HSC Commerce: Marketing and Salesmanship इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions

Solve the following differential equation:

(x² – y²)dx + 2xy dy = 0

Let p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r). Then, this law is known as ______.

Without using truth table, show that

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)

Without using truth table, show that

p ∧ [(~ p ∨ q) ∨ ~ q] ≡ p

Without using truth table, show that

~ [(p ∧ q) → ~ q] ≡ p ∧ q

Without using truth table, show that

~r → ~ (p ∧ q) ≡ [~ (q → r)] → ~ p

Without using truth table, show that

(p ∨ q) → r ≡ (p → r) ∧ (q → r)

Using the algebra of statement, prove that

[p ∧ (q ∨ r)] ∨ [~ r ∧ ~ q ∧ p] ≡ p

Using the algebra of statement, prove that

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

Using the algebra of statement, prove that (p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ (~ p ∧ q).

Find `"dy"/"dx"`, if x = at², y = 2at

Find `(dy)/(dx)`, if x = 2at², y = at⁴.

Find `"dy"/"dx"`, if x = e^3t, y = `"e"^((4"t" + 5))`

Find `"dy"/"dx"`, if x = `("u" + 1/"u")^2, "y" = (2)^(("u" + 1/"u"))`

Find `"dy"/"dx"`, if x = `sqrt(1 + "u"^2), "y" = log (1 + "u"^2)`

Find `"dy"/"dx"`, if Differentiate 5^x with respect to log x

Solve the following.

If x = `"a"(1 - 1/"t"), "y" = "a"(1 + 1/"t")`, then show that `"dy"/"dx" = - 1`

If x = `(4t)/(1 + t^2),  y = 3((1 - t^2)/(1 + t^2))` then show that `dy/dx = (-9x)/(4y)`.

If x = t . log t, y = t^t, then show that `dy/dx - y = 0`.

If x = 2at² , y = 4at, then `dy/dx = ?`