1
JEE Main 2026 (Online) 21st January Evening Shift
Numerical
+4
-1
Change Language
Let the maximum value of $\left(\sin ^{-1} x\right)^2+\left(\cos ^{-1} x\right)^2$ for $x \in\left[-\frac{\sqrt{3}}{2}, \frac{1}{\sqrt{2}}\right]$ be $\frac{\mathrm{m}}{\mathrm{n}} \pi^2$, where $\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$. Then $\mathrm{m}+\mathrm{n}$ is equal to $\_\_\_\_$。
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2
JEE Main 2026 (Online) 21st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A spherical body of radius $r$ and density $\sigma$ falls freely through a viscous liquid having density $\rho$ and viscosity $\eta$ and attains a terminal velocity $v_0$. Estimated maximum error in the quantity $\eta$ is : (Ignore errors associated with $\sigma$, $\rho$ and $g$, gravitational acceleration)

A

$2 \left[ \frac{\Delta r}{r} - \frac{\Delta v_0}{v_0} \right]$

B

$2 \left[ \frac{\Delta r}{r} + \frac{\Delta v_0}{v_0} \right]$

C

$\frac{2 \Delta r}{r} + \frac{\Delta v_0}{v_0}$

D

$2 \frac{\Delta r}{r} - \frac{\Delta v_0}{v_0}$

3
JEE Main 2026 (Online) 21st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Keeping the significant figures in view, the sum of the physical quantities 52.01 m, 153.2 m and 0.123 m is :

A

205.3 m

B

205 m

C

205.333 m

D

205.33 m

4
JEE Main 2026 (Online) 21st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A large drum having radius $R$ is spinning around its axis with angular velocity $\omega$, as shown in figure.
The minimum value of $\omega$ so that a body of mass $M$ remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass $M$ as $\mu$, is :JEE Main 2026 (Online) 21st January Evening Shift Physics - Circular Motion Question 7 English

A

$\sqrt{\dfrac{2g}{\mu R}}$

B

$\sqrt{\dfrac{g}{2\mu R}}$

C

$\sqrt{\dfrac{\mu g}{R}}$

D

$\sqrt{\dfrac{g}{\mu R}}$

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