Elective Mathematics

Question 1

1If x ⊕ y = x + y − 2, find the identity element.

Medium

A. −2 B. 2 C. 1 D. 0

Question 2

2The coefficient of x in (2 + x)⁴ is

Easy

A. 16 B. 32 C. 4 D. 8

Question 3

3A binary operation * is defined by a * b = a + b + ab. Find 2 * 3.

Easy

A. 5 B. 11 C. 6 D. 8

Question 4

4Which binary operation on the real numbers is commutative?

Easy

A. a * b = 2a + b B. a * b = a ÷ b C. a * b = a − b D. a * b = a + b + ab

Question 5

5A binary operation is defined by a * b = ab/(a + b) for positive reals. Is * commutative?

Hard

A. Only for a = b B. Only for integers C. No D. Yes

Question 6

6If a * b = 2a − b, find (3 * 1) * 2.

Easy

A. 8 B. 4 C. 10 D. 6

Question 7

7n(A) = 20, n(B) = 15 and n(A ∩ B) = 8. Find n(A ∪ B).

Easy

A. 27 B. 35 C. 12 D. 43

Question 8

8Find the coefficient of x² in the expansion of (1 + 2x)⁴.

Medium

A. 6 B. 8 C. 24 D. 16

Question 9

9Find the coefficient of x⁴ in (1 − 2x)⁶.

Hard

A. 60 B. 15 C. −240 D. 240

Question 10

10How many subsets does a set with 4 elements have?

Easy

A. 16 B. 4 C. 8 D. 24