1
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the system of equations

$$2 x+y-z=5$$

$$2 x-5 y+\lambda z=\mu$$

$$x+2 y-5 z=7$$

has infinitely many solutions, then $$(\lambda+\mu)^{2}+(\lambda-\mu)^{2}$$ is equal to

A
916
B
912
C
920
D
904
2
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The area of the region $$\left\{(x, y): x^{2} \leq y \leq\left|x^{2}-4\right|, y \geq 1\right\}$$ is

A
$$\frac{4}{3}(4 \sqrt{2}+1)$$
B
$$\frac{3}{4}(4 \sqrt{2}+1)$$
C
$$\frac{4}{3}(4 \sqrt{2}-1)$$
D
$$\frac{3}{4}(4 \sqrt{2}-1)$$
3
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The value of $${{{e^{ - {\pi \over 4}}} + \int\limits_0^{{\pi \over 4}} {{e^{ - x}}{{\tan }^{50}}xdx} } \over {\int\limits_0^{{\pi \over 4}} {{e^{ - x}}({{\tan }^{49}}x + {{\tan }^{51}}x)dx} }}$$ is

A
51
B
50
C
25
D
49
4
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The range of $$f(x)=4 \sin ^{-1}\left(\frac{x^{2}}{x^{2}+1}\right)$$ is

A
$$[0,2 \pi]$$
B
$$[0,2 \pi)$$
C
$$[0, \pi)$$
D
$$[0, \pi]$$
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