1
JEE Main 2022 (Online) 25th July Morning Shift
+4
-1

The number of $$\theta \in(0,4 \pi)$$ for which the system of linear equations

\begin{aligned} &3(\sin 3 \theta) x-y+z=2 \\ &3(\cos 2 \theta) x+4 y+3 z=3 \\ &6 x+7 y+7 z=9 \end{aligned}

has no solution, is :

A
6
B
7
C
8
D
9
2
JEE Main 2022 (Online) 30th June Morning Shift
+4
-1

Let $$A = \left[ {\matrix{ 1 & { - 2} & \alpha \cr \alpha & 2 & { - 1} \cr } } \right]$$ and $$B = \left[ {\matrix{ 2 & \alpha \cr { - 1} & 2 \cr 4 & { - 5} \cr } } \right],\,\alpha \in C$$. Then the absolute value of the sum of all values of $$\alpha$$ for which det(AB) = 0 is :

A
3
B
4
C
2
D
5
3
JEE Main 2022 (Online) 30th June Morning Shift
+4
-1

Let A and B be two square matrices of order 2. If $$det\,(A) = 2$$, $$det\,(B) = 3$$ and $$\det \left( {(\det \,5(det\,A)B){A^2}} \right) = {2^a}{3^b}{5^c}$$ for some a, b, c, $$\in$$ N, then a + b + c is equal to :

A
10
B
12
C
13
D
14
4
JEE Main 2022 (Online) 29th June Evening Shift
+4
-1

Let $$A = \left( {\matrix{ 2 & { - 1} \cr 0 & 2 \cr } } \right)$$. If $$B = I - {}^5{C_1}(adj\,A) + {}^5{C_2}{(adj\,A)^2} - \,\,.....\,\, - {}^5{C_5}{(adj\,A)^5}$$, then the sum of all elements of the matrix B is

A
$$-$$5
B
$$-$$6
C
$$-$$7
D
$$-$$8
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