1
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Let the acute angle bisector of the two planes x $$-$$ 2y $$-$$ 2z + 1 = 0 and 2x $$-$$ 3y $$-$$ 6z + 1 = 0 be the plane P. Then which of the following points lies on P?
A
$$\left( {3,1, - {1 \over 2}} \right)$$
B
$$\left( { - 2,0, - {1 \over 2}} \right)$$
C
(0, 2, $$-$$4)
D
(4, 0, $$-$$2)
2
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Which of the following is equivalent to the Boolean expression p $$\wedge$$ $$\sim$$ q ?
A
$$\sim$$ (q $$\to$$ p)
B
$$\sim$$ p $$\to$$ $$\sim$$ q
C
$$\sim$$ (p $$\to$$ $$\sim$$ q)
D
$$\sim$$ (p $$\to$$ q)
3
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :

JEE Main 2021 (Online) 1st September Evening Shift Mathematics - Probability Question 73 English
A
$${2 \over 7}$$
B
$${1 \over 18}$$
C
$${1 \over 7}$$
D
$${1 \over 9}$$
4
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If y = y(x) is the solution curve of the differential equation $${x^2}dy + \left( {y - {1 \over x}} \right)dx = 0$$ ; x > 0 and y(1) = 1, then $$y\left( {{1 \over 2}} \right)$$ is equal to :
A
$${3 \over 2} - {1 \over {\sqrt e }}$$
B
$$3 + {1 \over {\sqrt e }}$$
C
3 + e
D
3 $$-$$ e
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