Commerce (English Medium) कक्षा १२ - CBSE Important Questions

Answer the following question in 120-150 words: 

The peddler thinks that the whole world is a rattrap. This view of life is true only of himself and of no one else in the story. Comment.

Answer the following question in 120-150 words:    

Good human values are far above any other value system. How did Dr. Sadao succeed as a doctor as well as a patriot? 

Answer the following question in 120-150 words :

Derry sneaked into Mr. Lamb's garden and it became a turning point in his life. Comment. 

Answer the following question in 120-150 words:          
Untouchability is not only a crime, it is inhuman too. Why and how did Bama decide to fight against it?

Why was the 'Mahanavami Dibba' a centre of main Vijayanagara rituals? Explain.

Explain the role of village panchayats in the Mughal rural society.

“The power of the Jotedars was more effective than that of the zamindars.” Justify the statement with suitable arguments.

"Art and Literature as much as the writing of history have helped in keeping alive the memory of 1857." Explain the statement in reference to Rani Lakshmibai.

Let A = {x ∈ Z : 0 ≤ x ≤ 12}. Show that R = {(a, b) : a, b ∈ A, |a – b| is divisible by 4}is an equivalence relation. Find the set of all elements related to 1. Also write the equivalence class [2]

Show that the function f: ℝ → ℝ defined by f(x) = `x/(x^2 + 1), ∀x in R`is neither one-one nor onto. Also, if g: ℝ → ℝ is defined as g(x) = 2x - 1. Find fog(x)

If x = a cos θ + b sin θ, y = a sin θ − b cos θ, show that `y^2 (d^2y)/(dx^2)-xdy/dx+y=0`

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is `(4r)/3`. Also find maximum volume in terms of volume of the sphere

Find the intervals in which the function `f(x) = x^4/4 - x^3 - 5x^2 + 24x + 12`  is (a) strictly increasing, (b) strictly decreasing

An open tank with a square base and vertical sides is to be constructed from a metal sheet so as to hold a given quantity of water. Show that the cost of material will be least when the depth of the tank is half of its width. If the cost is to be borne by nearby settled lower-income families, for whom water will be provided, what kind of value is hidden in this question?

Find: `int(x+3)sqrt(3-4x-x^2dx)`

Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.

Find: `I=intdx/(sinx+sin2x)`

Solve the differential equation:

(1 + y²) dx = (tan⁻¹ y − x) dy

Find the shortest distance between the lines `vecr = (4hati - hatj) + lambda(hati+2hatj-3hatk)` and `vecr = (hati - hatj + 2hatk) + mu(2hati + 4hatj - 5hatk)`

A die, whose faces are marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event "number obtained is even" and B be the event "number obtained is red". Find if A and B are independent events.