1
JEE Main 2021 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let a, b and c be distinct positive numbers. If the vectors $$a\widehat i + a\widehat j + c\widehat k,\widehat i+\widehat k$$ and $$c\widehat i + c\widehat j + b\widehat k$$ are co-planar, then c is equal to :
A
$${2 \over {{1 \over a} + {1 \over b}}}$$
B
$${{a + b} \over 2}$$
C
$${1 \over a} + {1 \over b}$$
D
$$\sqrt {ab} $$
2
JEE Main 2021 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If [x] be the greatest integer less than or equal to x,

then $$\sum\limits_{n = 8}^{100} {\left[ {{{{{( - 1)}^n}n} \over 2}} \right]} $$ is equal to :
A
0
B
4
C
$$-$$2
D
2
3
JEE Main 2021 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The number of distinct real roots

of $$\left| {\matrix{ {\sin x} & {\cos x} & {\cos x} \cr {\cos x} & {\sin x} & {\cos x} \cr {\cos x} & {\cos x} & {\sin x} \cr } } \right| = 0$$ in the interval $$ - {\pi \over 4} \le x \le {\pi \over 4}$$ is :
A
4
B
1
C
2
D
3
4
JEE Main 2021 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$\left| {\overrightarrow a } \right| = 2,\left| {\overrightarrow b } \right| = 5$$ and $$\left| {\overrightarrow a \times \overrightarrow b } \right|$$ = 8, then $$\left| {\overrightarrow a .\,\overrightarrow b } \right|$$ is equal to :
A
6
B
4
C
3
D
5
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