If $\displaystyle \int \frac{\sin^{2}x+\cos^{2}x}{\sqrt{\sin^{2}x\,\cos^{2}x}\;\sin(x-\theta)}\,dx = A\sqrt{\cos\theta\,\tan x-\sin\theta}\;+\;B\sqrt{\cos\theta-\sin\theta}\,\cot x + C,$ where $C$ is the integration constant, then $AB$ is equal to:

1

Let $A$ be the point of intersection of the lines $3x+2y=14$ and $5x-y=6$, and $B$ be the point of intersection of the …

Topic: JEE Main 2024 (29 January Evening Shift)

2

Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is …

Topic: JEE Main 2024 (29 January Evening Shift)

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The distance of the point $(2,3)$ from the line $2x-3y+28=0$, measured parallel to the line $\sqrt{3}\,x-y+1=0$, is equ…

Topic: JEE Main 2024 (29 January Evening Shift)

2

Let a unit vector $\hat{\mathbf u}=x\hat i+y\hat j+z\hat k$ make angles $\dfrac{\pi}{2},\ \dfrac{\pi}{3}$ and $\dfrac{2…

Topic: JEE Main 2024 (29 January Evening Shift)

3

The function $f(x)=\dfrac{x}{x^{2}-6x-16}$, $x\in\mathbb{R}\setminus\{-2,8\}$:

Topic: JEE Main 2024 (29 January Evening Shift)

4

If $R$ is the smallest equivalence relation on the set $\{1,2,3,4\}$ such that $\{(1,2),(1,3)\}\subset R$, then the num…

Topic: JEE Main 2024 (29 January Evening Shift)

5

If the mean and variance of five observations are $\dfrac{24}{5}$ and $\dfrac{104}{25}$ respectively, and the mean of t…

Topic: JEE Main 2024 (29 January Evening Shift)

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Let $P(3,2,3)$, $Q(4,6,2)$ and $R(7,3,2)$ be the vertices of $\triangle PQR$. Then, the angle $\angle QPR$ is:

Topic: JEE Main 2024 (29 January Evening Shift)

7

Let $y=\log_{e}\!\left(\dfrac{1-x^{2}}{1+x^{2}}\right),\ -1

Topic: JEE Main 2024 (29 January Evening Shift)

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If $\log_e a,\ \log_e b,\ \log_e c$ are in an A.P. and $\log_e a-\log_e 2b,\ \log_e 2b-\log_e 3c,\ \log_e 3c-\log_e a$ …

Topic: JEE Main 2024 (29 January Evening Shift)

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If $\sin\!\left(\dfrac{y}{x}\right)=\log_e|x|+\dfrac{\alpha}{2}$ is the solution of the differential equation $x\cos\!\…

Topic: JEE Main 2024 (29 January Evening Shift)

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An integer is chosen at random from the integers $1,2,3,\ldots,50$. The probability that the chosen integer is a mult…

Topic: JEE Main 2024 (29 January Evening Shift)