1
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
The value of k $$\in$$R, for which the following system of linear equations

3x $$-$$ y + 4z = 3,

x + 2y $$-$$ 3z = $$-$$2

6x + 5y + kz = $$-$$3,

has infinitely many solutions, is :
A
3
B
$$-$$5
C
5
D
$$-$$3
2
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
Let $$A = \left[ {\matrix{ 2 & 3 \cr a & 0 \cr } } \right]$$, a$$\in$$R be written as P + Q where P is a symmetric matrix and Q is skew symmetric matrix. If det(Q) = 9, then the modulus of the sum of all possible values of determinant of P is equal to :
A
36
B
24
C
45
D
18
3
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Let the system of linear equations

4x + $$\lambda$$y + 2z = 0

2x $$-$$ y + z = 0

$$\mu$$x + 2y + 3z = 0, $$\lambda$$, $$\mu$$$$\in$$R.

has a non-trivial solution. Then which of the following is true?
A
$$\mu$$ = 6, $$\lambda$$$$\in$$R
B
$$\lambda$$ = 3, $$\mu$$$$\in$$R
C
$$\mu$$ = $$-$$6, $$\lambda$$$$\in$$R
D
$$\lambda$$ = 2, $$\mu$$$$\in$$R
4
JEE Main 2021 (Online) 18th March Morning Shift
+4
-1
The solutions of the equation $$\left| {\matrix{ {1 + {{\sin }^2}x} & {{{\sin }^2}x} & {{{\sin }^2}x} \cr {{{\cos }^2}x} & {1 + {{\cos }^2}x} & {{{\cos }^2}x} \cr {4\sin 2x} & {4\sin 2x} & {1 + 4\sin 2x} \cr } } \right| = 0,(0 < x < \pi )$$, are
A
$${\pi \over {12}},{\pi \over 6}$$
B
$${\pi \over 6},{{5\pi } \over 6}$$
C
$${{5\pi } \over {12}},{{7\pi } \over {12}}$$
D
$${{7\pi } \over {12}},{{11\pi } \over {12}}$$
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