Differentiation...

How many committee of five persons with a chairperson can be selected from $$12$$ persons.

Find the value of ?. 

The shortest distance between line $$y-x=1$$ and curve $$x={y}^{2}$$ is

How many $$3$$-digit even numbers can be formed from the digits $$1, 2, 3, 4, 5, 6$$ if the digits can be repeated?

Let $$y=a\cos t+b\sin t$$ then $$\dfrac{d^2y}{dt^2}=$$

Find the area of the triangle whose vertices are $$(-5, -1), (3, -5), (5, 2)$$

Let $$f(x)=\dfrac{1}{ax+b}$$ then $$f''(0)=$$

Ten students of the physics department decided to go on a educational trip.They hired a mini bus for the trip, but the bus can only carry eight students at a time and each student goes at least once. Find the minimum number of trips the bus has to make so that each students can go for equal number of trips.

The sides AB, BC, CA of a triangle ABC have $$3,4$$ and $$5$$ interior points respectively on them. The number of triangles that can be constructed using these points as vertices is-

If $$y=(x^{x})^{x}$$ then $$\dfrac {dy}{dx}=$$