HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

Integrate the following w.r.t.x: `(x + 5)/(x^3 + 3x^2 - x - 3)`

Integrate the following w.r.t.x : `sqrt(tanx)/(sinx*cosx)`

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 x⁵· y⁷ = (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"`.

Choose the correct alternative.

If y = 5^x . x⁵, then `"dy"/"dx" = ?` 

Choose the correct alternative.

If ax² + 2hxy + by² = 0 then `"dy"/"dx" = ?` 

Choose the correct alternative.

If `"x"^4."y"^5 = ("x + y")^("m + 1")` then `"dy"/"dx" = "y"/"x"` then m = ?

Choose the correct alternative.

If x = `("e"^"t" + "e"^-"t")/2, "y" = ("e"^"t" - "e"^-"t")/2`  then `"dy"/"dx"` = ? 

If y = `("x" + sqrt("x"^2 - 1))^"m"`, then `("x"^2 - 1) "dy"/"dx"` = ______.

State whether the following is True or False:

The derivative of `"x"^"m"*"y"^"n" = ("x + y")^("m + n")` is `"x"/"y"`

If `x^7 * y^9 = (x + y)^16`, then show that `dy/dx = y/x`

If `"x"^"a"*"y"^"b" = ("x + y")^("a + b")`, then show that `"dy"/"dx" = "y"/"x"`

Find `"dy"/"dx"` if x = `"e"^"3t",  "y" = "e"^(sqrt"t")`.