1
JEE Main 2020 (Online) 2nd September Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Area (in sq. units) of the region outside

$${{\left| x \right|} \over 2} + {{\left| y \right|} \over 3} = 1$$ and inside the ellipse $${{{x^2}} \over 4} + {{{y^2}} \over 9} = 1$$ is :
A
$$6\left( {4 - \pi } \right)$$
B
$$3\left( {4 - \pi } \right)$$
C
$$6\left( {\pi - 2} \right)$$
D
$$3\left( {\pi - 2} \right)$$
2
JEE Main 2020 (Online) 2nd September Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If a function f(x) defined by

$$f\left( x \right) = \left\{ {\matrix{ {a{e^x} + b{e^{ - x}},} & { - 1 \le x < 1} \cr {c{x^2},} & {1 \le x \le 3} \cr {a{x^2} + 2cx,} & {3 < x \le 4} \cr } } \right.$$

be continuous for some $$a$$, b, c $$ \in $$ R and f'(0) + f'(2) = e, then the value of of $$a$$ is :
A
$${e \over {{e^2} - 3e - 13}}$$
B
$${1 \over {{e^2} - 3e + 13}}$$
C
$${e \over {{e^2} - 3e + 13}}$$
D
$${e \over {{e^2} + 3e + 13}}$$
3
JEE Main 2020 (Online) 2nd September Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let S be the set of all $$\lambda $$ $$ \in $$ R for which the system of linear equations

2x – y + 2z = 2
x – 2y + $$\lambda $$z = –4
x + $$\lambda $$y + z = 4

has no solution. Then the set S :
A
contains more than two elements.
B
contains exactly two elements.
C
is a singleton.
D
is an empty set.
4
JEE Main 2020 (Online) 2nd September Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let A be a 2 $$ \times $$ 2 real matrix with entries from {0, 1} and |A| $$ \ne $$ 0. Consider the following two statements :

(P) If A $$ \ne $$ I2 , then |A| = –1
(Q) If |A| = 1, then tr(A) = 2,

where I2 denotes 2 $$ \times $$ 2 identity matrix and tr(A) denotes the sum of the diagonal entries of A. Then :
A
(P) is true and (Q) is false
B
Both (P) and (Q) are false
C
Both (P) and (Q) are true
D
(P) is false and (Q) is true
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