1
JEE Main 2023 (Online) 1st February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

The negation of the expression $$q \vee \left( {( \sim \,q) \wedge p} \right)$$ is equivalent to

A
$$( \sim \,p) \wedge ( \sim \,q)$$
B
$$( \sim \,p) \vee q$$
C
$$p \wedge ( \sim \,q)$$
D
$$( \sim \,p) \vee ( \sim \,q)$$
2
JEE Main 2023 (Online) 1st February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

For a triangle $$ABC$$, the value of $$\cos 2A + \cos 2B + \cos 2C$$ is least. If its inradius is 3 and incentre is M, then which of the following is NOT correct?

A
$$\overrightarrow {MA} \,.\,\overrightarrow {MB} = - 18$$
B
$$\sin 2A + \sin 2B + \sin 2C = \sin A + \sin B + \sin C$$
C
perimeter of $$\Delta ABC$$ is 18$$\sqrt3$$
D
area of $$\Delta ABC$$ is $${{27\sqrt 3 } \over 2}$$
3
JEE Main 2023 (Online) 1st February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$f(x) = \left| {\matrix{ {1 + {{\sin }^2}x} & {{{\cos }^2}x} & {\sin 2x} \cr {{{\sin }^2}x} & {1 + {{\cos }^2}x} & {\sin 2x} \cr {{{\sin }^2}x} & {{{\cos }^2}x} & {1 + \sin 2x} \cr } } \right|,\,x \in \left[ {{\pi \over 6},{\pi \over 3}} \right]$$. If $$\alpha$$ and $$\beta$$ respectively are the maximum and the minimum values of $$f$$, then

A
$${\alpha ^2} - {\beta ^2} = 4\sqrt 3 $$
B
$${\beta ^2} - 2\sqrt \alpha = {{19} \over 4}$$
C
$${\beta ^2} + 2\sqrt \alpha = {{19} \over 4}$$
D
$${\alpha ^2} + {\beta ^2} = {9 \over 2}$$
4
JEE Main 2023 (Online) 1st February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The area enclosed by the closed curve $$\mathrm{C}$$ given by the differential equation

$$\frac{d y}{d x}+\frac{x+a}{y-2}=0, y(1)=0$$ is $$4 \pi$$.

Let $$P$$ and $$Q$$ be the points of intersection of the curve $$\mathrm{C}$$ and the $$y$$-axis. If normals at $$P$$ and $$Q$$ on the curve $$\mathrm{C}$$ intersect $$x$$-axis at points $$R$$ and $$S$$ respectively, then the length of the line segment $$R S$$ is :

A
$$\frac{4 \sqrt{3}}{3}$$
B
$$2 \sqrt{3}$$
C
2
D
$$\frac{2 \sqrt{3}}{3}$$
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