CAT 1998 Question Paper

Possible numbers with unit's place as 5 = $$4 \times 3 \times 2 \times 1 = 24$$

Possible numbers with unit's place as 4 and ten's place 3,2,1 = $$3 \times 3 \times 2 \times 1 = 18$$

Possible numbers with unit's place as 3 and ten's place 2,1 = $$2 \times 3 \times 2 \times 1 = 12$$

Possible numbers with unit's place as 3 and ten's place 1 = $$1 \times 3 \times 2 \times 1 = 6$$

Total possible values = 24+18+12+6 = 60

In the first hour, they cover 6km. In the second hour they cover 6.5km. In the third hour, they cover 7km and so on.

Finally, they cover 72km in 9 hours.

Distance covered by A in 9 hours = 4*9 = 36km

=> They meet mid-way between A and B.

Options B,C and D are given vice-versa to given statements which is not necessarily true.

But according to option A, P is true, then Q and R will be true too but S will be false as for S, either Q or R should be false.

So answer will be A.

Area grazed by cow will be = Area of the larger circle - Sector APQ + Sector PBS + Sector CQR

Area of larger circle - Sector APQ = $$\pi r^2 - \frac{\pi r^2}{12}$$ = $$132 \pi$$

Sectors PBS and CQR are symmetrical and hence will have equal area.

In triangle ABC, AB = AC => ABC is isosceles triangle.

As A = 30° => B = C =75°

Hence, angle PBS = 180-75 = 105°

Hence, Area of sector PBS = 105/360 * $$\pi * 2^2$$ = $$ 7 \pi / 6$$

Thus area that can be grazed by the cow = $$132 \pi + 2*7 \pi /6$$ = $$403\pi /3$$

Among all positions for A, if it has first position then either B will be at the 3rd position or C and D will be together which is not possible Hence answer will be A) .

If A is not at the third place, then it has only two choices either 2nd or 4th position
So if A is at 2nd position, then B has only fourth position as choice and C can have either first or third position.
And if A is at 4th position, then B has only 2nd position and again C can have either first or third position.
Hence answer will be C.

If A and B are together, then it can't be at first and second place as C and D will be together which is not possible.
Now if A can be at third place and B is at second place then C and D can be placed accordingly.
Answer will be B).

Let's say price of turban is x.

So total price for 12 months will be = $$90+x$$

total price for 9 months = $$\frac{(90+x) \times 9}{12} = (65+x) $$

By solving above equation, we will get value of x= 10.

$$\frac{(\pi r^2)}{2 \pi r}$$ = $$\frac{2 \pi r}{ \pi r^2}$$
So r = 2
Hence required area = (Area of square) - (Area of 4 circles)
= $$(8^2) - (4 \pi (2^2))$$ (As side of square will be 4*2 = 8)
= $$16 (4- \pi)$$

The intended diagram can be drawn as follows:

ABCD is the square and the coins are placed (numbered 1,2,3,4)