JEE Main 2025 April 4 Shift 1 question paper gives valuable insights into the kind of questions, difficulty level, and effective methodologies to tackle different subjects. Students can find the JEE Main 2025 April 4 question paper and step-by-step solutions to judge their performance, understand the test format, measure the difficulty level, and check crucial topics included. This overall JEE Main 2025 April 4 Question Paper review comprises subject-wise difficulty levels, weightage proportion, and professional solutions, providing a good platform for students studying for upcoming shifts and days. JEE Main exam is over, the JEE Main 2025 April 4 Shift 1 question paper with solutions is updated and made available for practice and viewing.
Memory Based questions
Chemistry
4 April shift 1
Q.1 In the following, the number of paramagnetic molecules are : $\mathrm{O}_2, \mathrm{~N}_2, \mathrm{~F}_2, \mathrm{~B}_2, \mathrm{Cl}_2$
Q.2 Which of the following is the ratio of $5^{\text {th }}$ Bohr orbit $\left(r_5\right)$ of $\mathrm{He}^{+} \& \mathrm{Li}^{2+}$ ?
1) $\frac{2}{3}$
2) $\frac{3}{2}$
3) $\frac{9}{4}$
4) $\frac{4}{9}$
Q.3 Which of the following pair of ions have equal number of unpaired electrons
$1 \quad\mathrm{~V}^{2+}$ and $\mathrm{Ni}^{2+}$
$2\quad \mathrm{Cr}^{2+}$ and $\mathrm{Mn}^{2+}$
$3 \quad \mathrm{Fe}^{2+}$ and $\mathrm{Sc}^{2+}$
$4 \quad\mathrm{Mn}^{3+}$ and $\mathrm{Fe}^{2+}$
Q.4. Incorrect order of atomic radius is
1 $\mathrm{~B}<\mathrm{Al}$
2 $\ln <\mathrm{TI}$
3 $\mathrm{Al}<\mathrm{Ga}$
4 $\mathrm{Ga}<\ln$
Maths
4th April Shift 1 Maths
Q 1. Solve $\int_{-1}^1 \frac{1+2 x}{e^{-x}+e x} d x$.
1) $2\left(\tan ^{-1} e-\frac{\pi}{4}\right)$
2) $2\left(\tan ^{-1} e-\frac{\pi}{3}\right)$
3) $2\left(\tan ^{-1} e-\frac{\pi}{2}\right)$
4) $2\left(\frac{\pi}{2}-\tan ^{-1} \pi\right)$
Q 2. If the equation of an ellipse $E$ is $\frac{x^2}{9}+\frac{y^2}{16}=1$, then the length of latus rectum of $E$ is
$\begin{aligned} 1) & \frac{32}{5} \\ 2) & \frac{9}{2} \\ 3) & \frac{16}{3} \\ 4) & \frac{9}{5}\end{aligned}$
Q 3. The sum of the series $1+3+5^2+7+9^2+\ldots$ upto 80 terms is
1) 328160
2) 338160
3) 339400
4) 326870
Q 4. Foci of ellipse are (2,5) and (2,-3), eccentricity is 4/5. Find the length of the latus rectum.
Q 5. Let there be two A.P.'s with each having 2025 terms. Find the number of distinct terms in union of these two A.P.'s, i.e., AUB if first A.P. is $1,6,11, \ldots$ and second A.P. is $9,16,23, \ldots$
Physics
Q 1) A ring and a solid sphere were released from rest from the same height on enough rough inclined surface. Ratio of their speed when they reach at bottom is $\sqrt{\frac{7}{x}} \mathrm{~m} / \mathrm{s}$, then $x$ is $\qquad$
Q 2) Mean free path for an ideal gas is to be observed $20 \mu \mathrm{~m}$ while average speed of molecules of gas is observed to be $600 \mathrm{~m} / \mathrm{s}$, then frequency of collision is near by
Q.3) Find the equivalent capacitance between $A$ and $B$, where $C=16 \mu F$
