Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

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.

Find the sine of the angle between the vectors `vec"a" = 3hat"i" + hat"j" + 2hat"k"` and `vec"b" = 2hat"i" - 2hat"j" + 4hat"k"`.

If A, B, C, D are the points with position vectors `hat"i" + hat"j" - hat"k", 2hat"i" - hat"j" + 3hat"k", 2hat"i" - 3hat"k", 3hat"i" - 2hat"j" + hat"k"`, respectively, find the projection of `vec"AB"` along `vec"CD"`.

Position vector of a point P is a vector whose initial point is origin.

If the direction ratios of a line are 1, 1, 2, find the direction cosines of the line.

Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).

If a line makes an angle of 30°, 60°, 90° with the positive direction of x, y, z-axes, respectively, then find its direction cosines.

The x-coordinate of a point on the line joining the points Q(2, 2, 1) and R(5, 1, –2) is 4. Find its z-coordinate.