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

In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-

`y=sqrt(a^2-x^2)`              `x+y(dy/dx)=0`

Form the differential equation representing the family of curves y = a sin (x + b), where a, b are arbitrary constant.

Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis.

Form the differential equation of the family of circles having centre on y-axis and radius 3 unit.

Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.

Show that the function f given by:

`f(x)={((e^(1/x)-1)/(e^(1/x)+1),"if",x,!=,0),(-1,"if",x,=,0):}"`

is discontinuous at x = 0.

Find the particular solution of the differential equation `"dy"/"dx" = "xy"/("x"^2+"y"^2),`given that y = 1 when x = 0

Using integration, find the area of the region bounded by the parabola y² = 4x and the circle 4x² + 4y² = 9.

Using the method of integration, find the area of the region bounded by the lines 3x − 2y + 1 = 0, 2x + 3y − 21 = 0 and x − 5y + 9 = 0

Using integration, find the area of the smaller region bounded by the ellipse `"x"^2/9+"y"^2/4=1`and the line `"x"/3+"y"/2=1.`

Choose the correct alternative:

The constraint that in a college there are more scholarship holders in FYJC class (X) than in SYJC class (Y) is given by

Solve for x `tan^-1((1 - x)/(1 + x)) = 1/2 tan^-1x, x > 0`

The domain of the function y = sin^–1 (– x²) is ______.

The domain of y = cos^–1(x² – 4) is ______.

The domain of the function defined by f(x) = sin^–1x + cosx is ______.

The equation tan^–1x – cot^–1x = `(1/sqrt(3))` has ______.

Prove that `cot(pi/4 - 2cot^-1 3)` = 7

Show that `2tan^-1 (-3) = (-pi)/2 + tan^-1 ((-4)/3)`

If 2 tan^–1(cos θ) = tan^–1(2 cosec θ), then show that θ = π 4, where n is any integer.

Show that `cos(2tan^-1  1/7) = sin(4tan^-1  1/3)`