Some Most Important Questions For Physics, Chemistry and Maths
JEE Main 2025 Session 2 Physics Questions
1. A person traveling on a straight line moves with a uniform velocity $\mathrm{v}_1$ for a distance x and with a uniform velocity $\mathrm{v}_2$ for the next $\frac{3}{2} \mathrm{x}$ distance. The average velocity in this motion is $\frac{50}{7} \mathrm{~m} / \mathrm{s}$. If $\mathrm{v}_1$ is $5 \mathrm{~m} / \mathrm{s}$ then $\mathrm{v}_2=$ _____ $\mathrm{m} / \mathrm{s}$.
2. The moment of inertia of a rod of mass ' M ' and length 'L' about an axis passing through its center and normal to its length is ' $\alpha$ '. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. The moment of inertia of a cross about an axis passing through its center and normal to the plane containing the cross is :
1) $\alpha$2
2) $\alpha / 4$
3) $\alpha / 8$
4) $\alpha / 2$
3. A river is flowing from west to east direction with a speed of $9 \mathrm{~km} \mathrm{~h}^{-1}$. If a boat capable of moving at a maximum speed of $27 \mathrm{~km} \mathrm{~h}^{-1}$ in still water, crosses the river in half a minute, while moving with maximum speed at an angle of $150^{\circ}$ to direction of river flow, then the width of the river is :
1) 300 m
2) 112.5 m
3) 75 m
4) $112.5 \times \sqrt{3} \mathrm{~m}$
4. The equation for real gas is given by $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where $\mathrm{P}, \mathrm{V}, \mathrm{T}$ and R are the pressure, volume, temperature, and gas constant, respectively. The dimension of $\mathrm{ab}^{-2}$ is equivalent to that of:
1) Planck's constant
2) Compressibility
3) Strain
4) Energy density
5. Let $B_1$ be the magnitude of the magnetic field at the center of a circular coil of radius R carrying current I . Let $\mathrm{B}_2$ be the magnitude of magnetic field at an axial distance ' $x$ ' from the center. For $x: R=3: 4, \frac{B_2}{B_1}$ is :
1) $4: 5$
2) $16: 25$
3) $64: 125$
4) $25: 16$
JEE Main 2025 Session 2 Chemistry Questions
1.
Consider the following half cell reaction
$$
\mathrm{Cr}_2 \mathrm{O}_7^{2-}(\mathrm{aq})+6 \mathrm{e}^{-}+14 \mathrm{H}^{+}(\mathrm{aq}) \rightarrow 2 \mathrm{Cr}^{3+}(\mathrm{aq})+7 \mathrm{H}_2 \mathrm{O}(\mathrm{l})
$$
The reaction was conducted with the ratio of $\frac{\left[\mathrm{Cr}^{3+}\right]^2}{\left[\mathrm{Cr}_2 \mathrm{O}_7^{2-}\right]}=10^{-6}$. The pH value at which the EMF of the half cell will become zero is $\_\_\_\_$ . (nearest integer value)
[Given : standard half cell reduction potential
$$
\left.\mathrm{E}_{\mathrm{C}_2 \mathrm{O}_{-}^2+\mathrm{H}^* / \mathrm{Cr}^{3+}}^{\mathrm{o}}=1.33 \mathrm{~V}, \frac{2.303 \mathrm{RT}}{\mathrm{~F}}=0.059 \mathrm{~V}\right]
$$
2. The equilibrium constant for decomposition of $\mathrm{H}_2 \mathrm{O}(\mathrm{g})$
$$
\mathrm{H}_2 \mathrm{O}(\mathrm{~g}) \rightleftharpoons \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g})\left(\Delta \mathrm{G}^{\circ}=92.34 \mathrm{~kJ} \mathrm{~mol}^1\right)
$$
is $8.0 \times 10^{-3}$ at 2300 K and total pressure at equilibrium is 1 bar . Under this condition, the degree of dissociation ( $\alpha$ ) of water is $\_\_\_\_$ $\times 10^{-2}$ (nearest integer value).
[Assume $\alpha$ is negligible with respect to 1 ]
3. 20 mL of sodium iodide solution gave 4.74 g silver iodide when treated with excess of silver nitrate solution. The molarity of the sodium iodide solution is $\_\_\_\_$ M. (Nearest Integer value)
$$
\left(\text { Given : } \mathrm{Na}=23, \mathrm{I}=127, \mathrm{Ag}=108, \mathrm{~N}=14, \mathrm{O}=16 \mathrm{~g} \mathrm{~mol}^{-1}\right)
$$
4. The energy of an electron in first Bohr orbit of H -atom is -13.6 eV . The magnitude of energy value of electron in the first excited state of $\mathrm{Be}^{3+}$ is $\_\_\_\_$ eV . (nearest integer value)
JEE Main 2025 Session 2 Mathematics Questions
1. If the set of all $\mathrm{a} \in \mathrm{R}-\{1\}$, for which the roots of the equation $(1-a) x^2+2(a-3) x+9=0$ are positive is $(-\infty,-\alpha] \cup[\beta, \gamma)$, then $2 \alpha+\beta+\gamma$ is equal to $\_\_\_\_$
2. Let $\mathrm{A}(4,-2), \mathrm{B}(1,1)$ and $\mathrm{C}(9,-3)$ be the vertices of a triangle $A B C$. Then the maximum area of the parallelogram $A F D E$, formed with vertices $\mathrm{D}, \mathrm{E}$ and F on the sides $\mathrm{BC}, \mathrm{CA}$ and AB of the triangle ABC respectively, is $\_\_\_\_$
3. If $y=\cos \left(\frac{\pi}{3}+\cos ^{-1} \frac{x}{2}\right)$, then $(x-y)^2+3 y^2$ is equal to $\_\_\_\_$
4. If the sum of the first 10 terms of the series $\frac{4.1}{1+4.1^4}+\frac{4.2}{1+4.2^4}+\frac{4.3}{1+4.3^4}+\ldots$ is $\frac{m}{n}$, where $\operatorname{gcd}(m, n)=1$, then $m+n$ is equal to $\_\_\_\_$ .
5. Let $y=y(x)$ be the solution of the differential equation $\frac{d y}{d x}+2 y \sec ^2 x=2 \sec ^2 x+3 \tan x \cdot \sec ^2 x$ such that $y(0)=\frac{5}{4}$. Then $12\left(y\left(\frac{\pi}{4}\right)-e^{-2}\right)$ is equal to
