1
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The lines x = ay $$-$$ 1 = z $$-$$ 2 and x = 3y $$-$$ 2 = bz $$-$$ 2, (ab $$\ne$$ 0) are coplanar, if :
A
b = 1, a$$\in$$R $$-$$ {0}
B
a = 1, b$$\in$$R $$-$$ {0}
C
a = 2, b = 2
D
a = 2, b = 3
2
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If [x] denotes the greatest integer less than or equal to x, then the value of the integral $$\int_{ - \pi /2}^{\pi /2} {[[x] - \sin x]dx} $$ is equal to :
A
$$-$$ $$\pi$$
B
$$\pi$$
C
0
D
1
3
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If the real part of the complex number $${(1 - \cos \theta + 2i\sin \theta )^{ - 1}}$$ is $${1 \over 5}$$ for $$\theta \in (0,\pi )$$, then the value of the integral $$\int_0^\theta {\sin x} dx$$ is equal to:
A
1
B
2
C
$$-$$1
D
0
4
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$f:R - \left\{ {{\alpha \over 6}} \right\} \to R$$ be defined by $$f(x) = {{5x + 3} \over {6x - \alpha }}$$. Then the value of $$\alpha$$ for which (fof)(x) = x, for all $$x \in R - \left\{ {{\alpha \over 6}} \right\}$$, is :
A
No such $$\alpha$$ exists
B
5
C
8
D
6
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