1
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
Let P(3, 3) be a point on the hyperbola,
$${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. If the normal to it at P intersects the x-axis at (9, 0) and e is its eccentricity, then the ordered pair (a2, e2) is equal to :
A
$$\left( {{9 \over 2},2} \right)$$
B
$$\left( {{3 \over 2},2} \right)$$
C
(9,3)
D
$$\left( {{9 \over 2},3} \right)$$
2
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
Let $$f\left( x \right) = \int {{{\sqrt x } \over {{{\left( {1 + x} \right)}^2}}}dx\left( {x \ge 0} \right)}$$. Then f(3) – f(1) is eqaul to :
A
$$- {\pi \over {12}} + {1 \over 2} + {{\sqrt 3 } \over 4}$$
B
$${\pi \over {12}} + {1 \over 2} - {{\sqrt 3 } \over 4}$$
C
$$- {\pi \over 6} + {1 \over 2} + {{\sqrt 3 } \over 4}$$
D
$${\pi \over 6} + {1 \over 2} - {{\sqrt 3 } \over 4}$$
3
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
Let $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ (a > b) be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function,
$$\phi \left( t \right) = {5 \over {12}} + t - {t^2}$$, then a2 + b2 is equal to :
A
145
B
126
C
135
D
116
4
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
If 1+(1–22.1)+(1–42.3)+(1-62.5)+......+(1-202.19)= $$\alpha$$ - 220$$\beta$$,
then an ordered pair $$\left( {\alpha ,\beta } \right)$$ is equal to:
A
(11, 103)
B
(10, 103)
C
(10, 97)
D
(11, 97)
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