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

x and y are the sides of two squares such that y = x – x². Find the rate of change of the area of second square with respect to the area of first square.

The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when side is 10 cm is ______.

A ladder, 5 meter long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is ______.

I₂ is the matrix ____________.

Given that `"dy"/"dx"` = ye^x and x = 0, y = e. Find the value of y when x = 1.

Solve `x^2 "dy"/"dx" - xy = 1 + cos(y/x)`, x ≠ 0 and x = 1, y = `pi/2`

The integrating factor of the differential equation `"dy"/"dx" (x log x) + y` = 2logx is ______.

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.

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]

The instantaneous rate of change at t = 1 for the function f (t) = te^-t + 9 is ____________.

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 `vec"a"` and `vec"b"` are the position vectors of A and B, respectively, find the position vector of a point C in BA produced such that BC = 1.5 BA.

A vector `vec"r"` has magnitude 14 and direction ratios 2, 3, – 6. Find the direction cosines and components of `vec"r"`, given that `vec"r"` makes an acute angle with x-axis.