Given $a, b \in {0, 1, 2, 3, ......, 19, 20}$ , consider the system of equations
x + y + z = 4
2x + y + 3z = 6
x + 2y + az = b
Let
P denotes number of order pairs (a, b) so that system of equations has a unique solution.
Q denotes number of ordered pairs (a, b) so that system of equations has no solution.
R denotes number of ordered pairs (a, b) so that system of equations has infinite solutions, then $(P + Q + R)$ is:

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

answer is 441.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$D = - a, D_{1} = - 2 (a - b + 6)$
$D_{2} = - 2 a - b + 6, D_{3} = 6 - b$
For unique solution, $b \neq 0$
$∴ L = 20 \times 21 = 420$
For no solution, $a = 0, b \neq 6$ ,
$∴ M = 1 \times 20 = 20$
For infinitely many solutions.
a = 0, b = 6, N = $1 \times 1 = 1$

Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET