JEE Main 2025 28 Jan Shift 1 Question Paper With Solutions (Available)- Download Shift Wise Free Pdf and Most Asked Questions

Let for some function \( y = f(x) \), \(\int_0^x t f(t) \, dt = x^2 f(x), x > 0\) and \( f(2) = 3 \). Then \( f(6) \) is equal to:

• (1) 3
• (2) 1
• (3) 6
• (4) 2

The sum of the squares of all the roots of the equation \( x^2 + [2x - 3] - 4 = 0 \) is:

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

The sum of all local minimum values of the function \( f(x) \) as defined below is: \[ f(x) = \left\{ \begin{array}{ll} 1 - 2x & \text{if } x < -1
\frac{1}{3}(7 + 2|x|) & \text{if } -1 \leq x \leq 2
\frac{11}{18} (x-4)(x-5) & \text{if } x > 2 \end{array} \right. \]

• (1) \(\frac{167}{72}\)
• (2) \(\frac{171}{72}\)
• (3) \(\frac{131}{72}\)
• (4) \(\frac{157}{72}\)

Let \( \langle a_n \rangle \) be a sequence such that \( a_0 = 0 \), \( a_1 = \frac{1}{2} \), and \( 2a_{n+2} = 5a_{n+1} - 3a_n \).n= 0,1,2,3.... Then \( \sum_{k=1}^{100} a_k \) is equal to:

• (1) \( 3a_{99} + 100 \)
• (2) \( 3a_{99} - 100 \)
• (3) \( 3a_{100} + 100 \)
• (4) \( 3a_{100} - 100 \)

If the image of the point \( (4, 4, 3) \) in the line \( \frac{x-1}{2} = \frac{y-2}{1} = \frac{z-1}{3} \) is \( (a, \beta, \gamma) \), then \( a + \beta + \gamma \) is equal to:

• (1) 9
• (2) 7
• (3) 8
• (4) 12

The value of \( \cos \left( \sin^{-1} \left(-\frac{3}{5}\right) + \sin^{-1} \left(\frac{5}{13}\right) + \sin^{-1} \left(-\frac{33}{65}\right) \right) \) is:

• (1) \(\frac{32}{65}\)
• (2) 1
• (3) \(\frac{33}{65}\)
• (4) 0

Three defective oranges are accidentally mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If \( x \) denotes the number of defective oranges, then the variance of \( x \) is:

• (1) \(\frac{26}{75}\)
• (2) \(\frac{14}{25}\)
• (3) \(\frac{28}{75}\)
• (4) \(\frac{18}{25}\)

Let the equation of the circle, which touches x-axis at the point \( (a, 0) \) and cuts off an intercept of length \( b \) on y-axis be \( x^2 + y^2 - cx + dy + e = 0 \). If the circle lies below x-axis, then the ordered pair \( (2a, b^2) \) is equal to:

• (1) \( (y, \beta^2 - 4\alpha) \)
• (2) \( (\alpha, \beta^2 - 4\gamma) \)
• (3) \( (y, \beta^2 + 4\alpha) \)
• (4) \( (\alpha, \beta^2 + 4\gamma) \)

Let O be the origin, the point A be \( z_1 = \sqrt{3} + 2\sqrt{2}i \), the point B \( z_2 \) be such that \( \sqrt{3}|z_2| = |z_1| \) and \( \arg(z_2) = \arg(z_1) + \frac{\pi}{6} \). Then:

• (1) ABO is a scalene triangle
• (2) Area of triangle ABO is \(\frac{11}{4}\)
• (3) ABO is an obtuse angled isosceles triangle
• (4) Area of triangle ABO is \(\frac{11}{\sqrt{3}}\)

The area (in sq. units) of the region \((x, y) : 0 \leq y \leq 2|x| + 1, 0 \leq y \leq x^2 + 1, |x| \leq 3\) is:

• (1) \(\frac{64}{3}\)
• (2) \(\frac{17}{3}\)
• (3) \(\frac{32}{3}\)
• (4) \(\frac{80}{3}\)

