1
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 ________ .
2
JEE Main 2020 (Online) 4th September Morning Slot
Numerical
+4
-0
If the system of equations
x - 2y + 3z = 9
2x + y + z = b
x - 7y + az = 24,
has infinitely many solutions, then a - b is equal to.........
3
JEE Main 2020 (Online) 3rd September Evening Slot
Numerical
+4
-0
Let S be the set of all integer solutions, (x, y, z), of the system of equations
x – 2y + 5z = 0
–2x + 4y + z = 0
–7x + 14y + 9z = 0
such that 15 $$\le$$ x2 + y2 + z2 $$\le$$ 150. Then, the number of elements in the set S is equal to ______ .
4
JEE Main 2020 (Online) 3rd September Morning Slot
Numerical
+4
-0
Let A = $$\left[ {\matrix{ x & 1 \cr 1 & 0 \cr } } \right]$$, x $$\in$$ R and A4 = [aij].
If a11 = 109, then a22 is equal to _______ .