1
JEE Main 2017 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$\omega $$ be a complex number such that 2$$\omega $$ + 1 = z where z = $$\sqrt {-3} $$. If

$$\left| {\matrix{ 1 & 1 & 1 \cr 1 & { - {\omega ^2} - 1} & {{\omega ^2}} \cr 1 & {{\omega ^2}} & {{\omega ^7}} \cr } } \right| = 3k$$,

then k is equal to :
A
z
B
-1
C
1
D
-z
2
JEE Main 2017 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
The function $$f:R \to \left[ { - {1 \over 2},{1 \over 2}} \right]$$ defined as

$$f\left( x \right) = {x \over {1 + {x^2}}}$$, is
A
invertible
B
injective but not surjective.
C
surjective but not injective
D
neither injective nor surjective.
3
JEE Main 2017 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$5\left( {{{\tan }^2}x - {{\cos }^2}x} \right) = 2\cos 2x + 9$$,

then the value of $$\cos 4x$$ is :
A
$${1 \over 3}$$
B
$${2 \over 9}$$
C
$$ - {7 \over 9}$$
D
$$ - {3 \over 5}$$
4
JEE Main 2017 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
If two different numbers are taken from the set {0, 1, 2, 3, ........, 10}; then the probability that their sum as well as absolute difference are both multiple of 4, is :
A
$${{12} \over {55}}$$
B
$${{14} \over {45}}$$
C
$${{7} \over {55}}$$
D
$${{6} \over {55}}$$
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