MathsJEE Main 22 Jan 2026, Shift 2·Q6·MCQ·Moderate

Differential Equations · Variable separable differential equations

y = y(x)

satisfies the differential equation

16\left(\sqrt{x}\,\sqrt{9+\sqrt{x}}\right)\left(4 + \sqrt{9 + \sqrt{x}}\right)\cos y\,dy = (1 + 2\sin y)\,dx,\quad x > 0

and

y(256) = \dfrac{\pi}{2}

y(49) = \alpha

, then

2\sin\alpha

is equal to:

(1) $2\sqrt2 - 1$
(2) $2\left(\sqrt2 - 1\right)$
(3) $3\left(\sqrt2 - 1\right)$
(4) $\sqrt2 - 1$

We corrected a printing error in the original paper

Source printed the first factor as “ $\sqrt{x + 9\sqrt{x}}$ ”, with which none of the options is correct ( $2\sin\alpha \approx 1.466$ ); corrected to the intended “ $\sqrt{x}\,\sqrt{9+\sqrt{x}}$ ” (the source's own solution integrates with this factor), which gives the printed key (1).

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Differential Equations · Variable separable differential equations

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