Science (English Medium) इयत्ता १२ - CBSE Important Questions for Mathematics

If A and B are invertible square matrices of the same order, then which of the following is not correct?

The value of |A|, if A = `[(0, 2x - 1, sqrt(x)),(1 - 2x, 0, 2sqrt(x)),(-sqrt(x), -2sqrt(x), 0)]`, where x ∈ R⁺, is ______.

If `|[2x,5],[8,x]|=|[6,-2],[7,3]|`, write the value of x.

Using properties of determinants, prove that `|[2y,y-z-x,2y],[2z,2z,z-x-y],[x-y-z,2x,2x]|=(x+y+z)^3`

Find the value of a if `[[a-b,2a+c],[2a-b,3c+d]]=[[-1,5],[0,13]]`

If `|[x+1,x-1],[x-3,x+2]|=|[4,-1],[1,3]|`, then write the value of x.

Using properties of determinants prove the following: `|[1,x,x^2],[x^2,1,x],[x,x^2,1]|=(1-x^3)^2`

If ` x in N and |[x+3,-2],[-3x,2x]|=8` , then find the value of x.

Use elementary column operation C₂ → C₂ + 2C₁ in the following matrix equation :

`[[2,1],[2,0]] = [[3,1],[2,0]] [[1,0],[-1,1]]`

Using properties of determinants, show that ΔABC is isosceles if:`|[1,1,1],[1+cosA,1+cosB,1+cosC],[cos^2A+cosA,cos^B+cosB,cos^2C+cosC]|=0​`

For what values of k, the system of linear equations

x + y + z = 2
2x + y – z = 3
3x + 2y + kz = 4

has a unique solution?

Find λ and μ if

`(hati+3hatj+9k)xx(3hati-lambdahatj+muk)=0`

Using the properties of determinants, prove the following:

`|[1,x,x+1],[2x,x(x-1),x(x+1)],[3x(1-x),x(x-1)(x-2),x(x+1)(x-1)]|=6x^2(1-x^2)`

If `A=|[2,0,-1],[5,1,0],[0,1,3]|` , then find A^-1 using elementary row operations

Using the properties of determinants, solve the following for x:

`|[x+2,x+6,x-1],[x+6,x-1,x+2],[x-1,x+2,x+6]|=0`

Using properties of determinants, prove that

`|((x+y)^2,zx,zy),(zx,(z+y)^2,xy),(zy,xy,(z+x)^2)|=2xyz(x+y+z)^3`

Using properties of determinants, prove that

`|[x+y,x,x],[5x+4y,4x,2x],[10x+8y,8x,3x]|=x^3`

Using properties of determinants, prove that :

`|[1+a,1,1],[1,1+b,1],[1,1,1+c]|=abc + bc + ca + ab`

Using properties of determinants, prove that 

`|[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]|=2|[a,b,c],[p,q,r],[x,y,z]|`

Prove that the determinant `|(x,sin theta, cos theta),(-sin theta, -x, 1),(cos theta, 1, x)|` is independent of θ.