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MAH CET MCA Previous Year Questions (PYQs)

MAH CET MCA Trigonometry PYQ

MAH CET MCA PYQ
Find the distance from the eye at which a coin of $2\ \text{cm}$ diameter should be held so as to conceal the full moon whose angular diameter is $31'$.





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MAH CET MCA Previous Year PYQ MAH CET MCA MAH MCA CET 2025 (Shift 1) PYQ

Solution

Small–angle $\theta\ (\text{radians}) \approx \dfrac{\text{diameter}}{\text{distance}}$. $\theta = 31' = \dfrac{31\pi}{180\times60}$. $d = \dfrac{0.02}{\theta} = \dfrac{0.02\times10800}{31\pi} \approx 2.217\ \text{m}$.
MAH CET MCA PYQ
The number of real solutions of $\sqrt{1+\cos 2x}=\sqrt{2},\cos^{-1}(\cos x)$ in $\left[\frac{\pi}{2},\pi\right]$ is





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MAH CET MCA Previous Year PYQ MAH CET MCA MAH MCA CET 2025 (Shift 1) PYQ

Solution

$\sqrt{1+\cos 2x}=\sqrt{2},|\cos x|$. On $\left[\frac{\pi}{2},\pi\right]$, $\cos x\le 0$ so $|\cos x|=-\cos x$. LHS $=\sqrt{2},|\cos x|$, RHS $=\sqrt{2},|\cos x|$ only if $\cos^{-1}(\cos x)=|\cos x|$, which never holds for $x\in\left[\frac{\pi}{2},\pi\right]$. Hence no real solution.
MAH CET MCA PYQ
A pendulum swings through an angle of $30{^{\circ}}$ and describes an arc 8.8cm in length. The length of the pendulum is





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MAH CET MCA Previous Year PYQ MAH CET MCA MAH MCA CET 2024 PYQ

Solution


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