Let \(T_{n-1} = 28\), \(T_n = 56\), and \(T_{n+1} = 70\). Let A \((4\cos t, 4\sin t)\), B \((2\sin t, -2\cos t)\), and C \((3r_n - 1, r^2_n - n - 1)\) be the vertices of a triangle ABC, where \(t\) is a parameter. If \((3x - 1)^2 + (3y)^2 = a\), is the locus of the centroid of triangle ABC, then \(a\) equals:

• (1) 18
• (2) 8
• (3) 6
• (4) 20

The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is:

• (1) 5719
• (2) 4608
• (3) 5720
• (4) 4607

If \( f(x) = \frac{2^x}{2^x + \sqrt{2}} \), \(x \in \mathbb{R}\), then \(\sum_{k=1}^{81} f\left(\frac{k}{82}\right)\) is equal to:

• (1) 82
• (2) \(\frac{81}{2}\)
• (3) 41
• (4) \(81\sqrt{2}\)

Two numbers \(k_1\) and \(k_2\) are randomly chosen from the set of natural numbers. Then, the probability that the value of \(i^{k_1} + i^{k_2}\) (where \(i = \sqrt{-1}\)) is non-zero equals:

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

Let A \((x, y, z)\) be a point in \(xy\)-plane, which is equidistant from three points (0, 3, 2), (2, 0, 3) and (0, 0, 1). Let B \((1, 4, -1)\) and C \((2, 0, -2)\). Then among the statements: (S1): ABC is an isosceles right angled triangle, and
(S2): the area of \(\triangle ABC\) is \( \frac{9\sqrt{2}}{2} \).

• (1) only (S1) is true
• (2) both are true
• (3) only (S2) is true
• (4) both are false

Let \( f: \mathbb{R} \to \mathbb{R} \) be a function defined by \( f(x) = \left( 2 + 3a \right)x^2 + \left( \frac{a+2}{a-1} \right)x + b, a \neq 1 \). If \[ f(x + y) = f(x) + f(y) + 1 - \frac{2}{7}xy, \] then the value of \( 28 \sum_{i=1}^5 f(i) \) is:

• (1) 715
• (2) 735
• (3) 545
• (4) 675

If \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{96x^2 \cos^2 x}{1 + e^x} dx = \pi(a\pi^2 + \beta), \quad a, \beta \in \mathbb{Z}, \] then \( (a + \beta)^2 \) equals:

• (1) 100
• (2) 64
• (3) 144
• (4) 196

Let \( T_r \) be the \( r^{th} \) term of an A.P. If for some \( m \), \( T_m = \frac{1}{25} \), \( T_{25} = \frac{1}{20} \), and \( \sum_{r=1}^{25} T_r = 13 \), then \[ 5m \sum_{r=m}^{2m} T_r \text{ is equal to:} \]

• (1) 112
• (2) 142
• (3) 126
• (4) 98

Let ABCD be a trapezium whose vertices lie on the parabola \( y^2 = 4x \). Let the sides AD and BC of the trapezium be parallel to the y-axis. If the diagonal AC is of length \( \frac{25}{4} \) and it passes through the point \( (1, 0) \), then the area of ABCD is:

• (1) \( \frac{125}{8} \)
• (2) \( \frac{75}{8} \)
• (3) \( \frac{25}{2} \)
• (4) \( \frac{75}{4} \)

The relation \( R = \{(x, y) : x, y \in \mathbb{Z} \text{ and } x + y \text{ is even} \} \) is:

• (1) reflexive and transitive but not symmetric
• (2) reflexive and symmetric but not transitive
• (3) symmetric and transitive but not reflexive
• (4) an equivalence relation

If \(a = 1 + \sum_{r=1}^{6} (-3)^{r-1} \binom{12}{2r-1}\), then the distance of the point \((12, \sqrt{3})\) from the line \(\alpha x - \sqrt{3}y + 1 = 0\) is:

Let \(E_1: \frac{x^2}{9} + \frac{y^2}{4} = 1\) be an ellipse. Ellipses \(E_i\) are constructed such that their centers and eccentricities are the same as that of \(E_1\), and the length of the minor axis of \(E_{i+1}\) is the length of the major axis of \(E_i\). If \(A_i\) is the area of the ellipse \(E_i\), then \(\frac{5}{\pi} \sum_{i=1}^{\infty} A_i\) is equal to:

