JEE Maths PYQ Practice, chapter-wise

JEE Main 2023 (Online) 30th January Morning ShiftQuestion 7481

Among the statements: $(S1)$: $((p\vee q)\Rightarrow r)\Leftrightarrow(p\Rightarrow r)$ $(S2)$: $((p\vee q)\Rightarrow r)\Leftrightarrow((p\Rightarrow r)\vee(q\Rightarrow r))$

Mathematical Reasoning

Only $(S1)$ is a tautologyNeither $(S1)$ nor $(S2)$ is a tautologyOnly $(S2)$ is a tautologyBoth $(S1)$ and $(S2)$ are tautologies

JEE Main 2019 (Online) 8th April Morning ShiftQuestion 7482

If $2y=\left(\cot^{-1}\left(\frac{\sqrt3\cos x+\sin x}{\cos x-\sqrt3\sin x}\right)\right)^2$, $x\in\left(0,\frac\pi2\right)$, then $\frac{dy}{dx}$ is equal to

Differentiation and its Application

$\frac\pi6-x$$2x-\frac\pi3$$x-\frac\pi6$None of these

JEE Main 2019 (Online) 8th April Evening ShiftQuestion 7483

Let $f:[-1,3]\to\mathbb R$ be defined as $f(x)=\begin{cases}|x|+[x], & -1\le x<1\\ x+|x|, & 1\le x<2\\ x+[x], & 2\le x\le3,\end{cases}$ where $[t]$ denotes the greatest integer less than or equal to $t$. Then, $f$ is discontinuous at:

Limits & Continuity

only one pointonly two pointsfour or more pointsonly three points

JEE Main 2021 (Online) 1st September Evening ShiftQuestion 7484

Let $f:\mathbb R\to\mathbb R$ be a continuous function. Then $\displaystyle\lim_{x\to\pi/4}\frac{\frac\pi4\int_2^{\sec^2x}f(x)\,dx}{x^2-\frac{\pi^2}{16}}$ is equal to:

Limits & Continuity

$f(2)$$2f\left(\sqrt2\right)$$2f(2)$$4f(2)$

JEE Main 2025 (Online) 28th January Morning ShiftQuestion 7485

Let the equation of the circle, which touches $x$-axis at the point $(a,0)$, $a>0$ and cuts off an intercept of length $b$ on $y$-axis be $x^{2}+y^{2}-\alpha x+\beta y+\gamma=0$. If the circle lies below $x$-axis, then the ordered pair $(2a,b^{2})$ is equal to

Circle

$(\alpha,\ \beta^{2}+4\gamma)$$(\alpha,\ \beta^{2}-4\gamma)$$(\gamma,\ \beta^{2}-4\alpha)$$(\gamma,\ \beta^{2}+4\alpha)$

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