Commerce (English Medium) Class 12 - CBSE Important Questions

Which of the following empire issued gold coins for the very first time in first century CE?

Why have many scholars written the months after Independence as being Gandhiji's "finest hours? Explain.

Quit India movement was genuinely a mass movement bringing into its ambit hundreds of thousands of ordinary Indians. Elucidate the statement with suitable examples.

‘Gandhiji had mobilized a wider discontentment against the British rule in the Salt Satyagraha.’ Elucidate the statement with suitable examples.

Show that the relation R on R defined as R = {(a, b): a ≤ b}, is reflexive, and transitive but not symmetric.

A function f : [– 4, 4] `rightarrow` [0, 4] is given by f(x) = `sqrt(16 - x^2)`. Show that f is an onto function but not a one-one function. Further, find all possible values of 'a' for which f(a) = `sqrt(7)`.

Let A = {3, 5}. Then number of reflexive relations on A is ______.

If for any 2 x 2 square matrix A, `A("adj"  "A") = [(8,0), (0,8)]`, then write the value of |A|

If A is a skew symmetric matric of order 3, then prove that det A  = 0

If A is a square matrix of order 3 with |A| = 4 , then the write the value of |-2A| . 

If `[(2, 0),(5, 4)]` = P + Q, where P is symmetric, and Q is a skew-symmetric matrix, then Q is equal to ______.

If `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is non-singular matrix and a ∈ A, then the set A is ______.

If | A | = | kA |, where A is a square matrix of order 2, then sum of all possible values of k is ______.

If `"A" = [(1,1,1),(1,0,2),(3,1,1)]`, find A^-1. Hence, solve the system of equations x + y + z = 6, x + 2z = 7, 3x + y + z = 12.

 If x=a sin 2t(1+cos 2t) and y=b cos 2t(1−cos 2t), find `dy/dx `

if x^x+x^y+y^x=a^b, then find `dy/dx`.

If e^y (x + 1) = 1, show that `(d^2y)/(dx^2) = (dy/dx)^2`.

If sin y = xsin(a + y) prove that `(dy)/(dx) = sin^2(a + y)/sin a`

If x^y - y^x = a^b, find `(dy)/(dx)`.

If f(x) = x + 1, find `d/dx (fof) (x)`