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

Compute the magnitude of the following vector:

`veca = hati + hatj + hatk;` `vecb = 2hati - 7hatj - 3hatk`;  `vecc = 1/sqrt3 hati + 1/sqrt3 hatj - 1/sqrt3 hatk`

The value of is `hati.(hatj xx hatk)+hatj.(hatixxhatk)+hatk.(hatixxhatj)` is ______.

If θ is the angle between any two vectors `veca` and `vecb,` then `|veca.vecb| = |veca xx vecb|` when θ is equal to ______.

For the differential equation, find the general solution:

`dy/dx = (1 - cos x)/(1+cos x)`

For the differential equation, find the general solution:

`dy/dx = sqrt(4-y^2)      (-2 < y < 2)`

For the differential equation, find the general solution:

`dy/dx + y = 1(y != 1)`

For the differential equation, find the general solution:

sec² x tan y dx + sec² y tan x dy = 0

For the differential equation, find the general solution:

(e^x + e^–x) dy – (e^x – e–x) dx = 0

For the differential equation, find the general solution:

`dy/dx = (1+x^2)(1+y^2)`

For the differential equation, find the general solution:

y log y dx - x dy = 0

For the differential equation, find the general solution:

`x^5  dy/dx = - y^5`

For the differential equation, find the general solution:

`dy/dx = sin^(-1) x`

For the differential equation, find the general solution:

e^x tan y dx + (1 – e^x) sec² y dy = 0

For the differential equation find a particular solution satisfying the given condition:

`(x^3 + x^2 + x + 1) dy/dx = 2x^2 + x; y = 1` When x = 0

For the differential equation find a particular solution satisfying the given condition:

`x(x^2 - 1) dy/dx = 1` , y = 0  when x = 2

For the differential equation find a particular solution satisfying the given condition:

`cos (dx/dy) = a(a in R); y = 1` when x = 0

For the differential equation find a particular solution satisfying the given condition:

`dy/dx` = y tan x; y = 1 when x = 0

Find the equation of a curve passing through the point (0, 0) and whose differential equation is y′ = e ^x sin x.