1
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
2
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
3
JEE Main 2021 (Online) 25th July Evening Shift
+4
-1
If $$P = \left[ {\matrix{ 1 & 0 \cr {{1 \over 2}} & 1 \cr } } \right]$$, then P50 is :
A
$$\left[ {\matrix{ 1 & 0 \cr {25} & 1 \cr } } \right]$$
B
$$\left[ {\matrix{ 1 & {50} \cr 0 & 1 \cr } } \right]$$
C
$$\left[ {\matrix{ 1 & {25} \cr 0 & 1 \cr } } \right]$$
D
$$\left[ {\matrix{ 1 & 0 \cr {50} & 1 \cr } } \right]$$
4
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
The values of a and b, for which the system of equations

2x + 3y + 6z = 8

x + 2y + az = 5

3x + 5y + 9z = b

has no solution, are :
A
a = 3, b $$\ne$$ 13
B
a $$\ne$$ 3, b $$\ne$$ 13
C
a $$\ne$$ 3, b = 3
D
a = 3, b = 13
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