1
JEE Main 2020 (Online) 7th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If the system of linear equations
2x + 2ay + az = 0
2x + 3by + bz = 0
2x + 4cy + cz = 0,
where a, b, c $$ \in $$ R are non-zero distinct; has a non-zero solution, then:
A
$${1 \over a},{1 \over b},{1 \over c}$$ are in A.P.
B
a + b + c = 0
C
a, b, c are in G.P.
D
a,b,c are in A.P.
2
JEE Main 2019 (Online) 12th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
A value of $$\theta \in \left( {0,{\pi \over 3}} \right)$$, for which
$$\left| {\matrix{ {1 + {{\cos }^2}\theta } & {{{\sin }^2}\theta } & {4\cos 6\theta } \cr {{{\cos }^2}\theta } & {1 + {{\sin }^2}\theta } & {4\cos 6\theta } \cr {{{\cos }^2}\theta } & {{{\sin }^2}\theta } & {1 + 4\cos 6\theta } \cr } } \right| = 0$$, is :
A
$${\pi \over {18}}$$
B
$${\pi \over {9}}$$
C
$${{7\pi } \over {24}}$$
D
$${{7\pi } \over {36}}$$
3
JEE Main 2019 (Online) 12th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = $$\left[ {\matrix{ 2 & 3 \cr 5 & { - 1} \cr } } \right]$$, then AB is equal to :
A
$$\left[ {\matrix{ 4 & { - 2} \cr 1 & { - 4} \cr } } \right]$$
B
$$\left[ {\matrix{ { - 4} & { - 2} \cr { - 1} & 4 \cr } } \right]$$
C
$$\left[ {\matrix{ { - 4} & 2 \cr 1 & 4 \cr } } \right]$$
D
$$\left[ {\matrix{ 4 & { - 2} \cr { - 1} & { - 4} \cr } } \right]$$
4
JEE Main 2019 (Online) 12th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$B = \left[ {\matrix{ 5 & {2\alpha } & 1 \cr 0 & 2 & 1 \cr \alpha & 3 & { - 1} \cr } } \right]$$ is the inverse of a 3 × 3 matrix A, then the sum of all values of $$\alpha $$ for which det(A) + 1 = 0, is :
A
2
B
- 1
C
0
D
1
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