List of top Questions asked in JEE Advanced

The plot of log 𝑘_𝑓 versus \(\frac{1}{T}\) for a reversible reaction, A (g) ⇌ P (g) is shown. 

Pre-exponential factors for the forward and backward reactions are 10¹⁵s^-1 and 10¹¹s^-1 respectively. If the value of log K for the reaction at 500 K is 6, the value of |log kb| at 250K is_________[K = equilibrium constant of the reaction, 𝑘_𝑓 = rate constant of forward reaction, 𝑘_𝑏 = rate constant of backward reaction]

For \(x ∈ R\), let \(tan^{-1} (x) ∈ \) (\(-\frac{\pi}{2},\frac{\pi}{2}\)). Then the minimum value of function \(f: R \rightarrow R\) defined by \(f(x) =\) \(\int_{0}^{x\,tan^{-1}x}\frac{e^{(t-cos\,t)}}{1+t^{2023}}dt\)  is

Let f:[1,∞) \(\rightarrow\) R be a differentiable function such that f(1) = \(\frac{1}{3}\) and 3\(\int_{1}^{x}\)f(t)dt=xf(x)-\(\frac{x^3}{3}\),x∈[1,∞). Let e denote the base of the natural logarithm. Then the value of f(e) is

A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a building of height 3ℎ from the ground, as shown in the figure. A spherical ball of mass 𝑚 is released on the slide from rest at a height ℎ from the top of the terrace. The ball leaves the slide with a velocity \(\hat{u}_0=u_0\hat{x}\) and falls on the ground at a distance 𝑑 from the building making an angle θ with the horizontal. It bounces off with a velocity of v and reaches a maximum height of ℎ₁. The acceleration due to gravity is 𝑔 and the coefficient of restitution of the ground is \(\frac{1}{\sqrt3}\). Which of the following statement(s) is(are) correct?

The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by \(\vec{E}\)=30(2𝑥̂ + 𝑦̂)sin [2𝜋 (5×10¹⁴𝑡 −\(\frac{10^7}{3}z\))] Vm⁻¹. Which of the following option(s) is(are) correct? [Given: The speed of light in vacuum, 𝑐 = 3 × 10⁸ ms⁻¹]

A person of height 1.6 m is walking away from a lamp post of height 4 m along a straight line on the horizontal ground. The lamp post and the person are always vertical. If the speed of the person is 60 cm/sec, then find the speed of tip point of its shadow with respect to the person in cm/sec.

The complex(es), which can exhibit the type of isomerism shown by [Pt(NH₃)₂Br₂], is(are) [en = H₂NCH₂CH₂NH₂]

Match the reactions in List-I with the features of their products in List-II and choose the correct option 

	List-I		List-II
(P)	(-)-1-Bromo-2-ethylpentane (single enantiomer)	(1)	Inversion of configuration
(Q)	(-)-2-Bromopentane (single enantiomer)	(2)	Retention of configuration
(R)	(-)-3- Bromo-3-methylhexane (single enantiometer)	(3)	Mixture of enantiomers
(S)	(single enantiometer)	(4)	Mixture of structural isomers
		(5)	Mixture of diastereomers

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is 𝑛. The internal energy of one mole of the gas is 𝑈_𝑛 and the speed of sound in the gas is v_𝑛. At a fixed temperature and pressure, which of the following is the correct option?

In list - I some conversions are shown and in the list- II emitted particles are shown. Match the column

Taking the first reflection of M₁. If the final image coincides with s, then find n.

The degree of freedom of an ideal gas is n. The internal energy of 1 mole of the gas is U_n and the speed of sound n the gas is V_n. At a fixed temperature and pressure, which of the following is correct?

A ball is released on a smooth plane as shown. It strikes with the ground, the coefficient of restitution is \(\frac{1}{\sqrt{3}}\) Choose the correct options

Find the α, β, γ in the Y = \(C^\alpha h^\beta G^\gamma,\,\,\) 
\(\gamma\) = Young's Modulus
 \(c\) = speed of Light
 \(h\) = Plank's Constant
 \(G\) = gravitational Constant

A closed container constrains a homogeneous mixture made of, 2 moles of an ideal monatomic gas(\(\gamma=\frac{5}{3}\)) and one mole of an ideal diatomic gas(\(\gamma=\frac{7}{5}\)). Here, γ is the ratio of the specific heat at content pressure and constant volume of an ideal gas. The gas mixture does a work of 66 joules when heated at constant pressure. The change in its internal energy is ____Joule.

Let z be a complex number satisfying |z|³ + 2z² +4z̄ - 8= 0 , where z̄ denotes the complex conjugate of z. Let the imaginary part of z be non-zero. Match each entry in List-I to the correct entries in List II.

The correct option is:

A plane-polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is 𝛿 = 60° (see Figure-1). The angle of minimum deviation for red light from the same prism is 𝛿_min = 30° (see Figure-2). The refractive index of the prism material for blue light is √3. Which of the following statement(s) is(are) correct?

Let l₁ and l₂ be the lines r₁ = λ(\(\hat{i}+\hat{j}+\hat{k}\)) and r₂ = (\(\hat{j}-\hat{k}\)) + μ (\(\hat{i}+\hat{k}\)), respectively. Let X be the set of all the planes H containing line l₁. For a plane H, let d (H) denote the smallest possible distance between the points of l₂ and H. Let H₀ be a plane in X for which d (H₀) is the maximum value of d (H ) as H varies over all planes in X . Match each entry in List-I to the correct entries in List-II.

 The correct option is: 

Consider the given data with frequency distribution

xi	3	8	11	10	5	4
fi	5	2	3	2	4	4

Match each entry in List-I to the correct entries in List-II. 

	List-I		List-II
(P)	The mean of the above data is	(1)	2.5
(Q)	The median of the above data is	(2)	5
(R)	The mean deviation from the mean of the above data is	(3)	6
(S)	The mean deviation from the median of the above data is	(4)	2.7
		(5)	2.4

The correct option is: 

Let P be the plane √3x+2y+3z =16 and let and let S = {\(\alpha \hat{i}+\beta \hat{j}+\gamma\hat{k}:\alpha^2+\beta^2+\gamma^2=1\) and the distance of (α, β, γ) from the plane P is \(\frac{7}{2}\) }. Let u, v, and w be three distinct vectors in s such that |\(\vec{u}-\vec{v}\)| = |\(\vec{v}-\vec{w}\)| = |\(\vec{w}-\vec{u}\)|. Let V be the volume of the parallelepiped determined by vectors \(\vec{u},\vec{v},\vec{w}\). Then the value of \(\frac{80}{\sqrt3}\)V is

Let a and b be two nonzero real numbers. If the coefficient of x⁵ in the expansion of (\(ax^2+(\frac{70}{27bx})^4\) is equal to the coefficient of x^-5 in the expansion of \((ax-\frac{1}{bx^2})^7\). then the value of 2b is