1
JEE Main 2021 (Online) 31st August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Which of the following is not correct for relation R on the set of real numbers ?
A
(x, y) $$\in$$ R $$ \Leftrightarrow $$ 0 < |x| $$-$$ |y| $$\le$$ 1 is neither transitive nor symmetric.
B
(x, y) $$\in$$ R $$ \Leftrightarrow $$ 0 < |x $$-$$ y| $$\le$$ 1 is symmetric and transitive.
C
(x, y) $$\in$$ R $$ \Leftrightarrow $$ |x| $$-$$ |y| $$\le$$ 1 is reflexive but not symmetric.
D
(x, y) $$\in$$ R $$ \Leftrightarrow $$ |x $$-$$ y| $$\le$$ 1 is reflexive nd symmetric.
2
JEE Main 2021 (Online) 31st August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The integral $$\int {{1 \over {\root 4 \of {{{(x - 1)}^3}{{(x + 2)}^5}} }}} \,dx$$ is equal to : (where C is a constant of integration)
A
$${3 \over 4}{\left( {{{x + 2} \over {x - 1}}} \right)^{{1 \over 4}}} + C$$
B
$${3 \over 4}{\left( {{{x + 2} \over {x - 1}}} \right)^{{5 \over 4}}} + C$$
C
$${4 \over 3}{\left( {{{x - 1} \over {x + 2}}} \right)^{{1 \over 4}}} + C$$
D
$${4 \over 3}{\left( {{{x - 1} \over {x + 2}}} \right)^{{5 \over 4}}} + C$$
3
JEE Main 2021 (Online) 31st August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If p and q are the lengths of the perpendiculars from the origin on the lines,

x cosec $$\alpha$$ $$-$$ y sec $$\alpha$$ = k cot 2$$\alpha$$ and

x sin$$\alpha$$ + y cos$$\alpha$$ = k sin2$$\alpha$$

respectively, then k2 is equal to :
A
4p2 + q2
B
2p2 + q2
C
p2 + 2q2
D
p2 + 4q2
4
JEE Main 2021 (Online) 31st August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
cosec18$$^\circ$$ is a root of the equation :
A
x2 + 2x $$-$$ 4 = 0
B
4x2 + 2x $$-$$ 1 = 0
C
x2 $$-$$ 2x + 4 = 0
D
x2 $$-$$ 2x $$-$$ 4 = 0
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