Let \(\vec{a} = i + j + k\), \(\vec{b} = 2i + 2j + k\) and \(\vec{d} = \vec{a} \times \vec{b}\). If \(\vec{c}\) is a vector such that \(\vec{a} \cdot \vec{c} = |\vec{c}|\), \(\|\vec{c} - 2\vec{d}\| = 8\) and the angle between \(\vec{d}\) and \(\vec{c}\) is \(\frac{\pi}{4}\), then \(\left|10 - 3\vec{b} \cdot \vec{c} + |\vec{d}|\right|^2\) is equal to:

Let \(f(x)\) be defined as follows: \[ f(x) = \begin{cases} 3x, & \text{if } x < 0
\min(1+x+\lfloor x \rfloor, 2+x\lfloor x \rfloor), & \text{if } 0 \leq x \leq 2
5, & \text{if } x > 2 \end{cases} \] where \(\lfloor . \rfloor\) denotes the greatest integer function. If \(\alpha\) and \(\beta\) are the number of points, where \(f\) is not continuous and is not differentiable, respectively, then \(\alpha + \beta\) equals:

Let \(M\) denote the set of all real matrices of order 3 x 3 and let \(S = \{-3, -2, -1, 1, 2\}\). Let \[ S_1 = \{A = [a_{ij}] \in M : A = A^T \text{ and } a_{ij} \in S, \forall i, j\}, \] \[ S_2 = \{A = [a_{ij}] \in M : A = -A^T \text{ and } a_{ij} \in S, \forall i, j\}, \] \[ S_3 = \{A = [a_{ij}] \in M : a_{11} + a_{22} + a_{33} = 0 \text{ and } a_{ij} \in S, \forall i, j\}. \] If \(n(S_1 \cup S_2 \cup S_3) = 125\), then \(\alpha\) equals:

Consider a long thin conducting wire carrying a uniform current \( I \). A particle having mass \( M \) and charge \( q \) is released at a distance \( a \) from the wire with a speed \( v_0 \) along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance \( x \) from the wire. The value of \( x \) is:

• (1) \( \frac{a}{2} \)
• (2) \( a \left( 1 - \frac{mv_0}{q\mu_0 I} \right) \)
• (3) \( ae \left( -4 \frac{mv_0}{q\mu_0 I} \right) \)
• (4) \( a \left[ 1 - \frac{mv_0}{2q\mu_0 I} \right] \)

A thin prism \( P_1 \) with angle \( 4^\circ \) made of glass having refractive index 1.54 is combined with another thin prism \( P_2 \) made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism \( P_2 \) in degrees is:

• (1) 1.5
• (2) 3
• (3) \( \frac{16}{3} \)
• (4) 4

A hemispherical vessel is completely filled with a liquid of refractive index \( \mu \). A small coin is kept at the lowest point \( O \) of the vessel as shown in the figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point \( E \) (at the level of the vessel) is:
 

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

A particle of mass \( m \) and charge \( q \) is fastened to one end \( A \) of a massless string having equilibrium length \( l \), whose other end is fixed at point \( O \). The whole system is placed on a frictionless horizontal plane and is initially at rest. If a uniform electric field is switched on along the direction as shown in the figure, then the speed of the particle when it crosses the x-axis is:

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

Which of the following circuits has the same output as that of the given circuit?

