1
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Consider the following two binary relations on the set A = {a, b, c} :
R1 = {(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)} and
R2 = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}.
Then :
A
both R1 and R2 are not symmetric.
B
R1 is not symmetric but it is transitive.
C
R2 is symmetric but it is not transitive.
D
both R1 and R2 are transitive.
2
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$\lambda $$ $$ \in $$ R is such that the sum of the cubes of the roots of the equation,
x2 + (2 $$-$$ $$\lambda $$) x + (10 $$-$$ $$\lambda $$) = 0 is minimum, then the magnitude of the difference of the roots of this equation is :
A
$$4\sqrt 2 $$
B
$$2\sqrt 5 $$
C
$$2\sqrt 7 $$
D
20
3
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The set of all $$\alpha $$ $$ \in $$ R, for which w = $${{1 + \left( {1 - 8\alpha } \right)z} \over {1 - z}}$$ is purely imaginary number, for all z $$ \in $$ C satisfying |z| = 1 and Re z $$ \ne $$ 1, is :
A
an empty set
B
{0}
C
$$\left\{ {0,{1 \over 4}, - {1 \over 4}} \right\}$$
D
equal to R
4
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$A$$ be a matrix such that $$A.\left[ {\matrix{ 1 & 2 \cr 0 & 3 \cr } } \right]$$ is a scalar matrix and |3A| = 108.
Then A2 equals :
A
$$\left[ {\matrix{ 4 & { - 32} \cr 0 & {36} \cr } } \right]$$
B
$$\left[ {\matrix{ {36} & 0 \cr { - 32} & 4 \cr } } \right]$$
C
$$\left[ {\matrix{ 4 & 0 \cr { - 32} & {36} \cr } } \right]$$
D
$$\left[ {\matrix{ {36} & { - 32} \cr 0 & 4 \cr } } \right]$$
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