# Maths-1996 -Set II

**Q2) Find the work done by the force = + 2 + , acting on a particle, if the particle is displaced from the point with position vector 2 + + to the point with position vector 3 + 2 + 4.**

Ans2) Here = + 2 +

call A(2 + + ) and B(3 + 2 + 4)

… = – = (3 + 2 + 4) – (2 + + )

= + + 3

… work done = .

= ( + 2 + ) . ( + + 3)

= 1 . I + 2 . I + I . 3 = 6

**Q4) For the matrices A and B, verify that (AB’ ) = A’B’ where
A = 1 3
2 4
B = 1 4
2 5**

Ans4) Here

A =

1 3

2 4

B =

1 4

2 5

L.H.S. =

7 19

10 28= 7 10

18 28

R.H.S. = B’A’ =

1 2

4 5

1 2

3 4

=

7 10

18 28= L.H.S

**Q7) Two dice are thrown together. What is the probability that the sum of the numbers on the two faces is divisible by 3 or by 4?**

Ans7) Let P(3), P(4), P(3 and 4), P(3 or 4) respectively denote the Probs of the sum of the no.s on the two faces be divisible by 3, 4, 3 and 4, 3 or 4 then

P(3) = 12/16 = 1/3

… the favourable Pairs are

(1, 2); (1, 5); (2, 1); (2, 4); (3, 3); (3, 6); (4, 2); (4, 5); (5, 1); (5, 4); (6, 3); (6, 6)

P(4) = 9/36 = 1/4

… the favourable Pairs are

(1, 3); (2, 2); (2, 6); (3, 1); (3, 5); (4, 4); (5, 3); (6, 2); (6, 6)

P(3 and 4) = 1/36

(only one pair, (6, 6) is common)

P(3 or 4) = P(3) + P(4) – P(AB)

= 1/3 + 1/4 – 1/36 = (12 + 9 – 1)/36 = 5/9