Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

Find the equation of the tangent line to the curve y = x² − 2x + 7 which is parallel to the line 2x − y + 9 = 0.

If x = a sin t and `y = a (cost+logtan(t/2))` ,find `((d^2y)/(dx^2))`

Evaluate : `int_0^4(|x|+|x-2|+|x-4|)dx`

If y=2 cos(logx)+3 sin(logx), prove that `x^2(d^2y)/(dx2)+x dy/dx+y=0`

Evaluate `∫_0^(3/2)|x cosπx|dx`

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