1
JEE Main 2020 (Online) 3rd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If the value of the integral
$$\int\limits_0^{{1 \over 2}} {{{{x^2}} \over {{{\left( {1 - {x^2}} \right)}^{{3 \over 2}}}}}} dx$$

is $${k \over 6}$$, then k is equal to :
A
$$2\sqrt 3 + \pi $$
B
$$3\sqrt 2 - \pi $$
C
$$3\sqrt 2 + \pi $$
D
$$2\sqrt 3 - \pi $$
2
JEE Main 2020 (Online) 3rd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let e1 and e2 be the eccentricities of the ellipse,
$${{{x^2}} \over {25}} + {{{y^2}} \over {{b^2}}} = 1$$(b < 5) and the hyperbola,
$${{{x^2}} \over {16}} - {{{y^2}} \over {{b^2}}} = 1$$ respectively satisfying e1e2 = 1. If $$\alpha $$
and $$\beta $$ are the distances between the foci of the
ellipse and the foci of the hyperbola
respectively, then the ordered pair ($$\alpha $$, $$\beta $$) is equal to :
A
(8, 10)
B
(8, 12)
C
$$\left( {{{24} \over 5},10} \right)$$
D
$$\left( {{{20} \over 3},12} \right)$$
3
JEE Main 2020 (Online) 3rd September Evening Slot
Numerical
+4
-0
Change Language
Let S be the set of all integer solutions, (x, y, z), of the system of equations
x – 2y + 5z = 0
–2x + 4y + z = 0
–7x + 14y + 9z = 0
such that 15 $$ \le $$ x2 + y2 + z2 $$ \le $$ 150. Then, the number of elements in the set S is equal to ______ .
Your input ____
4
JEE Main 2020 (Online) 3rd September Evening Slot
Numerical
+4
-0
Change Language
If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that 4th A.M. is equal to 2nd G.M., then m is equal to _________ .
Your input ____
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