For a particular ideal gas, which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

A bead of mass \( m \) slides without friction on the wall of a vertical circular hoop of radius \( R \) as shown in figure. The bead moves under the combined action of gravity and a massless spring \( k \) attached to the bottom of the hoop. The equilibrium length of the spring is \( R \). If the bead is released from the top of the hoop with (negligible) zero initial speed, the velocity of the bead, when the length of spring becomes \( R \), would be (spring constant is \( k \), \( g \) is acceleration due to gravity):

• (1) \( \sqrt{\frac{3Rg + kR^2}{m}} \)
• (2) \( \sqrt{\frac{2Rg + kR^2}{m}} \)
• (3) \( \sqrt{\frac{2gR + kR^2}{m}} \)
• (4) \( \sqrt{\frac{2Rg + 4kR^2}{m}} \)

Due to presence of an em-wave whose electric component is given by \( E = 100 \sin(\omega t - kx) \, \text{NC}^{-1} \), a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as:

• (1) \( 200 \sin(\omega t - kx) \, \text{NC}^{-1} \)
• (2) \( 25 \sin(\omega t - kx) \, \text{NC}^{-1} \)
• (3) \( 50 \sin(\omega t - kx) \, \text{NC}^{-1} \)
• (4) \( 400 \sin(\omega t - kx) \, \text{NC}^{-1} \)

Three infinitely long wires with linear charge density \( \lambda \) are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?

• (1) \( (x + y)(y + z)(z + x) = \text{constant} \)
• (2) \( xyz = \text{constant} \)
• (3) \( xy + yz + zx = \text{constant} \)
• (4) \( (x^2 + y^2)(y^2 + z^2)(z^2 + x^2) = \text{constant} \)

Consider the following statements: Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface of a liquid. As the temperature of liquid rises, the coefficient of viscosity increases. As the temperature of gas increases, the coefficient of viscosity increases. The onset of turbulence is determined by Reynolds number. In a steady flow, two streamlines never intersect. Choose the correct answer from the options given below:

• (1) A, B, C Only
• (2) C, D, E Only
• (3) B, C, D Only
• (4) A, D, E Only

Find the equivalent resistance between two ends of the following circuit: % Circuit Description \textit{The circuit consists of three resistors, two of \(\frac{r}{3}\) in series connected in parallel with another resistor of \(r\).

• (1) \(\frac{r}{6}\)
• (2) \(r\)
• (3) \(\frac{r}{9}\)
• (4) \(\frac{r}{3}\)

Choose the correct nuclear process from the below options:

• (1) \(n \rightarrow p + e^- + \overline{\nu}\)
• (2) \(n \rightarrow p + e^+ + \nu\)
• (3) \(n \rightarrow p + e^- + \nu\)
• (4) \(n \rightarrow p + e^+ + \overline{\nu}\)

A Carnot engine (E) is working between two temperatures 473K and 273K. In a new system two engines - engine \(E_1\) works between 473K to 373K and engine \(E_2\) works between 373K to 273K. If \(\eta_{12}\), \(\eta_1\) and \(\eta_2\) are the efficiencies of the engines \(E\), \(E_1\) and \(E_2\), respectively, then:

• (1) \(\eta_{12} < \eta_1 + \eta_2\)
• (2) \(\eta_{12} = \eta_1 + \eta_2\)
• (3) \(\eta_{12} = \eta_1 \eta_2\)
• (4) \(\eta_{12} > \eta_1 + \eta_2\)

Given below are two statements: one is labelled as Assertion \(A\) and the other as Reason \(R\): Assertion \(A\): A sound wave has higher speed in solids than in gases.
Reason \(R\): Gases have higher value of Bulk modulus than solids.

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

In the experiment for measurement of viscosity \( \eta \) of a given liquid with a ball having radius \( R \), consider following statements: A. Graph between terminal velocity \( V \) and \( R \) will be a parabola.
B. The terminal velocities of different diameter balls are constant for a given liquid.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of \( \eta \) will change.

• (1) \(B\), \(D\) and \(E\) Only
• (2) \(C\), \(D\) and \(E\) Only
• (3) \(A\), \(B\) and \(E\) Only
• (4) \(A\), \(C\) and \(D\) Only

Two capacitors \( C_1 \) and \( C_2 \) are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are \( U_1 \) and \( U_2 \), respectively. Which of the given statements is true?

