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

Find the angle between the following pair of lines:

`vecr = 2hati - 5hatj + hatk + lambda(3hati - 2hatj + 6hatk) and vecr = 7hati - 6hatk + mu(hati + 2hatj + 2hatk)`

Find the angle between the following pair of lines:

`vecr = 3hati + hatj - 2hatk + lambda(hati - hatj - 2hatk) and vecr = 2hati - hatj -56hatk + mu(3hati - 5hatj - 4hatk)`

Find the angle between the following pairs of lines: 

`(x-2)/2 = (y-1)/5 = (z+3)/(-3)` and `(x+2)/(-1) = (y-4)/8 = (z -5)/4`

Find the angle between the following pairs of lines:

`x/y = y/2 = z/1` and `(x-5)/4 = (y-2)/1 = (z - 3)/8`

Find the values of p so the line `(1-x)/3 = (7y-14)/2p = (z-3)/2` and `(7-7x)/(3p) = (y -5)/1 = (6-z)/5` are at right angles.

Find the angle between the lines whose direction ratios are a, b, c and b − c, c − a, a − b.

Find `bb(dy/dx)` in the following:

2x + 3y = sin x

Find `bb(dy/dx)` in the following:

2x + 3y = sin y

Find `bb(dy/dx)` in the following:

ax + by² = cos y

Find `bb(dy/dx)` in the following:

xy + y² = tan x + y

Find `bb(dy/dx)` in the following:

x² + xy + y² = 100

Find `bb(dy/dx)` in the following:

x³ + x²y + xy² + y³ = 81

Find `bb(dy/dx)` in the following:

sin² y + cos xy = k

Find `bb(dy/dx)` in the following:

sin² x + cos² y = 1

Find `bb(dy/dx)` in the following:

`y = sin^(-1)((2x)/(1+x^2))`

Show that the given differential equation is homogeneous and solve them.

(x² + xy) dy = (x² + y²) dx

Show that the given differential equation is homogeneous and solve them.

`y' = (x + y)/x`

Show that the given differential equation is homogeneous and solve them.

(x – y) dy – (x + y) dx = 0

Show that the given differential equation is homogeneous and solve them.

(x² – y²) dx + 2xy dy = 0

Show that the given differential equation is homogeneous and solve them.

`x^2 dy/dx = x^2 - 2y^2 + xy`