For $\alpha, \beta, \gamma, \delta \in \mathbb{N}$, if $\displaystyle \int \left( \left(\dfrac{x}{e}\right)^{2x} + \left(\dfrac{e}{x}\right)^{2x} \right) \log_e x \, dx = \dfrac{1}{\alpha} \left(\dfrac{x}{e}\right)^{\beta x} - \dfrac{1}{\gamma} \left(\dfrac{e}{x}\right)^{\delta x} + C$, where $e = \displaystyle \sum_{n=0}^{\infty} \dfrac{1}{n!}$ and $C$ is the constant of integration, then $\alpha + 2\beta + 3\gamma - 4\delta$ is equal to:
Previous 10 Questions — JEE Main 2023 (10 April Evening Shift)
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Let $f$ be a continuous function satisfying
$\displaystyle \int_{0}^{t^2} \big(f(x) + x^2\big)\,dx = \dfrac{4}{3}t^3,…
Topic: JEE Main 2023 (10 April Evening Shift)
If the coefficients of $x$ and $x^2$ in $(1 + x)^p (1 - x)^q$ are $4$ and $-5$ respectively,
then $2p + 3q$ is equal …
Topic: JEE Main 2023 (10 April Evening Shift)
Let $g(x) = f(x) + f(1 - x)$ and $f''(x) > 0, \; x \in (0, 1)$.
If $g$ is decreasing in the interval $(0, \alpha)$ an…
Topic: JEE Main 2023 (10 April Evening Shift)
Let the number $(22)^{2022} + (2022)^{22}$ leave the remainder $\alpha$ when divided by $3$
and $\beta$ when divided …
Topic: JEE Main 2023 (10 April Evening Shift)
Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate…
Topic: JEE Main 2023 (10 April Evening Shift)
The set $S = \{ z = x + i y : \dfrac{2z - 3i}{4z + 2i} \text{ is a real number} \}$ is given.
Then which of the follo…
Topic: JEE Main 2023 (10 April Evening Shift)
Next 10 Questions — JEE Main 2023 (10 April Evening Shift)
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Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution
where $\displaystyle \sum f_i = 62$.…
Topic: JEE Main 2023 (10 April Evening Shift)
Let $\vec{a} = 2\hat{i} + 7\hat{j} - \hat{k}$, $\vec{b} = 3\hat{i} + 5\hat{k}$ and $\vec{c} = \hat{i} - \hat{j} + 2\hat…
Topic: JEE Main 2023 (10 April Evening Shift)
If the points $\mathbf{P}$ and $\mathbf{Q}$ are respectively the circumcenter and the orthocentre of a $\triangle ABC$,…
Topic: JEE Main 2023 (10 April Evening Shift)
Let $A$ be the point $(1, 2)$ and $B$ be any point on the curve $x^2 + y^2 = 16$.
If the centre of the locus of the p…
Topic: JEE Main 2023 (10 April Evening Shift)
Let $A = \{2, 3, 4\}$ and $B = \{8, 9, 12\}$.
Then the number of elements in the relation
$R = \{ ((a_1, b_1), (a_2…
Topic: JEE Main 2023 (10 April Evening Shift)
