1
JEE Main 2020 (Online) 4th September Morning Slot
MCQ (Single Correct Answer)
+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
2
JEE Main 2020 (Online) 4th September Morning Slot
MCQ (Single Correct Answer)
+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)
3
JEE Main 2020 (Online) 4th September Morning Slot
MCQ (Single Correct Answer)
+4
-1
Let x0 be the point of Local maxima of $$f(x) = \overrightarrow a .\left( {\overrightarrow b \times \overrightarrow c } \right)$$, where
$$\overrightarrow a = x\widehat i - 2\widehat j + 3\widehat k$$, $$\overrightarrow b = - 2\widehat i + x\widehat j - \widehat k$$, $$\overrightarrow c = 7\widehat i - 2\widehat j + x\widehat k$$. Then the value of
$$\overrightarrow a .\overrightarrow b + \overrightarrow b .\overrightarrow c + \overrightarrow c .\overrightarrow a$$ at x = x0 is :
A
14
B
-30
C
-4
D
-22
4
JEE Main 2020 (Online) 4th September Morning Slot
MCQ (Single Correct Answer)
+4
-1
The integral $$\int {{{\left( {{x \over {x\sin x + \cos x}}} \right)}^2}dx}$$ is equal to
(where C is a constant of integration):
A
$$\sec x - {{x\tan x} \over {x\sin x + \cos x}} + C$$
B
$$\sec x + {{x\tan x} \over {x\sin x + \cos x}} + C$$
C
$$\tan x - {{x\sec x} \over {x\sin x + \cos x}} + C$$
D
$$\tan x + {{x\sec x} \over {x\sin x + \cos x}} + C$$
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