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

Show that four points A, B, C and D whose position vectors are 

`4hati+5hatj+hatk,-hatj-hatk-hatk, 3hati+9hatj+4hatk and 4(-hati+hatj+hatk)` respectively are coplanar.

If x cos(a+y)= cosy then prove that `dy/dx=(cos^2(a+y)/sina)`

Hence show that `sina(d^2y)/(dx^2)+sin2(a+y)(dy)/dx=0`

Evaluate `int_(-1)^2|x^3-x|dx`

Find the coordinate of the point P where the line through A(3, –4, –5) and B(2, –3, 1) crosses the plane passing through three points L(2, 2, 1), M(3, 0, 1) and N(4, –1, 0).
Also, find the ratio in which P divides the line segment AB.

Evaluate :

`∫_(-pi)^pi (cos ax−sin bx)^2 dx`

If x = a cos θ + b sin θ, y = a sin θ − b cos θ, show that `y^2 (d^2y)/(dx^2)-xdy/dx+y=0`

find `∫_2^4 x/(x^2 + 1)dx`

Evaluate :

`∫_0^π(4x sin x)/(1+cos^2 x) dx`

If `int_0^a1/(4+x^2)dx=pi/8` , find the value of a.

Evaluate :

`int_e^(e^2) dx/(xlogx)`

Find the second order derivative of the function.

x² + 3x + 2

Find the second order derivative of the function.

x²⁰

Find the second order derivative of the function.

x . cos x

Find the second order derivative of the function.

log x

Find the second order derivative of the function.

x³ log x

Find the second order derivative of the function.

e^x sin 5x

Find the second order derivative of the function.

e^6x cos 3x

Find the second order derivative of the function.

tan^–1 x

Find the second order derivative of the function.

log (log x)

Find the second order derivative of the function.

sin (log x)