1
JEE Main 2021 (Online) 27th August Evening Shift
Numerical
+4
-1
Let S be the sum of all solutions (in radians) of the equation $${\sin ^4}\theta + {\cos ^4}\theta - \sin \theta \cos \theta = 0$$ in [0, 4$$\pi$$]. Then $${{8S} \over \pi }$$ is equal to ____________.
2
JEE Main 2021 (Online) 27th August Evening Shift
Numerical
+4
-1
The probability distribution of random variable X is given by :

X 1 2 3 4 5
P(X) K 2K 2K 3K K

Let p = P(1 < X < 4 | X < 3). If 5p = $$\lambda$$K, then $$\lambda$$ equal to ___________.
3
JEE Main 2021 (Online) 27th August Evening Shift
Numerical
+4
-1
Let z1 and z2 be two complex numbers such that $$\arg ({z_1} - {z_2}) = {\pi \over 4}$$ and z1, z2 satisfy the equation | z $$-$$ 3 | = Re(z). Then the imaginary part of z1 + z2 is equal to ___________.
4
JEE Main 2021 (Online) 27th August Evening Shift
Numerical
+4
-1
Let S = {1, 2, 3, 4, 5, 6, 9}. Then the number of elements in the set T = {A $$\subseteq$$ S : A $$\ne$$ $$\phi$$ and the sum of all the elements of A is not a multiple of 3} is _______________.
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