1
JEE Main 2022 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1

The number of real values of $$\lambda$$, such that the system of linear equations

2x $$-$$ 3y + 5z = 9

x + 3y $$-$$ z = $$-$$18

3x $$-$$ y + ($$\lambda$$2 $$-$$ | $$\lambda$$ |)z = 16

has no solutions, is

A
0
B
1
C
2
D
4
2
JEE Main 2022 (Online) 25th July Morning Shift
MCQ (Single Correct Answer)
+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
3
JEE Main 2022 (Online) 30th June Morning Shift
MCQ (Single Correct Answer)
+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
4
JEE Main 2022 (Online) 30th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus

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
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