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JEE MAIN 2025
07-04-2025 S2
Question
An inductor of reactance $100 \Omega$, a capacitor of reactance $50 \Omega$, and a resistor of resistance $50 \Omega$ are connected in series with an AC source of $10 \mathrm{~V}, 50 \mathrm{~Hz}$. Average power dissipated by the circuit is $\_\_\_\_$
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Showing 18 questions
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There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If...
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Let 𝐴 be a 2 × 2 symmetric matrix such that $A\left[\begin{array}{l}1 \\ 1\end{array}\right]=\left[\begin{array}{l}3 \\ 7\end{array}\right]$ and the determinant of...
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Consider the function $\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x)=\frac{2 x}{\sqrt{1+9 x^2}}$. If the composition of $...
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Let f: ℝ → ℝ be a thrice differentiable function such that f(0) = 0, f(1) = 1, f(2) =...
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If $\int \operatorname{cosec}^5 x d x=\alpha \cot x \operatorname{cosec} x\left(\operatorname{cosec}^2 x+\frac{3}{2}\right)+\beta \log _e\left|\tan \frac{x}{2}\right|+C$ where $\alpha, \beta \in \mathbb{R}$ and...
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Let $S=\left\{\sin ^2 2 \theta:\left(\sin ^4 \theta+\cos ^4 \theta\right) x^2+(\sin 2 \theta) x+\left(\sin ^6 \theta+\cos ^6 \theta\right)=0\right.$ has real roots...
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Let P the point of intersection of the lines $\frac{x-2}{1}=\frac{y-4}{5}=\frac{z-2}{1}$ and $\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-3}{2}$. Then, the shortest distance of $P$ from the...
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Let $y=y(x)$ be the solution of the differential equation $\left(x^2+4\right)^2 d y+\left(2 x^3 y+8 x y-2\right) d x=0$. If $y(0)=$...
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Let P Q be a chord of the parabola $y^2=12 x$ and the midpoint of PQ be at $(4,1)$. Then,...
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Consider a hyperbola $H$ having centre at the origin and foci and the $x$-axis. Let $C_1$ be the circle touching...
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Let f(x) = 3 $ \sqrt{\mathrm{x}-2}+\sqrt{4-\mathrm{x}}$ be a real valued function. If $\alpha$ and $\beta$ are respectively the minimum and...
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If the value of the integral $\int_{-1}^1 \frac{\cos \alpha x}{1+3^x} d x$ is $\frac{2}{\pi}$. Then, a value of $\alpha$ is
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