1
JEE Main 2022 (Online) 27th June Morning Shift
Numerical
+4
-1
Change Language

The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is _____________.

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2
JEE Main 2022 (Online) 27th June Morning Shift
Numerical
+4
-1
Change Language

If the coefficient of x10 in the binomial expansion of $${\left( {{{\sqrt x } \over {{5^{{1 \over 4}}}}} + {{\sqrt 5 } \over {{x^{{1 \over 3}}}}}} \right)^{60}}$$ is $${5^k}\,.\,l$$, where l, k $$\in$$ N and l is co-prime to 5, then k is equal to _____________.

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3
JEE Main 2022 (Online) 27th June Morning Shift
Numerical
+4
-1
Change Language
Let

$${A_1} = \left\{ {(x,y):|x| \le {y^2},|x| + 2y \le 8} \right\}$$ and

$${A_2} = \left\{ {(x,y):|x| + |y| \le k} \right\}$$. If 27 (Area A1) = 5 (Area A2), then k is equal to :

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4
JEE Main 2022 (Online) 27th June Morning Shift
Numerical
+4
-1
Change Language

A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x $$-$$ y + 4 = 0, then the area of R is ____________.

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