HSC Arts कक्षा १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions

Choose the correct alternative:

The value of `int_0^"a" (sqrt("a"^2 - x^2))^3  "d"x` is

If F is the constant force generated by the motor of an automobile of mass M, its velocity V is given by `"M""dv"/"dt"` = F – kV, where k is a constant. Express V in terms of t given that V = 0 when t = 0

The velocity v, of a parachute falling vertically satisfies the equation `"v" (dv)/(dx) = "g"(1 - v^2/k^2)` where g and k are constants. If v and are both initially zero, find v in terms of x

Find the equation of the curve whose slope is `(y - 1)/(x^2 + x)` and which passes through the point (1, 0)

Solve the following differential equation:

`("d"y)/("d"x) = sqrt((1 - y^2)/(1 - x^2)`

Solve the following differential equation:

`y"d"x + (1 + x^2)tan^-1x  "d"y`= 0

Solve the following differential equation:

`sin  ("d"y)/("d"x)` = a, y(0) = 1

Solve the following differential equation:

`("d"y)/("d"x) = "e"^(x + y) - x^3"e"^y`

Solve the following differential equation:

(e^y + 1)cos x dx + e^y sin x dy = 0

Solve the following differential equation:

`(ydx - xdy) cot (x/y)` = ny² dx

Solve the following differential equation:

`("d"y)/("d"x) - xsqrt(25 - x^2)` = 0

Solve the following differential equation:

x cos y dy = e^x(x log x + 1) dx

Solve the following differential equation:

`tan y ("d"y)/("d"x) = cos(x + y) + cos(x - y)`

Solve the following differential equation:

`("d"y)/("d"x) = tan^2(x + y)`

Solve the following differential equation:

`[x + y cos(y/x)] "d"x = x cos(y/x) "d"y`

Solve the following differential equation:

`(x^3 + y^3)"d"y - x^2 y"d"x` = 0

Solve the following differential equation:

`y"e"^(x/y) "d"x = (x"e"^(x/y) + y) "d"y`

Solve the following differential equation:

`2xy"d"x + (x^2 + 2y^2)"d"y` = 0

Solve the following differential equation:

`(y^2 - 2xy) "d"x = (x^2 - 2xy) "d"y`

Solve the following differential equation:

`x ("d"y)/("d"x) = y - xcos^2(y/x)`