1
JEE Main 2021 (Online) 22th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$\int\limits_0^{100\pi } {{{{{\sin }^2}x} \over {{e^{\left( {{x \over \pi } - \left[ {{x \over \pi }} \right]} \right)}}}}dx = {{\alpha {\pi ^3}} \over {1 + 4{\pi ^2}}},\alpha \in R} $$ where [x] is the greatest integer less than or equal to x, then the value of $$\alpha$$ is :
A
200 (1 $$-$$ e$$-$$1)
B
100 (1 $$-$$ e)
C
50 (e $$-$$ 1)
D
150 (e$$-$$1 $$-$$ 1)
2
JEE Main 2021 (Online) 22th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Let three vectors $$\overrightarrow a $$, $$\overrightarrow b $$ and $$\overrightarrow c $$ be such that $$\overrightarrow a \times \overrightarrow b = \overrightarrow c $$, $$\overrightarrow b \times \overrightarrow c = \overrightarrow a $$ and $$\left| {\overrightarrow a } \right| = 2$$. Then which one of the following is not true?
A
$$\overrightarrow a \times \left( {(\overrightarrow b + \overrightarrow c ) \times (\overrightarrow b \times \overrightarrow c )} \right) = \overrightarrow 0 $$
B
Projection of $$\overrightarrow a $$ on $$(\overrightarrow b \times \overrightarrow c )$$ is 2
C
$$\left[ {\matrix{ {\overrightarrow a } & {\overrightarrow b } & {\overrightarrow c } \cr } } \right] + \left[ {\matrix{ {\overrightarrow c } & {\overrightarrow a } & {\overrightarrow b } \cr } } \right] = 8$$
D
$${\left| {3\overrightarrow a + \overrightarrow b - 2\overrightarrow c } \right|^2} = 51$$
3
JEE Main 2021 (Online) 22th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The values of $$\lambda$$ and $$\mu$$ such that the system of equations $$x + y + z = 6$$, $$3x + 5y + 5z = 26$$, $$x + 2y + \lambda z = \mu $$ has no solution, are :
A
$$\lambda$$ = 3, $$\mu$$ = 5
B
$$\lambda$$ = 3, $$\mu$$ $$\ne$$ 10
C
$$\lambda$$ $$\ne$$ 2, $$\mu$$ = 10
D
$$\lambda$$ = 2, $$\mu$$ $$\ne$$ 10
4
JEE Main 2021 (Online) 22th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If the shortest distance between the straight lines $$3(x - 1) = 6(y - 2) = 2(z - 1)$$ and $$4(x - 2) = 2(y - \lambda ) = (z - 3),\lambda \in R$$ is $${1 \over {\sqrt {38} }}$$, then the integral value of $$\lambda$$ is equal to :
A
3
B
2
C
5
D
$$-$$1
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