CBSE Guess > Papers > Important Questions > Class XII > 2010 > Maths > Mathematics By Mr. M.P.Keshari

CBSE CLASS XII

Q.3. Let * be a binary operation on the set Q of rational numbers given as a*b = (2a – b)2, a, b ε Q. Find 3*5 and 5*3. Is 3*5 = 5*3 ?

Solution :

We have, a*b = (2a – b)²
3*5 = (6 – 5)² = (1)² = 1.
5*3 = (10 – 3)² = (7)² = 49.
Therefore, 3*5 ≠ 5*3. [Proved.]

Q.4. Let * be the binary operation on N given by a*b = LCM of a and b. Find the value of 20*16. Is *

1. commutative,
2. associative ?

Solution :

We have, a*b = LCM of a and b = LCM(a, b).
Therefore, 20*16 = LCM(20, 16) = 80.

1. Let a, bε N
   Therefore, a*b = LCM(a, b) = LCM(b, a) = b*a.
   Hence, * is commutative. [Proved.]
   
   
2. Let a, b,c ε N
   Therefore, (a*b)*c = LCM[LCM(a, b)*c] = LCM(a, b, c) and
   a*(b*c) = LCM[a*LCM(b, c)] = LCM (a, b, c)
   Therefore, (a*b)*c = a*(b*c)
   Hence, * is accociative. [Proved.]

Q.5. Let * be a binary operation on N given by a*b = HCF (a, b), a, b ε N. Write the value of 22*4.

Solution :

We have, a*b = HCF (a, b).
Therefore, 22*4 = HCF (22, 4) = 2. [Ans.]

Q.6. If the binary operation * on the set of integers Z, is defined by a*b = a + 3b2, then find the value of 2*4.

Solution :

We have, a*b = a + 3b².
Therefore, 2*4 = 2 + 3(4)²
= 2 + 48
= 50. [Ans.]

Q.7. Let * be a binary operation on set Q of rational numbers defined as a*b = ab/5. Write the identity for *, if any.

Solution :

The identity for * is 5, as, 5*a = 5a/5 = a = a*5.

Paper By Mr. M.P.Keshari
Email Id : [email protected]
Ph No. : 09434150289