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JEE Main 2021 (Online) 27th July Evening Shift
Numerical
+4
-1
If the real part of the complex number $$z = {{3 + 2i\cos \theta } \over {1 - 3i\cos \theta }},\theta \in \left( {0,{\pi \over 2}} \right)$$ is zero, then the value of sin23$$\theta$$ + cos2$$\theta$$ is equal to _______________.
2
JEE Main 2021 (Online) 25th July Evening Shift
Numerical
+4
-1
The equation of a circle is Re(z2) + 2(Im(z))2 + 2Re(z) = 0, where z = x + iy. A line which passes through the center of the given circle and the vertex of the parabola, x2 $$-$$ 6x $$-$$ y + 13 = 0, has y-intercept equal to ______________.
3
JEE Main 2021 (Online) 25th July Morning Shift
Numerical
+4
-1
Let $$S = \left\{ {n \in N\left| {{{\left( {\matrix{ 0 & i \cr 1 & 0 \cr } } \right)}^n}\left( {\matrix{ a & b \cr c & d \cr } } \right) = \left( {\matrix{ a & b \cr c & d \cr } } \right)\forall a,b,c,d \in R} \right.} \right\}$$, where i = $$\sqrt { - 1}$$. Then the number of 2-digit numbers in the set S is _____________.