ISC (Arts) कक्षा १२ - CISCE Important Questions for Applied Mathematics

If a relation R on the set {a, b, c} defined by R = {(b, b)}, then classify the relation.

Solve:

sin^–1 (x) + sin^–1 (1 – x) = cos^–1 x

If the function f : R → R be defined by f(x) = 2x − 3 and g : R → R by g(x) = x³ + 5, then find the value of (fog)⁻¹ (x).

Let f : W → W be defined as

`f(n)={(n-1, " if n is odd"),(n+1, "if n is even") :}`

Show that f is invertible a nd find the inverse of f. Here, W is the set of all whole
numbers.

The binary operation *: R x R → R is defined as a *b = 2a + b Find (2 * 3)*4

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

If the function `f(x) = sqrt(2x - 3)` is invertible then find its inverse. Hence prove that `(fof^(-1))(x) = x`

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

Let \[f\left(x\right) = x^3\] be a function with domain {0, 1, 2, 3}. Then domain of \[f^{-1}\] is ______.

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.

A relation R on (1, 2, 3) is given by R = {(1, 1), (2, 2), (1, 2), (3, 3), (2, 3)}. Then the relation R is ______.

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?

If f(x) = [4 – (x – 7)³]^1/5 is a real invertible function, then find f^–1(x).

Let A = R – {2} and B = R – {1}. If f: A `→` B is a function defined by f(x) = `(x - 1)/(x - 2)` then show that f is a one-one and an onto function.

Let L be a set of all straight lines in a plane. The relation R on L defined as 'perpendicular to' is ______.