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JEE Advanced 2025 Paper 2 Online
Numerical
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If

$$ \alpha=\int\limits_{\frac{1}{2}}^2 \frac{\tan ^{-1} x}{2 x^2-3 x+2} d x $$

then the value of $\sqrt{7} \tan \left(\frac{2 \alpha \sqrt{7}}{\pi}\right)$ is _________.

(Here, the inverse trigonometric function $\tan ^{-1} x$ assumes values in $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$.)

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2
JEE Advanced 2025 Paper 2 Online
MCQ (Single Correct Answer)
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A temperature difference can generate e.m.f. in some materials. Let S be the e.m.f. produced per unit temperature difference between the ends of a wire, σ the electrical conductivity and κ the thermal conductivity of the material of the wire. Taking M, L, T, I and K as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity $Z = \frac{S^2 \sigma}{\kappa}$ is :

A

[M0L0T0I0K0]

B

[M0L0T0I0K−1]

C

[M1L2T−2I−1K−1]

D

[M1L2T−4I−1K−1]

3
JEE Advanced 2025 Paper 2 Online
MCQ (Single Correct Answer)
+3
-1
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Two co-axial conducting cylinders of same length $\ell$ with radii $\sqrt{2}R$ and $2R$ are kept, as shown in Fig. 1. The charge on the inner cylinder is $Q$ and the outer cylinder is grounded. The annular region between the cylinders is filled with a material of dielectric constant $\kappa=5$. Consider an imaginary plane of the same length $\ell$ at a distance $R$ from the common axis of the cylinders. This plane is parallel to the axis of the cylinders. The cross-sectional view of this arrangement is shown in Fig. 2. Ignoring edge effects, the flux of the electric field through the plane is ($\epsilon_0$ is the permittivity of free space):

JEE Advanced 2025 Paper 2 Online Physics - Electrostatics Question 4 English
A

$\frac{Q}{30\epsilon_0}$

B

$\frac{Q}{15\epsilon_0}$

C

$\frac{Q}{60\epsilon_0}$

D

$\frac{Q}{120\epsilon_0}$

4
JEE Advanced 2025 Paper 2 Online
MCQ (Single Correct Answer)
+3
-1
Change Language

As shown in the figures, a uniform rod OO' of length l is hinged at the point O and held in place vertically between two walls using two massless springs of same spring constant. The springs are connected at the midpoint and at the top-end (O') of the rod, as shown in Fig. 1 and the rod is made to oscillate by a small angular displacement. The frequency of oscillation of the rod is f₁. On the other hand, if both the springs are connected at the midpoint of the rod, as shown in Fig. 2 and the rod is made to oscillate by a small angular displacement, then the frequency of oscillation is f₂. Ignoring gravity and assuming motion only in the plane of the diagram, the value of $ \frac{f_1}{f_2} $ is:

JEE Advanced 2025 Paper 2 Online Physics - Simple Harmonic Motion Question 2 English
A

2

B

$\sqrt{2}$

C

$\sqrt{\frac{5}{2}}$

D

$\sqrt{\frac{2}{5}}$

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