Arts (English Medium) Class 12 - CBSE Question Bank Solutions

An appropriate substitution to solve the differential equation `"dx"/"dy" = (x^2 log(x/y) - x^2)/(xy log(x/y))` is ______.

Integrating factor of the differential equation `x "dy"/"dx" - y` = sinx is ______.

Integrating factor of the differential equation `"dy"/"dx" - y` = cos x is e^x.

One root of the equation `abs ((3"x" - 8, 3,3),(3, 3"x" - 8, 3),(3,3,3"x" - 8)) = 0` is ____________.

Given that `"dy"/"dx" = "e"^-2x` and y = 0 when x = 5. Find the value of x when y = 3.

Solve the differential equation `"dy"/"dx" + 2xy` = y

Solve: ydx – xdy = x²ydx.

Solve the differential equation `"dy"/"dx"` = 1 + x + y² + xy², when y = 0, x = 0.

Solve: `("d"y)/("d"x) = cos(x + y) + sin(x + y)`. [Hint: Substitute x + y = z]

Solution of `x("d"y)/("d"x) = y + x tan  y/x` is `sin(y/x)` = cx

The differential equation of all non horizontal lines in a plane is `("d"^2x)/("d"y^2)` = 0

If `"sin"^-1("x"^2 - 7"x" + 12) = "n"pi, AA "n" in "I"`, then x = ____________.

If `"cos"^-1  "x + sin"^-1  "x" = pi`, then the value of x is ____________.

If sin^-1 x – cos^-1 x `= pi/6,` then x = ____________.

If tan^-1 3 + tan^-1 x = tan^-1 8, then x = ____________.

`"sin"^-1 (-1/2)`

`"tan"^-1 (sqrt3)`

`"sin"^-1 (1/sqrt2)`

`"cos"^-1 1/2 + 2  "sin"^-1  1/2` is equal to ____________.

If tan^-1 (x – 1) + tan^-1 x + tan^-1 (x + 1) = tan^-1 3x, then the values of x are ____________.