HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Write the converse, inverse, contrapositive of the following statement.

If 2 + 5 = 10, then 4 + 10 = 20.

Write the converse, inverse, contrapositive of the following statement.

If a man is bachelor, then he is happy.

Write the converse, inverse, contrapositive of the following statement.

If I do not work hard, then I do not prosper.

State the dual of the following statement by applying the principle of duality.

(p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q)

State the dual of the following statement by applying the principle of duality.

p ∨ (q ∨ r) ≡ ~[(p ∧ q) ∨ (r ∨ s)]

State the dual of the following statement by applying the principle of duality.

2 is even number or 9 is a perfect square.

Write the dual of the following.

(~p ∧ q) ∨ (p ∧ ~q) ∨ (~p ∧ ~q)

Write the dual of the following.

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)

Write the dual of the following.

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (q ∨ r)

Write the dual of the following.

~(p ∨ q) ≡ ~p ∧ ~q

Express the truth of the following statement by the Venn diagram.

Some members of the present Indian cricket are not committed.

Find `"dy"/"dx" if, sqrt"x" + sqrt"y" = sqrt"a"`

Find `"dy"/"dx"` if, x³ + y³ + 4x³y = 0 

Find `"dy"/"dx"` if, x³ + x²y + xy² + y³ = 81

Find `"dy"/"dx"` if, ye^x + xe^y = 1 

Find `"dy"/"dx"` if, `"x"^"y" = "e"^("x - y")`

Find `"dy"/"dx"` if, xy = log (xy)

If `"x"^5 * "y"^7 = ("x + y")^12` then show that, `"dy"/"dx" = "y"/"x"`

If log (x + y) = log (xy) + a then show that, `"dy"/"dx" = (- "y"^2)/"x"^2`.

Solve the following:

If `"e"^"x" + "e"^"y" = "e"^((x + y))` then show that, `"dy"/"dx" = - "e"^"y - x"`.