### 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 (x3 – 1 ) equal to? x2 4 x3
 a. 75 16 b. 63 8 c. 95 8 d. None of these