Arts (English Medium) Class 12 - CBSE Important Questions

The order and the degree of the differential equation `(1 + 3 dy/dx)^2 = 4 (d^3y)/(dx^3)` respectively are ______.

The general solution of the differential equation ydx – xdy = 0; (Given x, y > 0), is of the form

(Where 'c' is an arbitrary positive constant of integration)

If `(a + bx)e^(y/x)` = x then prove that `x(d^2y)/(dx^2) = (a/(a + bx))^2`.

The degree of the differential equation `[1 + (dy/dx)^2]^3 = ((d^2y)/(dx^2))^2` is ______.

If `veca ` and `vecb` are two unit vectors such that `veca+vecb` is also a  unit vector, then find the angle between `veca` and `vecb`

If a unit vector `veca` makes angles `pi/3` with `hati,pi/4` with `hatj` and acute angles θ with ` hatk,` then find the value of θ.

If `veca and vecb` are two vectors such that `|veca+vecb|=|veca|,` then prove that vector `2veca+vecb` is perpendicular to vector `vecb`

Write the number of vectors of unit length perpendicular to both the vectors `veca=2hati+hatj+2hatk and vecb=hatj+hatk`

Write the position vector of the point which divides the join of points with position vectors `3veca-2vecb and 2veca+3vecb` in the ratio 2 : 1.

The two adjacent sides of a parallelogram are `2hati-4hatj-5hatk and 2 hati+2hatj+3hatj` . Find the two unit vectors parallel to its diagonals. Using the diagonal vectors, find the area of the parallelogram.

Find the position vector of the foot of perpendicular and the perpendicular distance from the point P with position vector

`2hati+3hatj+4hatk` to the plane `vecr` . `(2hati+hatj+3hatk)−26=0` . Also find image of P in the plane.

Write the value of `vec a .(vecb xxveca)`

If `veca=hati+2hatj-hatk, vecb=2hati+hatj+hatk and vecc=5hati-4hatj+3hatk` then find the value of `(veca+vecb).vec c`

If `veca=4hati-hatj+hatk` then find a unit vector parallel to the vector `veca+vecb`

Show that the four points A(4, 5, 1), B(0, –1, –1), C(3, 9, 4) and D(–4, 4, 4) are coplanar.

If `veca=2hati+hatj+3hatk and vecb=3hati+5hatj-2hatk` ,then find ` |veca xx vecb|`

Find the angle between the vectors `hati-hatj and hatj-hatk`

Find x such that the four points A(4, 1, 2), B(5, x, 6) , C(5, 1, -1) and D(7, 4, 0) are coplanar.

A line passing through the point A with position vector `veca=4hati+2hatj+2hatk` is parallel to the vector `vecb=2hati+3hatj+6hatk` . Find the length of the perpendicular drawn on this line from a point P with vector `vecr_1=hati+2hatj+3hatk`

If  `vec a, vec b, vec c`  are unit vectors such that `veca+vecb+vecc=0`, then write the value of  `vec a.vecb+vecb.vecc+vecc.vec a`.