1
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
$$\frac{4}{(3 \sqrt{6}-2)}$$
2
JEE Main 2024 (Online) 5th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

For the function

$$f(x)=\sin x+3 x-\frac{2}{\pi}\left(x^2+x\right), \text { where } x \in\left[0, \frac{\pi}{2}\right],$$

consider the following two statements :

(I) $$f$$ is increasing in $$\left(0, \frac{\pi}{2}\right)$$.

(II) $$f^{\prime}$$ is decreasing in $$\left(0, \frac{\pi}{2}\right)$$.

Between the above two statements,

A
only (I) is true.
B
both (I) and (II) are true.
C
only (II) is true.
D
neither (I) nor (II) is true.
3
JEE Main 2024 (Online) 5th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$\mathrm{A}(1,-1,2), \mathrm{B}(5,7,-6), \mathrm{C}(3,4,-10)$$ and $$\mathrm{D}(-1,-4,-2)$$ are the vertices of a quadrilateral ABCD, then its area is :

A
$$24 \sqrt{7}$$
B
$$48 \sqrt{7}$$
C
$$24 \sqrt{29}$$
D
$$12 \sqrt{29}$$
4
JEE Main 2024 (Online) 5th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$y=y(x)$$ is the solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}+2 y=\sin (2 x), y(0)=\frac{3}{4}$$, then $$y\left(\frac{\pi}{8}\right)$$ is equal to :

A
$$\mathrm{e}^{-\pi / 8}$$
B
$$\mathrm{e}^{\pi / 4}$$
C
$$\mathrm{e}^{-\pi / 4}$$
D
$$\mathrm{e}^{\pi / 8}$$
JEE Main Papers
2023
2021
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12