1
JEE Main 2020 (Online) 2nd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If a curve y = f(x), passing through the point (1, 2), is the solution of the differential equation,
2x2dy= (2xy + y2)dx, then $$f\left( {{1 \over 2}} \right)$$ is equal to :
A
$${1 \over {1 - {{\log }_e}2}}$$
B
$${1 \over {1 + {{\log }_e}2}}$$
C
$${{ - 1} \over {1 + {{\log }_e}2}}$$
D
$${1 + {{\log }_e}2}$$
2
JEE Main 2020 (Online) 2nd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Consider a region R = {(x, y) $$ \in $$ R : x2 $$ \le $$ y $$ \le $$ 2x}. if a line y = $$\alpha $$ divides the area of region R into two equal parts, then which of the following is true?
A
3$$\alpha $$2 - 8$$\alpha $$ + 8 = 0
B
$$\alpha $$3 - 6$$\alpha $$3/2 - 16 = 0
C
3$$\alpha $$2 - 8$$\alpha $$3/2 + 8 = 0
D
$$\alpha $$3 - 6$$\alpha $$2 + 16 = 0
3
JEE Main 2020 (Online) 2nd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let EC denote the complement of an event E. Let E1 , E2 and E3 be any pairwise independent events with P(E1) > 0

and P(E1 $$ \cap $$ E2 $$ \cap $$ E3) = 0.

Then P($$E_2^C \cap E_3^C/{E_1}$$) is equal to :
A
$$P\left( {E_3^C} \right)$$ - P(E2)
B
$$P\left( {E_2^C} \right)$$ + P(E3)
C
$$P\left( {E_3^C} \right)$$ - $$P\left( {E_2^C} \right)$$
D
P(E3) - $$P\left( {E_2^C} \right)$$
4
JEE Main 2020 (Online) 2nd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
For some $$\theta \in \left( {0,{\pi \over 2}} \right)$$, if the eccentricity of the
hyperbola, x2–y2sec2$$\theta $$ = 10 is $$\sqrt 5 $$ times the
eccentricity of the ellipse, x2sec2$$\theta $$ + y2 = 5, then the length of the latus rectum of the ellipse, is :
A
$$\sqrt {30} $$
B
$$2\sqrt 6 $$
C
$${{4\sqrt 5 } \over 3}$$
D
$${{2\sqrt 5 } \over 3}$$
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