JEE Main 2025 April 4 Shift 1 Question Paper with Solutions Available - Download PDF

JEE Main 2025 April 4 Shift 1 Question Paper Pattern and Structure

JEE Main 2025 Marking Scheme

JEE Main 2025 April 4 Shift 1 Question Paper with Solutions

JEE Main 2025 April 4 Shift 1 exam, the question paper and solutions is made available on this webpage. These materials is prove helpful for the aspirants appearing for subsequent shifts, providing them with a complete overview of the structure and difficulty of the exam. By going through the JEE Main 2025 April 4 Shift 1 Question Paper with Solutions PDF they can spot critical concepts, attempt problem-solving techniques, and prepare well for future exams. You can also download JEE Main 2025 April 4 Shift 1 Paper PDF.

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 $C=16 \mu F$

JEE Main 2025 April 4 Shift 1 Answer Key & Solution PDF Download

Once the answer key is officially published, candidates can verify their answers and assess their performance through the direct link to the JEE Main 2025 April 3 Answer Key PDF Download. After all the shifts are completed, the question paper of JEE Main 2025 April 3 All Shifts will be posted here. The JEE Main 2025 April 3 Answer Key Download and solutions from each expert will be posted on this page.

JEE Main 2025 Previous Year Question Paper

Referring to the Previous years papers are crucial to understand how the question paper is expected to be like. You can also go through the previous year's question paper given below: