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1
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
Let A and B be two 3 $$\times$$ 3 real matrices such that (A2 $$-$$ B2) is invertible matrix. If A5 = B5 and A3B2 = A2B3, then the value of the determinant of the matrix A3 + B3 is equal to :
A
2
B
4
C
1
D
0
2
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
Let $$A = \left[ {\matrix{ 1 & 2 \cr { - 1} & 4 \cr } } \right]$$. If A$$-$$1 = $$\alpha$$I + $$\beta$$A, $$\alpha$$, $$\beta$$ $$\in$$ R, I is a 2 $$\times$$ 2 identity matrix then 4($$\alpha$$ $$-$$ $$\beta$$) is equal to :
A
5
B
$${8 \over 3}$$
C
2
D
4
3
JEE Main 2021 (Online) 25th July Evening Shift
+4
-1
The number of distinct real roots

of $$\left| {\matrix{ {\sin x} & {\cos x} & {\cos x} \cr {\cos x} & {\sin x} & {\cos x} \cr {\cos x} & {\cos x} & {\sin x} \cr } } \right| = 0$$ in the interval $$- {\pi \over 4} \le x \le {\pi \over 4}$$ is :
A
4
B
1
C
2
D
3
4
JEE Main 2021 (Online) 25th July Evening Shift
If $$P = \left[ {\matrix{ 1 & 0 \cr {{1 \over 2}} & 1 \cr } } \right]$$, then P50 is :
$$\left[ {\matrix{ 1 & 0 \cr {25} & 1 \cr } } \right]$$
$$\left[ {\matrix{ 1 & {50} \cr 0 & 1 \cr } } \right]$$
$$\left[ {\matrix{ 1 & {25} \cr 0 & 1 \cr } } \right]$$
$$\left[ {\matrix{ 1 & 0 \cr {50} & 1 \cr } } \right]$$