Commerce (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

If `"y" = ("x" + sqrt(1 + "x"^2))^"n",  "then" (1 + "x"^2)  ("d"^2 "y")/"dx"^2 + "x" ("dy")/("dx")` is ____________.

If `"y = a"^"x", "b"^(2"x" -1), "then" ("d"^2"y")/"dx"^2` is ____________.

If `"y" = (varphi "n x")/"x",` then the value of y'' (e) is ____________.

If `"x" = "a" ("cos"  theta + theta  "sin"  theta), "y = a" ("sin"  theta - theta  "cos"  theta), "then" ("d"^2 "y")/("dx"^2) =` ____________.

If `"y"^2 = "ax"^2 + "bx + c", "then"  "d"/"dx" ("y"^3 "y"_"z") =` ____________.

If `sqrt(("x + y")) + sqrt (("y - x")) = "a", "then"  "dy"/"dx" =` ____________.

If `"xy"^2 = "ax"^2 + "bxy" + "y"^2, "then find"  "dy"/"dx"`

If `"y = tan"^-1 [("sin x + cos x")/("cos x - sin x")], "then"  "dy"/"dx"` is equal to ____________.

If f(x) = `"log"_("x"^2) ("log x")`, then f(e) is ____________.

Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`

Find: `int e^x.sin2xdx`

Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`

Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.

Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.

Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.

Find `int e^x ((1 - sinx)/(1 - cosx))dx`.

Find: `int e^(x^2) (x^5 + 2x^3)dx`.

Differentiate the following function with respect to x: `(log x)^x+x^(logx)`

If `y=log[x+sqrt(x^2+a^2)]` show that `(x^2+a^2)(d^2y)/(dx^2)+xdy/dx=0`

Evaluate: `int(5x-2)/(1+2x+3x^2)dx`