Class 12th

The given system of eqⁿ in matrix form is AK = B.

Then, |A| = 5 x 3 - 7 x 2 = 15 - 14 = 1 ≠ 0

∴ The system has a unique solution.

∴ k = 2 and y = -3

The given system of eqⁿ in matrix form is AK = B

= 5 x 28 -13 + 4 x (-9)

= 140 - 13 - 76

= 51 ≠ 0 .

The given system of eqⁿ are consistent

The given system of eqⁿ using matrix form can be written as AK = B

$=3\left(0-5\right)+1\left(0+3\right)-2\left(0-6\right)$

= -15 + 3 + 12

 = -15 + 15

= 0

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer-b

Explanation- from the figure we can say that diode D1 is reverse biased and diode D2 is forward biased so current will flow from B to A.

The given system of eqⁿ using matrix method can be expressed as

                 AK = B

$=\left(6a-2a\right)-\left(4a-2a\right)+\left(2a-3a\right)$

= 4a – 2a – a

= a ≠ 0.

Hence, the given system of eqⁿ is consistent

This is a Multiple Choice Questions as classified in NCERT Exemplar

Explanation - When p-n junction is forward biased, it opposes the potential barrier junction, when p-n junction is reverse biased, it supports the potential barrier junction, resulting increase in potential barrier across the junction.

The given system of equation can be written in the form AK = B

Hence the given system of eqⁿ are inconsistent.

The given system of eqⁿ can be written in the form AK = B where

Now, = 2 – (-1) = 2 + 1 = 3 ≠ 0.

∴ The system of eqⁿis consistent.

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- (d)

Explanation- when we increase temperature conductivity increases because number density is increasing after increasing temperature which decreases the relaxation time

The given system of equation can be written in the form of AK = B

Now,  = 3 * 1 - 2 * 2 = 3 - 4 = -1 ≠ 0.

∴ The system has unique solⁿ  and hence equation are consistent