• (A) \( C_1 > C_2, U_1 < U_2 \)
• (B) \( C_2 > C_1, U_2 > U_1 \)
• (C) \( C_2 > C_1, U_2 < U_1 \)
• (D) \( C_1 > C_2, U_1 > U_2 \)

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is:

• (A) \( \frac{9}{8} \)
• (B) \( \frac{27}{32} \)
• (C) \( \frac{32}{27} \)
• (D) \( \frac{8}{9} \)

The center of mass of a thin rectangular plate (fig - x) with sides of length \( a \) and \( b \), whose mass per unit area (\( \sigma \)) varies as \( \sigma = \sigma_0 \frac{x}{ab} \) (where \( \sigma_0 \) is a constant), would be

• (A) \( \left(\frac{2}{3} a, \frac{2}{3} b\right) \)
• (B) \( \left(\frac{1}{3} a, \frac{1}{2} b\right) \)
• (C) \( \left(\frac{1}{2} a, \frac{1}{2} b\right) \)
• (D) \( \left(\frac{2}{3} a, \frac{1}{2} b\right) \)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: In a central force field, the work done is independent of the path chosen. Reason R: Every force encountered in mechanics does not have an associated potential energy. In the light of the above statements, choose the most appropriate answer from the options given below.

• (A) A is true but R is false
• (B) Both A and R are true and R is the correct explanation of A
• (C) Both A and R are true but R is NOT the correct explanation of A
• (D) A is false but R is true

A proton of mass 'mp' has same energy as that of a photon of wavelength 'λ'. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is.

• (A) \( \frac{1}{c\sqrt{2m_p}} \frac{E}{\lambda} \)
• (B) \( \frac{1}{c\sqrt{m_p}} \frac{E}{\lambda} \)
• (C) \( \frac{1}{2c\sqrt{m_p}} \frac{E}{\lambda} \)
• (D) \( \frac{1}{c\sqrt{2m_p}} \frac{2E}{\lambda} \)

In a measurement, it is asked to find the modulus of elasticity per unit torque applied on the system. The measured quantity has the dimension of \( [M^a L^b T^c] \). If \( b = 3 \), the value of \( c \) is:

A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm, respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be \( \frac{x}{100} \), where \( x \) is:

The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in a similar way. The moment of inertia of a solid sphere which has the same radius as the disc and rotating in similar way, is \( n \) times higher than the moment of inertia of the given ring. Here, \( n = \):

Two iron solid discs of negligible thickness have radii \( R_1 \) and \( R_2 \) and moment of inertia \( I_1 \) and \( I_2 \), respectively. For \( R_2 = 2R_1 \), the ratio of \( I_1 \) and \( I_2 \) would be \( \frac{1}{x} \), where \( x \) is:

A double slit interference experiment performed with a light of wavelength 600 nm forms an interference fringe pattern on a screen with 10th bright fringe having its centre at a distance of 10 mm from the central maximum. Distance of the centre of the same 10th bright fringe from the central maximum when the source of light is replaced by another source of wavelength 660 nm would be:

The products A and B in the following reactions, respectively, are:

• (A) CH$_3$-CH$_2$-CH$_2$-NO$_2$, CH$_3$-CH$_2$-CH$_2$-NC
• (B) CH$_3$-CH$_2$-CH$_2$-ONO, CH$_3$-CH$_2$-CH$_2$-CN
• (C) CH$_3$-CH$_2$-CH$_2$-NO$_2$, CH$_3$-CH$_2$-CH$_2$-CN
• (D) CH$_3$-CH$_2$-CH$_2$-ONO, CH$_3$-CH$_2$-CH$_2$-NC

The correct order of stability of following carbocations is:

• (A) C $>$ B $>$ A $>$ D
• (B) A $>$ B $>$ C $>$ D
• (C) B $>$ C $>$ A $>$ D
• (D) C $>$ A $>$ B $>$ D

Given below are two statements:
Statement I: In the oxalic acid vs KMnO$_4$ (in the presence of dil H$_2$SO$_4$) titration the solution needs to be heated initially to 60°C, but no heating is required in Ferrous ammonium sulphate (FAS) vs KMnO$_4$ titration (in the presence of dil H$_2$SO$_4$). Statement II: In oxalic acid vs KMnO$_4$ titration, the initial formation of MnSO$_4$ takes place at high temperature, which then acts as catalyst for further reaction. In the case of FAS vs KMnO$_4$, heating oxidizes Fe$^{2+$ into Fe$^{3+$ by oxygen of air and error may be introduced in the experiment. In the light of the above statements, choose the correct answer from the options given below:

