Examination Questions in Algebra

1. If x + 1 = 1, then the value of x2 + 3x + 1 is
x x2 + 7x + 1
a. 2 b. 0 c. ½ d. 1

2. If a + b + c = 0, find the value of

1 + 1 + 1 + 1 + 1 + 1
a3 b3 c3 (a + b)3 (b + c)3 (c + a)3
a. 3abc b. 1 c. 0 d. – 1

3. If x + y = 4 and 1 + 1 = 4, then the value of x3 + y3 is
x y
a. 64 b. 4 c. 25 d. 52

4. Given that a + b + c = 2 and ab + bc + ca = 1, then the value of (a + b)2 + (b + c)2 + (c + a)2 is

a. 16 b. 6 c. 8 d. 10

5. (a2 + 2a)2 + 12(a2 + 2a) – 45 can be expressed as

  1. (a – 1)(a + 3)(a2 + 2a + 15)
  2. (a + 1)(a + 3)(a2 + 2a + 15)
  3. (a + 1)(a – 3)(a2 + 2a + 15)
  4. (a – 1)(a – 3)(a2 + 2a + 15)

6. If 3(a2 + b2 + c2) = (a + b + c)2, then the relation between a, b, c is

a. a = b = c b. a = b ≠ c c. a < b < c d. a > b > c

7. If a = 2.234, b = 3.121 and c = -5.355, then the value of a3 + b3 + c3 – 3abc is

a. – 1 b. 0 c. 1 d. 2

8. The equations 3x + 4y = 10 and – x + 2y = 0 have the solution (a, b). The value of a + b is

a. 1 b. 2 c. 3 d. 4

9. If x2 + 4x + 3 = 0, then the value of x3 is
x6 + 27x3 + 27
a. – 1
2
b. 1
c.   1
2
d. –1

10. If 999x + 888y = 1332 and 888x + 999y = 555, then x2 – y2 is equal to

a. 7 b. 8 c. 9 d. 5

11. If a – b = 4, and a2 + b2 = 40 where a and b are positive integers, then a3 + b6 is equal to

a. 264 b. 280 c. 300 d. 324

12. If (x2 + 1) = 17, then what is (x31) equal to?
x24x3
a. 75
16
b. 63
8
c. 95
8
d. None of these