JEE MAIN 2025 ONLINE 29TH JANUARY EVENING SHIFT

Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time t = 0, for the first time. The maximum possible number of crossing(s) (including the crossing at t = 0) is ________.

Consider the following low-spin complexes

$$\mathrm{K}_3\left[\mathrm{Co}\left(\mathrm{NO}_2\right)_6\right], \mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right], \mathrm{K}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right], \mathrm{Cu}_2\left[\mathrm{Fe}(\mathrm{CN})_6\right] \text { and } \mathrm{Zn}_2\left[\mathrm{Fe}(\mathrm{CN})_6\right]$$

The sum of the spin-only magnetic moment values of complexes having yellow colour is ________ B.M. (answer in nearest integer)

If $ 24 \int\limits_0^{\frac{\pi}{4}} \bigg[\sin \left| 4x - \frac{\pi}{12} \right| + [2 \sin x] \bigg] dx = 2\pi + \alpha $, where $[\cdot]$ denotes the greatest integer function, then $\alpha$ is equal to ________.

$\text { A physical quantity } Q \text { is related to four observables } a, b, c, d \text { as follows : }$

$Q = \frac{ab^4}{cd}$

where, $\mathrm{a}=(60 \pm 3) \mathrm{Pa} ; \mathrm{b}=(20 \pm 0.1) \mathrm{m} ; \mathrm{c}=(40 \pm 0.2) \mathrm{Nsm}^{-2}$ and $\mathrm{d}=(50 \pm 0.1) \mathrm{m}$, then the percentage error in Q is $\frac{x}{1000}$, where $x=$ _________ .

Isomeric hydrocarbons → negative Baeyer’s test

(Molecular formula C₉H₁₂)

The total number of isomers from above with four different non-aliphatic substitution sites is -

Let $a_1, a_2, \ldots, a_{2024}$ be an Arithmetic Progression such that $a_1+\left(a_5+a_{10}+a_{15}+\ldots+a_{2020}\right)+a_{2024}=2233$. Then $a_1+a_2+a_3+\ldots+a_{2024}$ is equal to _________.