ISC (Arts) इयत्ता १२ - CISCE Important Questions

If f : R `rightarrow` R is defined by `f(x) = (2x - 7)/4`, show that f(x) is one-one and onto.

Statement 1: The intersection of two equivalence relations is always an equivalence relation.

Statement 2: The Union of two equivalence relations is always an equivalence relation.

Which one of the following is correct?

if A =`((5,a),(b,0))` is symmetric matrix show that a = b

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 ______.

Answer the following question.
Discuss the relationship between the income of the consumer and demand for a commodity with respect to normal goods, inferior goods, and necessities.