1
JEE Main 2021 (Online) 25th February Morning Shift
Numerical
+4
-1
If the system of equations

kx + y + 2z = 1

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

$$-$$2x $$-$$2y $$-$$4z = 3

has infinitely many solutions, then k is equal to __________.
2
JEE Main 2021 (Online) 24th February Morning Shift
Numerical
+4
-1 Let P = $$\left[ {\matrix{ 3 & { - 1} & { - 2} \cr 2 & 0 & \alpha \cr 3 & { - 5} & 0 \cr } } \right]$$, where $$\alpha$$ $$\in$$ R. Suppose Q = [ qij] is a matrix satisfying PQ = kl3 for some non-zero k $$\in$$ R.
If q23 = $$- {k \over 8}$$ and |Q| = $${{{k^2}} \over 2}$$, then a2 + k2 is equal to ______.
3
JEE Main 2021 (Online) 24th February Morning Shift
Numerical
+4
-1 Let M be any 3 $$\times$$ 3 matrix with entries from the set {0, 1, 2}. The maximum number of such matrices, for which the sum of diagonal elements of MTM is seven, is ________.
4
JEE Main 2020 (Online) 6th September Evening Slot
Numerical
+4
-0
The sum of distinct values of $$\lambda$$ for which the system of equations

$$\left( {\lambda - 1} \right)x + \left( {3\lambda + 1} \right)y + 2\lambda z = 0$$
$$\left( {\lambda - 1} \right)x + \left( {4\lambda - 2} \right)y + \left( {\lambda + 3} \right)z = 0$$
$$2x + \left( {3\lambda + 1} \right)y + 3\left( {\lambda - 1} \right)z = 0$$

has non-zero solutions, is ________ .
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