1
JEE Main 2021 (Online) 27th August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If the matrix $$A = \left( {\matrix{ 0 & 2 \cr K & { - 1} \cr } } \right)$$ satisfies $$A({A^3} + 3I) = 2I$$, then the value of K is :
A
$${1 \over 2}$$
B
$$-$$$${1 \over 2}$$
C
$$-$$1
D
1
2
JEE Main 2021 (Online) 27th August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$S = \left\{ {z \in C:{{z - i} \over {z + 2i}} \in R} \right\}$$, then :
A
S contains exactly two elements
B
S contains only one element
C
S is a circle in the complex plane
D
S is a straight line in the complex plane
3
JEE Main 2021 (Online) 27th August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let y = y(x) be the solution of the differential equation

$${{dy} \over {dx}} = 2(y + 2\sin x - 5)x - 2\cos x$$ such that y(0) = 7. Then y($$\pi$$) is equal to :
A
$$2{e^{{\pi ^2}}} + 5$$
B
$${e^{{\pi ^2}}} + 5$$
C
$$3{e^{{\pi ^2}}} + 5$$
D
$$7{e^{{\pi ^2}}} + 5$$
4
JEE Main 2021 (Online) 27th August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let us consider a curve, y = f(x) passing through the point ($$-$$2, 2) and the slope of the tangent to the curve at any point (x, f(x)) is given by f(x) + xf'(x) = x2. Then :
A
$${x^2} + 2xf(x) - 12 = 0$$
B
$${x^3} + xf(x) + 12 = 0$$
C
$${x^3} - 3xf(x) - 4 = 0$$
D
$${x^2} + 2xf(x) + 4 = 0$$
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