JEE Maths PYQ Practice, chapter-wise

JEE Main 2023 (Online) 30th January Morning ShiftQuestion 5511

If $[t]$ denotes the greatest integer $\le t$, then the value of $\frac{3(e-1)}{e}\int_1^2x^2e^{[x]+[x^3]}\,dx$ is :

Definite Integration

$e^9-e$$e^8-e$$e^7-1$$e^8-1$

JEE Main 2019 (Online) 10th January Morning ShiftQuestion 5512

The sum of all two digit positive numbers which when divided by $7$ yield $2$ or $5$ as remainder is

Sequence and Series · Arithmetic Progression

$1356$$1365$$1256$$1465$

JEE Main 2023 (Online) 30th January Morning ShiftQuestion 5513

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 5514

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 5515

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

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