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

Find the distance of the point (−1, −5, −10) from the point of intersection of the line `vecr=2hati-hatj+2hatk+lambda(3hati+4hatj+2hatk) ` and the plane `vec r (hati-hatj+hatk)=5`

Find the direction ratios of the normal to the plane, which passes through the points (1, 0, 0) and (0, 1, 0) and makes angle π/4 with the plane x + y = 3. Also find the equation of the plane

Find the coordinates of the foot of perpendicular drawn from the point A (-1,8,4) to the line joining the points B(0,-1,3) and C(2,-3,-1). Hence find the image of the point A in the line BC.

Evaluate `int_0^(pi)e^2x.sin(pi/4+x)dx`

Find the distance between the point (−1, −5, −10) and the point of intersection of the line `(x-2)/3=(y+1)/4=(z-2)/12` and the plane x-y+z=5

If lines `(x−1)/2=(y+1)/3=(z−1)/4 and  (x−3)/1=(y−k)/2=z/1` intersect, then find the value of k and hence find the equation of the plane containing these lines.

Find the distance of the point (2, 12, 5) from the point of intersection of the line 

`vecr=2hati-4hat+2hatk+lambda(3hati+4hatj+2hatk) `

If A= `[(cos alpha, -sin alpha), (sin alpha, cos alpha)]` then A + A' = I then the value of α is  ______.

Differentiate the following w.r.t. x:

`e^x/sinx`

Differentiate the following w.r.t. x: 

`e^(sin^(-1) x)`

Differentiate the following w.r.t. x:

`e^(x^3)`

Differentiate the following w.r.t. x: 

sin (tan^–1 e^–x)

Differentiate the following w.r.t. x:

log (cos e^x)

Differentiate the following w.r.t. x:

`e^x + e^(x^2) + "..." + e^(x^5)`

Differentiate the following w.r.t. x:

`sqrt(e^(sqrtx))`, x > 0

Differentiate the following w.r.t. x:

log (log x), x > 1

Differentiate the following w.r.t. x: 

`cos x/log x`, x > 0

Differentiate the following w.r.t. x:

cos (log x + e^x), x > 0

Differentiate the function with respect to x:

(log x)^{log x}, x > 1

Differentiate the function with respect to x:

cos (a cos x + b sin x), for some constant a and b.