• (A) Both Statement I and Statement II are false
• (B) Both Statement I and Statement II are true
• (C) Statement I is false but Statement II is true
• (D) Statement I is true but Statement II is false

A molecule (P) on treatment with acid undergoes rearrangement and gives (Q). (Q) on ozonolysis followed by reflux under alkaline condition gives (R). The structure of (R) is given below. The structure of (P) is:
 

Given below are two statements:

• (A) Both Statement I and Statement II are incorrect
• (B) Both Statement I and Statement II are correct
• (C) Statement I is correct but Statement II is incorrect
• (D) Statement I is incorrect but Statement II is correct

In a multielectron atom, which of the following orbitals described by three quantum numbers will have the same energy in absence of electric and magnetic fields? A. \( n = 1, l = 0, m_l = 0 \) B. \( n = 2, l = 0, m_l = 0 \) C. \( n = 2, l = 1, m_l = 1 \) D. \( n = 3, l = 2, m_l = 1 \) E. \( n = 3, l = 2, m_l = 0 \) Choose the correct answer from the options given below:

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

Given below are two statements: Statement I: D-glucose pentaacetate reacts with 2,4-dinitrophenylhydrazine. Statement II: Starch, on heating with concentrated sulfuric acid at 100°C and 2-3 atmosphere pressure, produces glucose. In the light of the above statements, choose the correct answer from the options given below:

• (1) Both Statement I and Statement II are true
• (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 false

Both acetaldehyde and acetone (individually) undergo which of the following reactions? A. Iodoform Reaction B. Cannizzaro Reaction C. Aldol Condensation D. Tollen's Test E. Clemmensen Reduction Choose the correct answer from the options given below:

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

Which of the following oxidation reactions are carried out by both \( K_2Cr_2O_7 \) and \( KMnO_4 \) in acidic medium? A. \( I^- \rightarrow I_2 \) B. \( S^{2-} \rightarrow S \) C. \( Fe^{2+} \rightarrow Fe^{3+} \) D. \( I^- \rightarrow IO_3^- \) E. \( S_2O_3^{2-} \rightarrow SO_4^{2-} \) Choose the correct answer from the options given below:

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

Match the LIST-I with LIST-II (Redox Reactions). \begin{tabular{|c|c| \hline LIST-I (Redox Reaction) & LIST-II (Type of Redox Reaction)
\hline A. \( CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l) \) & I. Disproportionation reaction
B. \( 2NaH(s) \rightarrow 2Na(s) + H_2(g) \) & II. Combination reaction
C. \( V_2O_5(s) + 5Ca(s) \rightarrow 2V(s) + 5CaO(s) \) & III. Decomposition reaction
D. \( 2H_2O(aq) \rightarrow 2H_2(g) + O_2(g) \) & IV. Displacement reaction
\hline \end{tabular Choose the correct answer from the options given below:

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

Consider the following elements In, Tl, Al, Pb, and Ge. The most stable oxidation states of elements with highest and lowest first ionisation enthalpies, respectively, are:

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

The metal ion whose electronic configuration is not affected by the nature of the ligand and which gives a violet color in non-luminous flame under hot condition in borax bead test is:

• (A) Ti$^{3+}$
• (B) Cr$^{3+}$
• (C) Ni$^{2+}$
• (D) Mn$^{2+}$

A weak acid HA has degree of dissociation x. Which option gives the correct expression of \(pH - pK_a\)?

