Science (English Medium) Class 12 - CBSE Important Questions

Find the area enclosed between the parabola 4y = 3x² and the straight line 3x - 2y + 12 = 0.

Find the particular solution of the differential equation:

2y e^x/y dx + (y - 2x e^x/y) dy = 0 given that x = 0 when y = 1.

Solve the differential equation `cos^2 x dy/dx` + y = tan x

Find the particular solution of the differential equation `(x - y) dy/dx = (x + 2y)` given that y = 0 when x = 1.

Find `(dy)/(dx)` at x = 1, y = `pi/4` if `sin^2 y + cos xy = K`

Prove that x² – y² = c(x² + y²)² is the general solution of the differential equation (x³ – 3xy²)dx = (y³ – 3x²y)dy, where C is parameter

The integrating factor of the differential equation \[\left( 1 - y^2 \right)\frac{dx}{dy} + yx = ay\left( - 1 < y < 1 \right)\] is ______.

Solve the differential equation:  ` (dy)/(dx) = (x + y )/ (x - y )`

Find the particular solution of the differential equation `x (dy)/(dx) - y = x^2.e^x`, given y(1) = 0.

Find the general solution of the differential equation `x (dy)/(dx) = y(logy - logx + 1)`.

Find the general solution of the differential equation:

`log((dy)/(dx)) = ax + by`.

Degree of the differential equation `sinx + cos(dy/dx)` = y² is ______.

Find the general solution of the differential equation:

(xy – x²) dy = y² dx

The sum of the order and the degree of the differential equation `d/dx[(dy/dx)^3]` is ______.

if `hat"i" + hat"j" + hat"k", 2hat"i" + 5hat"j", 3hat"i" + 2 hat"j" - 3hat"k" and  hat"i" - 6hat"j" - hat"k"` respectively are the position vectors A, B, C and D, then find the angle between the straight lines AB and CD. Find whether `vec"AB" and vec"CD"` are collinear or not.

A line l passes through point (– 1, 3, – 2) and is perpendicular to both the lines `x/1 = y/2 = z/3` and `(x + 2)/-3 = (y - 1)/2 = (z + 1)/5`. Find the vector equation of the line l. Hence, obtain its distance from the origin.

Two vectors `veca = a_1 hati + a_2 hatj + a_3 hatk` and `vecb = b_1 hati + b_2 hatj + b_3 hatk` are collinear if ______.

Find the Cartesian equation of the line which passes through the point (−2, 4, −5) and is parallel to the line `(x+3)/3=(4-y)/5=(z+8)/6`

Find the distance between the planes 2x - y +  2z = 5 and 5x - 2.5y + 5z = 20

If a line makes angles 90°, 135°, 45° with the x, y and z axes respectively, find its direction cosines.