1
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
$$ - {3 \over 5}$$
2
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
$${{6} \over {55}}$$
3
JEE Main 2017 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
For three events A, B and C,

P(Exactly one of A or B occurs)
= P(Exactly one of B or C occurs)
= P (Exactly one of C or A occurs) = $${1 \over 4}$$
and P(All the three events occur simultaneously) = $${1 \over {16}}$$.

Then the probability that at least one of the events occurs, is :
A
$${7 \over {16}}$$
B
$${7 \over {64}}$$
C
$${3 \over {16}}$$
D
$${7 \over {32}}$$
4
JEE Main 2017 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$\overrightarrow a = 2\widehat i + \widehat j -2 \widehat k$$ and $$\overrightarrow b = \widehat i + \widehat j$$.

Let $$\overrightarrow c $$ be a vector such that $$\left| {\overrightarrow c - \overrightarrow a } \right| = 3$$,

$$\left| {\left( {\overrightarrow a \times \overrightarrow b } \right) \times \overrightarrow c } \right| = 3$$ and the angle between $$\overrightarrow c $$ and $\overrightarrow a \times \overrightarrow b$ is $$30^\circ $$.

Then $$\overrightarrow a .\overrightarrow c $$ is equal to :
A
2
B
5
C
$${1 \over 8}$$
D
$${{25} \over 8}$$
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