1
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If x, y, z are in arithmetic progression with common difference d, x $$\ne$$ 3d, and the determinant of the matrix $$\left[ {\matrix{ 3 & {4\sqrt 2 } & x \cr 4 & {5\sqrt 2 } & y \cr 5 & k & z \cr } } \right]$$ is zero, then the value of k2 is :
A
72
B
12
C
36
D
6
2
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
The value of $$\sum\limits_{r = 0}^6 {\left( {{}^6{C_r}\,.\,{}^6{C_{6 - r}}} \right)} $$ is equal to :
A
924
B
1024
C
1124
D
1324
3
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let y = y(x) be the solution of the differential equation

$$\cos x(3\sin x + \cos x + 3)dy = (1 + y\sin x(3\sin x + \cos x + 3))dx,0 \le x \le {\pi \over 2},y(0) = 0$$. Then, $$y\left( {{\pi \over 3}} \right)$$ is equal to :
A
$$2{\log _e}\left( {{{\sqrt 3 + 7} \over 2}} \right)$$
B
$$2{\log _e}\left( {{{3\sqrt 3 - 8} \over 4}} \right)$$
C
$$2{\log _e}\left( {{{2\sqrt 3 + 10} \over {11}}} \right)$$
D
$$2{\log _e}\left( {{{2\sqrt 3 + 9} \over 6}} \right)$$
4
JEE Main 2021 (Online) 17th March Evening Shift
Numerical
+4
-1
Change Language
Let $$A = \left[ {\matrix{ a & b \cr c & d \cr } } \right]$$ and $$B = \left[ {\matrix{ \alpha \cr \beta \cr } } \right] \ne \left[ {\matrix{ 0 \cr 0 \cr } } \right]$$ such that AB = B and a + d = 2021, then the value of ad $$-$$ bc is equal to ___________.
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