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

If `sin (sin^(−1)  1/5+cos^(−1) x)=1`, then find the value of x.

Prove that `cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2;x in (0,pi/4) `

Prove that `2tan^(-1)(1/5)+sec^(-1)((5sqrt2)/7)+2tan^(-1)(1/8)=pi/4`

Evaluate : `int(x-3)sqrt(x^2+3x-18)  dx`

Show that the function f in `A=R-{2/3} ` defined as `f(x)=(4x+3)/(6x-4)` is one-one and onto hence find f^-1

Prove that: `tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4`

Solve for x : tan^-1 (x - 1) + tan^-1x + tan^-1 (x + 1) = tan^-1 3x

Prove that `tan^(-1)((6x-8x^3)/(1-12x^2))-tan^(-1)((4x)/(1-4x^2))=tan^(-1)2x;|2x|<1/sqrt3`

Show that the following two lines are coplanar:

`(x−a+d)/(α−δ)= (y−a)/α=(z−a−d)/(α+δ) and (x−b+c)/(β−γ)=(y−b)/β=(z−b−c)/(β+γ)`

Evaluate :

`int(sqrt(cotx)+sqrt(tanx))dx`

Find : `int((2x-5)e^(2x))/(2x-3)^3dx`

Find: `int(x+3)sqrt(3-4x-x^2dx)`

Prove that:

`tan^(-1)""1/5+tan^(-1)""1/7+tan^(-1)""1/3+tan^(-1)""1/8=pi/4`

Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.

Find `intsqrtx/sqrt(a^3-x^3)dx`

Find the absolute maximum and absolute minimum values of the function f given by f(x)=sin²x-cosx,x ∈ (0,π)

Show that lines: 

`vecr=hati+hatj+hatk+lambda(hati-hat+hatk)`

`vecr=4hatj+2hatk+mu(2hati-hatj+3hatk)` are coplanar 

Also, find the equation of the plane containing these lines.

Three persons A, B and C apply for a job of Manager in a Private Company. Chances of their selection (A, B and C) are in the ratio 1 : 2 :4. The probabilities that A, B and C can introduce changes to improve profits of the company are 0.8, 0.5 and 0.3, respectively. If the change does not take place, find the probability that it is due to the appointment of C

Find the particular solution of the differential equation x²dy = (2xy + y²) dx, given that y = 1 when x = 1.

If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.