1
JEE Main 2022 (Online) 29th June Morning Shift
+4
-1

If the system of linear equations

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

x $$-$$ 3y + 2z = 1

x + 4y + $$\delta$$z = k, where $$\delta$$, k $$\in$$ R has infinitely many solutions, then $$\delta$$ + k is equal to:

A
$$-$$3
B
3
C
6
D
9
2
JEE Main 2022 (Online) 29th June Morning Shift
+4
-1

Let $$A = [{a_{ij}}]$$ be a square matrix of order 3 such that $${a_{ij}} = {2^{j - i}}$$, for all i, j = 1, 2, 3. Then, the matrix A2 + A3 + ...... + A10 is equal to :

A
$$\left( {{{{3^{10}} - 3} \over 2}} \right)A$$
B
$$\left( {{{{3^{10}} - 1} \over 2}} \right)A$$
C
$$\left( {{{{3^{10}} + 1} \over 2}} \right)A$$
D
$$\left( {{{{3^{10}} + 3} \over 2}} \right)A$$
3
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1

If the system of linear equations

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

$$x + y + z = 4$$

$$x - y + |\lambda |z = 4\lambda - 4$$

where, $$\lambda$$ $$\in$$ R, has no solution, then

A
$$\lambda$$ = 7
B
$$\lambda$$ = $$-$$7
C
$$\lambda$$ = 8
D
$$\lambda$$2 = 1
4
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1

Let A be a matrix of order 3 $$\times$$ 3 and det (A) = 2. Then det (det (A) adj (5 adj (A3))) is equal to _____________.

A
512 $$\times$$ 106
B
256 $$\times$$ 106
C
1024 $$\times$$ 106
D
256 $$\times$$ 1011
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