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
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
3
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
4
JEE Main 2021 (Online) 22th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let A = [aij] be a real matrix of order 3 $$\times$$ 3, such that ai1 + ai2 + ai3 = 1, for i = 1, 2, 3. Then, the sum of all the entries of the matrix A3 is equal to :
A
2
B
1
C
3
D
9
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