1
JEE Main 2021 (Online) 31st August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If the following system of linear equations

2x + y + z = 5

x $$-$$ y + z = 3

x + y + az = b

has no solution, then :
A
$$a = - {1 \over 3},b \ne {7 \over 3}$$
B
$$a \ne {1 \over 3},b = {7 \over 3}$$
C
$$a \ne - {1 \over 3},b = {7 \over 3}$$
D
$$a = {1 \over 3},b \ne {7 \over 3}$$
2
JEE Main 2021 (Online) 31st August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The length of the latus rectum of a parabola, whose vertex and focus are on the positive x-axis at a distance R and S (> R) respectively from the origin, is :
A
4(S + R)
B
2(S $$-$$ R)
C
4(S $$-$$ R)
D
2(S + R)
3
JEE Main 2021 (Online) 31st August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If the function
$$f(x) = \left\{ {\matrix{ {{1 \over x}{{\log }_e}\left( {{{1 + {x \over a}} \over {1 - {x \over b}}}} \right)} & , & {x < 0} \cr k & , & {x = 0} \cr {{{{{\cos }^2}x - {{\sin }^2}x - 1} \over {\sqrt {{x^2} + 1} - 1}}} & , & {x > 0} \cr } } \right.$$ is continuous

at x = 0, then $${1 \over a} + {1 \over b} + {4 \over k}$$ is equal to :
A
$$-$$5
B
5
C
$$-$$4
D
4
4
JEE Main 2021 (Online) 31st August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $${{dy} \over {dx}} = {{{2^{x + y}} - {2^x}} \over {{2^y}}}$$, y(0) = 1, then y(1) is equal to :
A
log2(2 + e)
B
log2(1 + e)
C
log2(2e)
D
log2(1 + e2)
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