1
JEE Main 2021 (Online) 26th February Evening Shift
+4
-1
Consider the following system of equations :

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

2x + 6y $$-$$ 11z = b

x $$-$$ 2y + 7z = c,

where a, b and c are real constants. Then the system of equations :
A
has no solution for all a, b and c
B
has a unique solution when 5a = 2b + c
C
has infinite number of solutions when 5a = 2b + c
D
has a unique solution for all a, b and c
2
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A2 is 1, then the possible number of such matrices is :
A
6
B
4
C
1
D
12
3
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
The value of $$\left| {\matrix{ {(a + 1)(a + 2)} & {a + 2} & 1 \cr {(a + 2)(a + 3)} & {a + 3} & 1 \cr {(a + 3)(a + 4)} & {a + 4} & 1 \cr } } \right|$$ is :
A
$$-$$2
B
0
C
(a + 2)(a + 3)(a + 4)
D
(a + 1)(a + 2)(a + 3)
4
JEE Main 2021 (Online) 25th February Evening Shift
+4
-1
Let A be a 3 $$\times$$ 3 matrix with det(A) = 4. Let Ri denote the ith row of A. If a matrix B is obtained by performing the operation R2 $$\to$$ 2R2 + 5R3 on 2A, then det(B) is equal to :
A
64
B
16
C
128
D
80
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