If a∗b = a^2 + b^2, then the value of (4∗5)∗3 is (a) (4^2 +5^2) + 3^2 (b) (4+5)^2 + 3^2 (c) 41^2 + 3^2 (d) (4 + 5 + 3)^2 Watch Solution
If a * b denote the bigger among a and b and if a ⋅ b = (a * b) + 3, then 4.7 = (a) 14 (b) 31 (c) 10 (d) 8 Watch Solution
On the power set p of a non-empty set A, we define an operation Δ by XΔY=(X∩Y)∪(X∩Y)Then which are of the following statements is true about Δ (a) commutative and associative without an identity (b) commutative but not associative with an identity (c) associative but not commutative without an identity (d) associative and commutative with an identity Watch Solution
If the binary operation * on Z is defined by a⋅b=a^2-b^2 + ab + 4, then value of (2 * 3) * 4 is (a) 233 (b) 33 (c) 55 (d) -55 Watch Solution
For the binary operation * on Z defined by a * b = a + b + 1 the identity element is (a) 0 (b) -1 (c) 1 (d) 2 Watch Solution
If a binary operation * is defined on the set Z of integers as a * b = 3a – b, then the value of (2 * 3) *4 is (a) 2 (b) 3 (c) 4 (d) 5 Watch Solution
Q+ denote the set of all positive rational numbers. If the binary operation ⊙ on Q^+ is defined as a a⊙b = ab/2, then the inverse of 3 is (a) 4/3 (b) 2 (c) 1/3 (d) 2/3 Watch Solution
If G is the set of all matrices of the form [[x x] [x x]], where x∈R-{0} then the identity element with respect to the multiplication of matrices as binary operation, is Watch Solution
Q^+ is the set of all positive rational numbers with the binary operation * defined by a∗b = ab/2 for all a, b ∈Q^+. The inverse of an element a ∈Q^+ is (a) a (b) 1/a (c) 2/a (d) 4/a Watch Solution
If the binary operation ⊙ is defined on the se tQ^+ of all positive rational numbers by a⊙b = ab/4. Then, 3⊙(1/5⊙1/2) is equal to (a) 3/160 (b) 5/160 (c) 3/10 (d) 3/40 Watch Solution
Let * be a binary operation defined on set Q-{1} by the rule a∗b = a + b – ab. Then, the identity element for ∗ is (a) 1 (b) (a-1)/a (c) a/(a-1) (d) 0 Watch Solution
Which of the following is true? A.∗ defined by a∗b=(a+b)/2 is a binary operation on Z. B. * defined by a∗b=(a+b)/2 is a binary operation on Q. C. all binary commutative operations are associative D. subtraction is a binarv operation on N. Watch Solution
The binary operation * defined on N by a * b = a + b + ab for all a, b ∈ N is (a) commutative only (b) associative only (c) commutative and associative both (d) none of these Watch Solution
If a binary operation * is defined by a⋅b = a^2 + b^2 + ab + 1, then (2 * 3) * 2 is equal to (a) 20 (b) 40 (c) 400 (d) 445 Watch Solution
Let * be a binary operation on R defined by a * b = ab + 1. Then, * is (a) commutative but not associative (b) associative but not commutative (c) neither commutative nor associative (d) both commutative and associative Watch Solution
Subtraction of integers is (a) commutative but not associative (b) commutative and associative (c) associative but not commutative (d) neither commutative nor associative Watch Solution
The law a + b = b + a is called (a) closure law (b) associative law (c) commutative law (d) distributive law Watch Solution
An operation * is defined on the set Z of non-zero integers by a∗b = a/b for all a, b ∈Z. Then the property satisfied is (a) closure (b) commutative (c) associative (d) none of these Watch Solution
On Z an operation * is defined by a⋅b = a^2 + b^2 for all a, b ∈ Z. The operation * on Z is (a) commutative and associative (b) associative but not commutative (c) not associative (d) not a binary operation Watch Solution
A binary operation * on Z defined by a * b = 3a + b for all a, b ∈ Z, is (a) commutative (b) associative (c) not commutative (d) commutative and associative Watch Solution
Let * be a binary operation on Q+ defined by a∗b = ab/100 for all a, b ∈Q+. The inverse of 0.1 is (a) 10^5 (b) 10^4 (c) 10^6 (d) none of these Watch Solution
Let * be a binary operation on N defined by a * b = a + b + 10 for all a, b ∈ N. The identity element for * in N is (a) -10 (b) 0 (c) 10 (d) non-existent Watch Solution
Consider the binary operation * defined on Q – {1} by the rule a * b = a + b – ab for all a, b ∈ Q – {1}. The identity element in Q – {1} is (a) 0 (b) 1 (c) 1/2 (d) -1 Watch Solution
For the binary operation * defined on R-{1} by the rule a∗b = a + b + ab for all a, b ∈R−{1}, the inverse of a is (a) -a (b) -a/(a+1) (c) 1/a (d) a^2 Watch Solution
For the multiplication of matrices as a binary operation on the set of all matrices of the form [[a -b ][b a]], a, b ∈R the inverse of [[2 -3][3 2]] is Watch Solution
On the set Q^+ of all positive rational numbers a binary operation * is defined by a∗b = ab/2 for all a, b ∈Q^+. The inverse of 8 is (a) 1/8 (b) 1/2 (c) 2 (d) 4 Watch Solution
Let * be a binary operation defined on Q+ by the rule a∗b = ab/3 for all a, b ∈Q^+. The inverse of 4∗6 is (a) 9/8 (b) 2/3 (c) 3/2 (d) none of these Watch Solution
The number of binary operation that can be defined on a set of 2 elements is (a) 8 (b) 4 (c) 16 (d) 64 Watch Solution
The number of commutative binary operations that can be defined on a set of 2 elements is (a) 8 (b) 6 (c) 4 (d) 2 Watch Solution
