1
JEE Main 2020 (Online) 2nd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let a, b, c $$ \in $$ R be all non-zero and satisfy
a3 + b3 + c3 = 2. If the matrix

A = $$\left( {\matrix{ a & b & c \cr b & c & a \cr c & a & b \cr } } \right)$$

satisfies ATA = I, then a value of abc can be :
A
3
B
$${1 \over 3}$$
C
-$${1 \over 3}$$
D
$${2 \over 3}$$
2
JEE Main 2020 (Online) 2nd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If the sum of first 11 terms of an A.P.,
a1, a2, a3, .... is 0 (a $$ \ne $$ 0), then the sum of the A.P.,
a1 , a3 , a5 ,....., a23 is ka1 , where k is equal to :
A
$${{121} \over {10}}$$
B
-$${{121} \over {10}}$$
C
$${{72} \over 5}$$
D
-$${{72} \over 5}$$
3
JEE Main 2020 (Online) 2nd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let f : (–1, $$\infty $$) $$ \to $$ R be defined by f(0) = 1 and
f(x) = $${1 \over x}{\log _e}\left( {1 + x} \right)$$, x $$ \ne $$ 0. Then the function f :
A
decreases in (–1, $$\infty $$)
B
decreases in (–1, 0) and increases in (0, $$\infty $$)
C
increases in (–1, $$\infty $$)
D
increases in (–1, 0) and decreases in (0, $$\infty $$)
4
JEE Main 2020 (Online) 2nd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The imaginary part of
$${\left( {3 + 2\sqrt { - 54} } \right)^{{1 \over 2}}} - {\left( {3 - 2\sqrt { - 54} } \right)^{{1 \over 2}}}$$ can be :
A
-2$$\sqrt 6 $$
B
6
C
$$\sqrt 6 $$
D
-$$\sqrt 6 $$
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