1
JEE Main 2022 (Online) 26th June Evening Shift
Numerical
+4
-1
Out of Syllabus
Change Language
If $$\left( {{}^{40}{C_0}} \right) + \left( {{}^{41}{C_1}} \right) + \left( {{}^{42}{C_2}} \right) + \,\,.....\,\, + \,\,\left( {{}^{60}{C_{20}}} \right) = {m \over n}{}^{60}{C_{20}}$$ m and n are coprime, then m + n is equal to ___________.
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2
JEE Main 2022 (Online) 26th June Evening Shift
Numerical
+4
-1
Change Language

If a1 (> 0), a2, a3, a4, a5 are in a G.P., a2 + a4 = 2a3 + 1 and 3a2 + a3 = 2a4, then a2 + a4 + 2a5 is equal to ___________.

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3
JEE Main 2022 (Online) 26th June Evening Shift
Numerical
+4
-1
Change Language

The integral $${{24} \over \pi }\int_0^{\sqrt 2 } {{{(2 - {x^2})dx} \over {(2 + {x^2})\sqrt {4 + {x^4}} }}} $$ is equal to ____________.

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4
JEE Main 2022 (Online) 26th June Evening Shift
Numerical
+4
-1
Out of Syllabus
Change Language

Let a line L1 be tangent to the hyperbola $${{{x^2}} \over {16}} - {{{y^2}} \over 4} = 1$$ and let L2 be the line passing through the origin and perpendicular to L1. If the locus of the point of intersection of L1 and L2 is $${({x^2} + {y^2})^2} = \alpha {x^2} + \beta {y^2}$$, then $$\alpha$$ + $$\beta$$ is equal to _____________.

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