• (A) log(1 + 2x)
• (B) 0
• (C) log\(\left(\frac{x}{1-x}\right)\)
• (D) log\(\left(\frac{1-x}{x}\right)\)

The molecules having square pyramidal geometry are:

• (A) BrF$_5$ & XeOF$_4$
• (B) SbF$_5$ & XeOF$_4$
• (C) BrF$_5$ & PCl$_5$
• (D) SbF$_5$ & PCl$_5$

The compounds that produce CO$_2$ with aqueous NaHCO$_3$ solution are:

• (A) A and C Only
• (B) A, B, and E Only
• (C) A, C, and D Only
• (D) A and B Only

Consider ‘n’ is the number of lone pair of electrons present in the equatorial position of the most stable structure of \( \text{ClF}_3 \). The ions from the following with ‘n’ number of unpaired electrons are: A. \( \text{V}^{3+} \)
B. \( \text{Ti}^{3+} \)
C. \( \text{Cu}^{2+} \)
D. \( \text{Ni}^{2+} \)
E. \( \text{Ti}^{2+} \)
Choose the correct answer from the options given below:

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

The incorrect decreasing order of atomic radii is:

• (1) \( \text{Mg} > \text{Al} > \text{C} > \text{O} \)
• (2) \( \text{Al} > \text{B} > \text{N} > \text{F} \)
• (3) \( \text{Be} > \text{Mg} > \text{Al} > \text{Si} \)
• (4) \( \text{Si} > \text{P} > \text{Cl} > \text{F} \)

What is the freezing point depression constant of a solvent, 50 g of which contain 1 g non-volatile solute (molar mass 256 g mol\(^{-1}\)) and the decrease in freezing point is 0.40 K?

• (1) 5.12 K kg mol\(^{-1}\)
• (2) 4.43 K kg mol\(^{-1}\)
• (3) 1.86 K kg mol\(^{-1}\)
• (4) 3.72 K kg mol\(^{-1}\)

Ice and water are placed in a closed container at a pressure of 1 atm and temperature 273.15K. If pressure of the system is increased 2 times, keeping temperature constant, then identify correct observation from the following:

• (1) Volume of system increases.
• (2) The amount of ice decreases.
• (3) Liquid phase disappears completely.
• (4) The solid phase (ice) disappears completely.

For a given reaction \( R \rightarrow P \), \( t_{1/2} \) is related to \([A_0]\) as given in table. Given: \( \log 2 = 0.30 \). Which of the following is true? \begin{tabular{|c|c| \hline [A] (mol/L) & t$_{1/2}$ (min)
\hline 0.100 & 200
0.025 & 100
\hline \end{tabular

• (1) A. The order of the reaction is \( \frac{1}{2} \).
• (2) B. If \( [A_0] \) is 1 M, then \( t_{1/2} \) is \( 200/\sqrt{10} \) min.
• (3) C. The order of the reaction changes to 1 if the concentration of reactant changes from 0.100 M to 0.500 M.
• (4) D. \( t_{1/2} \) is 800 min for \( [A_0] = 1.6 \) M.

The formation enthalpies, \( \Delta H_f^\circ \) for \( \text{H}_2 \) and \( \text{O}_2 \) are 220.0 and 250.0 kJ mol\(^{-1}\), respectively, at 298.15 K, and \( \Delta H_f^\circ \) for \( \text{H}_2\text{O} \) (g) is -242.0 kJ mol\(^{-1}\) at the same temperature. The average bond enthalpy of the O-H bond in water at 298.15 K is:

Quantitative analysis of an organic compound (X) shows the following percentage composition. C: 14.5% Cl: 64.46% H: 1.8% Empirical formula mass of the compound (X) is:

Given below is the plot of the molar conductivity vs \( \sqrt{c} \) concentration for KCl in aqueous solution. If, for the higher concentration of KCl solution, the resistance of the conductivity cell is 100 \( \Omega \), then the resistance of the same cell with the dilute solution is 'x' \( \Omega \). The value of \( x \) is:

Consider the following sequence of reactions: \includegraphics[width=0.5\linewidth]{74.png 11.25 mg of chlorobenzene will produce \( x \times 10^{-1} \) mg of product B. Consider the reactions result in complete conversation. Given molar mass of C, H, O, N, and Cl as 12, 1, 16, 14, and 35.5 g mol\(^{-1}\), respectively, the value of \( x \) is:

The molarity of a 70% (mass/mass) aqueous solution of a monobasic acid (X) is:
{Given: Density of aqueous solution of \( X \) is 1.25 g/mL Molar mass of the acid \( X \) is 70 g/mol

 Also Check: Good Score in JEE Main 2025