Science (English Medium) कक्षा १२ - CBSE Important Questions

If sin [cot⁻¹ (x+1)] = cos(tan⁻¹x), then find x.

If (tan⁻¹x)² + (cot⁻¹x)² = 5π²/8, then find x.

If tan^-1x+tan^-1y=π/4,xy<1, then write the value of x+y+xy.

Prove that

`tan^(-1) [(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))]=pi/4-1/2 cos^(-1)x,-1/sqrt2<=x<=1`

If `tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4` ,find the value of x

If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.

if `2[[3,4],[5,x]]+[[1,y],[0,1]]=[[7,0],[10,5]]` , find (x−y).

Solve the following matrix equation for x: `[x 1] [[1,0],[−2,0]]=0`

Solve the following matrix equation for x: `[x 1] [[1,0],[−2,0]]=0`

Two schools P and Q want to award their selected students on the values of discipline, politeness and punctuality. The school P wants to award Rs x each, Rs y each and Rs z each for the three respective values to its 3, 2 and 1 students with a total award money of Rs 1,000. School Q wants to spend Rs 1,500 to award its 4, 1 and 3 students on the respective values (by giving the same award money for the three values as before). If the total amount of awards for one prize on each value is Rs 600, using matrices, find the award money for each value.
Apart from the above three values, suggest one more value for awards.

Matrix A = `[(0,2b,-2),(3,1,3),(3a,3,-1)]`is given to be symmetric, find values of a and b

Matrix A = `[(0,2b,-2),(3,1,3),(3a,3,-1)]`is given to be symmetric, find values of a and b

If `A=([2,0,1],[2,1,3],[1,-1,0])` find A² - 5A + 4I and hence find a matrix X such that  A² - 5A + 4I + X = 0

If `A=([2,0,1],[2,1,3],[1,-1,0])` find A² - 5A + 4I and hence find a matrix X such that  A² - 5A + 4I + X = 0

If `[[x-y,z],[2x-y,w]]=[[-1,4],[0,5]]` find the value of x+y.

If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A^–1) = (det A)^k

Show that all the diagonal elements of a skew symmetric matrix are zero.

Show that all the diagonal elements of a skew symmetric matrix are zero.

Let A = `((2,-1),(3,4))`, B = `((5,2),(7,4))`, C= `((2,5),(3,8))` find a matrix D such that CD − AB = O

Given `A = [(2,-3),(-4,7)]` compute `A^(-1)` and show that `2A^(-1) = 9I - A`