ISC (Arts) कक्षा १२ - CISCE Important Questions

Given two matrices A and B 

`A = [(1,-2,3),(1,4,1),(1,-3, 2)]  and B  = [(11,-5,-14),(-1, -1,2),(-7,1,6)]`

find AB and use this result to solve the following system of equations:

x - 2y + 3z = 6, x + 4x + z = 12, x - 3y + 2z = 1

Given two matrices A and B 

`A = [(1,-2,3),(1,4,1),(1,-3, 2)]  and B  = [(11,-5,-14),(-1, -1,2),(-7,1,6)]`

find AB and use this result to solve the following system of equations:

x - 2y + 3z = 6, x + 4x + z = 12, x - 3y + 2z = 1

Show that (A + A') is symmetric matrix, if `A = ((2,4),(3,5))`

Show that (A + A') is symmetric matrix, if `A = ((2,4),(3,5))`

Solve the following system of linear equation using matrix method: 
`1/x + 1/y +1/z = 9`

`2/x + 5/y+7/z = 52`

`2/x+1/y-1/z=0`

Write the negation of the following statements :
(a) Radha likes tea or coffee.
(b) `∃x cc` R such that x + 3 ≥ 10.

If A = `[(1,2), (1,3)]`, find A² - 3A

If the matrix `((6,-"x"^2),(2"x"-15 , 10))` is symmetric, find the value of x.

If A is a square matrix of order 3, then |2A| is equal to ______.

If A is a square matrix of order 3, then |2A| is equal to ______.

For what value of k the matrix `[(0, k),(-6, 0)]` is a skew symmetric matrix?

Assertion: Let the matrices A = `((-3, 2),(-5, 4))` and B = `((4, -2),(5, -3))` be such that A¹⁰⁰B = BA¹⁰⁰

Reason: AB = BA implies AB = BA for all positive integers n.

Assertion: Let the matrices A = `((-3, 2),(-5, 4))` and B = `((4, -2),(5, -3))` be such that A¹⁰⁰B = BA¹⁰⁰

Reason: AB = BA implies AB = BA for all positive integers n.

If A and B are symmetric matrices of the same order, then AB – BA is ______.

A matrix which is both symmetric and skew symmetric matrix is a ______.

A matrix which is both symmetric and skew symmetric matrix is a ______.

Define marginal utility. 

Differentiate between the expansion of demand and an increase in demand, using diagrams.

Figures (A), (B) and (C) given below represent different types of Demand curves.

(A)	(B)	(C)

What kind of goods do each of these Demand curves represent? Give a reason for each of the curves.

Draw a straight-line demand curve joining both the axes. Indicate the following on the demand curve.

Elasticity of demand is equal to zero