1
JEE Main 2022 (Online) 29th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of values of a $$\in$$ N such that the variance of 3, 7, 12, a, 43 $$-$$ a is a natural number is :

A
0
B
2
C
5
D
infinite
2
JEE Main 2022 (Online) 29th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60$$^\circ$$. The pole subtends an angle 30$$^\circ$$ at the top of the tower. Then the height of the tower is :

A
$$15\sqrt 3 $$
B
$$20\sqrt 3 $$
C
20 + $$10\sqrt 3 $$
D
30
3
JEE Main 2022 (Online) 29th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Negation of the Boolean statement (p $$\vee$$ q) $$\Rightarrow$$ (($$\sim$$ r) $$\vee$$ p) is equivalent to :

A
p $$\wedge$$ ($$\sim$$ q) $$\wedge$$ r
B
($$\sim$$ p) $$\wedge$$ ($$\sim$$ q) $$\wedge$$ r
C
($$\sim$$ p) $$\wedge$$ q $$\wedge$$ r
D
p $$\wedge$$ q $$\wedge$$ ($$\sim$$ r)
4
JEE Main 2022 (Online) 29th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let n $$\ge$$ 5 be an integer. If 9n $$-$$ 8n $$-$$ 1 = 64$$\alpha$$ and 6n $$-$$ 5n $$-$$ 1 = 25$$\beta$$, then $$\alpha$$ $$-$$ $$\beta$$ is equal to

A
1 + nC2 (8 $$-$$ 5) + nC3 (82 $$-$$ 52) + ...... + nCn (8n $$-$$ 1 $$-$$ 5n $$-$$ 1)
B
1 + nC3 (8 $$-$$ 5) + nC4 (82 $$-$$ 52) + ...... + nCn (8n $$-$$ 2 $$-$$ 5n $$-$$ 2)
C
nC3 (8 $$-$$ 5) + nC4 (82 $$-$$ 52) + ...... + nCn (8n $$-$$ 2 $$-$$ 5n $$-$$ 2)
D
nC4 (8 $$-$$ 5) + nC5 (82 $$-$$ 52) + ...... + nCn (8n $$-$$ 3 $$-$$ 5n $$-$$ 3)
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