from the centre of the screen where intensity becomes half of the maximum intensity for the first time is \[\_ \times 10^{-6} \, \text{m}.\]

A coil of 200 turns and area \(0.20 \, \text{m}^2\) is rotated at half a revolution per second and is placed in a uniform magnetic field of \(0.01 \, \text{T}\) perpendicular to the axis of rotation of the coil. The maximum voltage generated in the coil is \[\frac{2\pi}{\beta} \, \text{volt}.\]The value of \(\beta\) is:

A uniform rod AB of mass 2 kg and length 30 cm is 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 a right angle will be \[\frac{\pi}{x} \, s, \, \text{where} \, x = \_.\]

A particular hydrogen-like ion emits the radiation of frequency \(3 \times 10^{15}\) Hz when it makes a transition from \(n = 2\) to \(n = 1\). The frequency of radiation emitted in the transition from \(n = 3\) to \(n = 1\) is \(\frac{x}{9} \times 10^{15}\) Hz, when \(x =\) _____ .

In the given reactions identify A and B.

• (1) A: 2–Pentyne    B: trans–2–butene
• (2) A: n–Pentane    B: trans–2–butene
• (3) A: 2–Pentyne    B: Cis–2–butene
• (4) A: n–Pentane    B: Cis–2–butene

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

• (1) \( 10^7 \left( \frac{W}{M} \right)^3 \)
• (2) \( 10^7 \left( \frac{W}{M} \right)^5 \)
• (3) \( 10^3 \left( \frac{W}{M} \right)^5 \)
• (4) \( 10^5 \left( \frac{W}{M} \right)^5 \)

Given below are two statements:
Statement (I): \( \text{SiO}_2 \) and \( \text{GeO}_2 \) are acidic while \( \text{SnO} \) and \( \text{PbO} \) are amphoteric in nature.
Statement (II): Allotropic forms of carbon are due to property of catenation and \( p\pi-d\pi \) bond formation.
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 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 set of meta directing functional groups from the following sets is:

• (1) –CN, –NH\(_2\), –NHR, –OCH\(_3\)
• (2) –NO\(_2\), –NH\(_2\), –COOH, –COOR
• (3) –NO\(_2\), –CHO, –SO\(_3\)H, –COR
• (4) –CN, –CHO, –NHCOCH\(_3\), –COOR

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

• (1) Spin free Complex, Spin paired Complex
• (2) Spin paired Complex, Spin free Complex
• (3) Outer orbital Complex, Inner orbital Complex
• (4) Inner orbital Complex, Spin paired Complex

The transition metal having highest \(3^\text{rd}\) ionisation enthalpy is:

• (1) Cr
• (2) Mn
• (3) V
• (4) Fe

Match List - I with List - II

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

Match List - I with List - II.

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

Given below are two statements :
Statement (I) : Dimethyl glyoxime forms a six-membered covalent chelate when treated with NiCl2 solution in presence of NH4OH.
Statement (II) : Prussian blue precipitate contains iron 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) Statement I is false but Statement II is true
• (2) Both Statement I and Statement II are true
• (3) Both Statement I and Statement II are false
• (4) Statement I is true but Statement II is false

• (1) Gluconic acid
• (2) Succinic acid
• (3) Oxalic acid
• (4) Malonic acid

Lassaigne's test is used for detection of :

• (1) Nitrogen and Sulphur only
• (2) Nitrogen, Sulphur and Phosphorous Only
• (3) Phosphorous and halogens only
• (4) Nitrogen, Sulphur, phosphorous and halogens

The strongest reducing agent amont the following is:

• (1) \( \text{NH}_3 \)
• (2) \( \text{SbH}_3 \)
• (3) \( \text{BiH}_3 \)
• (4) \( \text{PH}_3 \)

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 oxidising in nature.
Reason (R): Extra stability to half-filled electronic configuration is observed than incompletely filled electronic configuration.
In the light of the above statement, choose the most appropriate answer from the options given below:

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

The functional group that shows negative resonance effect is:

• (1) –NH\(_2\)
• (2) –OH
• (3) –COOH
• (4) –OR

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

• (1) 1
• (2) 4
• (3) 2
• (4) 3

Which among the following has highest boiling point?

• (1) \( \text{CH}_3\text{CH}_2\text{CH}_2\text{CH}_3 \)
• (2) \( \text{CH}_3\text{CH}_2\text{CH}_2\text{CH}_2\text{–OH} \)
• (3) \( \text{CH}_3\text{CH}_2\text{CH}_2\text{CHO} \)
• (4) \( \text{H}_5\text{C}_2 - \text{O} - \text{C}_2\text{H}_5 \)

Given below are two statements:
Statement (I): A \(\pi\) bonding MO has lower electron density above and below the inter-nuclear axis.
Statement (II): The \(\pi^*\) 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) Both Statement I and Statement II are false
• (2) Both Statement I and Statement II are true
• (3) Statement I is false but Statement II is true
• (4) Statement I is true but Statement II is false

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

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

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

• (1) \( \text{CuSO}_4.5\text{H}_2\text{O} \)
• (2) \( \text{K}_2\text{Cr}_2\text{O}_7 \)
• (3) \( \text{K}_2\text{CrO}_4 \)
• (4) \( \text{KMnO}_4 \)

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

• (1) \( \text{H}_2\text{O} \)
• (2) \( \text{NH}_3 \)
• (3) \( \text{C}_2\text{H}_5\text{OH} \)
• (4)

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

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

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

The following data were obtained during the first order thermal decomposition of a gas A at constant volume:\[\text{A(g)} \rightarrow 2\text{B(g)} + \text{C(g)}\]\[\begin{array}{|c|c|c|}\hline\text{S.No} & \text{Time/s} & \text{Total pressure/(atm)} \\\hline1 & 0 & 0.1 \\2 & 115 & 0.28 \\\hline\end{array}\]The rate constant of the reaction is _____ \(\times 10^{-2}\) s\(^{-1}\) (nearest integer).

For a certain reaction at 300 K, \( K = 10 \), then \( \Delta G^\circ \) for the same reaction is \[- \, \_ \times 10^{-1} \, \text{kJ mol}^{-1}.\](Given \( R = 8.314 \, \text{JK}^{-1} \text{mol}^{-1} \))

The amount of electricity in Coulomb required for the oxidation of 1 mol of \( \text{H}_2\text{O} \) to \( \text{O}_2 \) is \[\_ \times 10^5 \, \text{C}.\]

Following Kjeldahl's method, 1g of organic compound released ammonia that neutralized 10 mL of 2M H\(_2\)SO\(_4\). The percentage of nitrogen in the compound is _________.%.

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\(_\text{red}\)):\[E^\circ_{\text{MnO}_4^-/\text{Mn}^{2+}} = +1.51 \, \text{V}\]\[E^\circ_{\text{CO}_2/\text{H}_2 \text{C}_2 \text{O}_4} = -0.49 \, \text{V}\]If the equilibrium constant of the above reaction is given as \(K_\text{eq} = 10^x\), then the value of (x = ________ ) (nearest integer).

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

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