1
JEE Main 2024 (Online) 5th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the function $$f(x)=\frac{\sin 3 x+\alpha \sin x-\beta \cos 3 x}{x^3}, x \in \mathbf{R}$$, is continuous at $$x=0$$, then $$f(0)$$ is equal to :

A
4
B
$$-$$2
C
$$-$$4
D
2
2
JEE Main 2024 (Online) 5th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the line $$2 x+3 y-\mathrm{k}=0, \mathrm{k}>0$$, intersect the $$x$$-axis and $$y$$-axis at the points $$\mathrm{A}$$ and $$\mathrm{B}$$, respectively. If the equation of the circle having the line segment $$A B$$ as a diameter is $$x^2+y^2-3 x-2 y=0$$ and the length of the latus rectum of the ellipse $$x^2+9 y^2=k^2$$ is $$\frac{m}{n}$$, where $$m$$ and $$n$$ are coprime, then $$2 \mathrm{~m}+\mathrm{n}$$ is equal to

A
12
B
13
C
11
D
10
3
JEE Main 2024 (Online) 5th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The value of $$\int_\limits{-\pi}^\pi \frac{2 y(1+\sin y)}{1+\cos ^2 y} d y$$ is :

A
$$\frac{\pi}{2}$$
B
$$\pi^2$$
C
$$\frac{\pi^2}{2}$$
D
$$2 \pi^2$$
4
JEE Main 2024 (Online) 5th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Suppose $$\theta \in\left[0, \frac{\pi}{4}\right]$$ is a solution of $$4 \cos \theta-3 \sin \theta=1$$. Then $$\cos \theta$$ is equal to :

A
$$\frac{6-\sqrt{6}}{(3 \sqrt{6}-2)}$$
B
$$\frac{4}{(3 \sqrt{6}+2)}$$
C
$$\frac{6+\sqrt{6}}{(3 \sqrt{6}+2)}$$
D
$$\frac{4}{(3 \sqrt{6}-2)}$$
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