Hopefully, you guys have started on the Set B. You will find the following solutions useful. Click on the question. Please do attempt them during this December Holidays. 🙂

If you do have any questions, please WhatsApp me. 🙂

(i)

By Pythagoras’ Theorem, Length of side of isosceles

Area

(ii)

Let

Thus is minimum when

.

(i)

(ii)

(iii)

is the length of projection of onto .

Area

(i)

Since

, fg exists.

(ii)

Since the line cuts at more than one point, is not a one-one function, thus the inverse does not exist.

(iii)

Let

Since

(a)

(i)

(ii)

Let be number of sessions he needs to run

Using GC,

(b)

(i)

m

(ii)

Thus, he can be cycle more than 600km in total.

(i)

First, scale the curve 5 units parallel to the y = axis.

Then, translate the curve 2 units in the positive y – direction.

(ii)

(iii)

Using GC,

and

(i)

(ii)

Normal to

(iii)

Using GC:

(iv)

Let F be the foot of perpendicular from A to .

for some