1
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$\sum\limits_{r = 1}^{50} {{{\tan }^{ - 1}}{1 \over {2{r^2}}} = p} $$, then the value of tan p is :
A
$${{101} \over {102}}$$
B
$${{50} \over {51}}$$
C
100
D
$${{51} \over {50}}$$
2
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Two fair dice are thrown. The numbers on them are taken as $$\lambda$$ and $$\mu$$, and a system of linear equations

x + y + z = 5

x + 2y + 3z = $$\mu$$

x + 3y + $$\lambda$$z = 1

is constructed. If p is the probability that the system has a unique solution and q is the probability that the system has no solution, then :
A
$$p = {1 \over 6}$$ and $$q = {1 \over 36}$$
B
$$p = {5 \over 6}$$ and $$q = {5 \over 36}$$
C
$$p = {5 \over 6}$$ and $$q = {1 \over 36}$$
D
$$p = {1 \over 6}$$ and $$q = {5 \over 36}$$
3
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The locus of the mid points of the chords of the hyperbola x2 $$-$$ y2 = 4, which touch the parabola y2 = 8x, is :
A
y3(x $$-$$ 2) = x2
B
x3(x $$-$$ 2) = y2
C
y2(x $$-$$ 2) = x3
D
x2(x $$-$$ 2) = y3
4
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The value of

$$2\sin \left( {{\pi \over 8}} \right)\sin \left( {{{2\pi } \over 8}} \right)\sin \left( {{{3\pi } \over 8}} \right)\sin \left( {{{5\pi } \over 8}} \right)\sin \left( {{{6\pi } \over 8}} \right)\sin \left( {{{7\pi } \over 8}} \right)$$ is :
A
$${1 \over {4\sqrt 2 }}$$
B
$${1 \over 4}$$
C
$${1 \over 8}$$
D
$${1 \over {8\sqrt 2 }}$$
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