Algebra Worksheet-3

Algebra Worksheet-3

1. (3x – 5y)³ – (5x – 2y)³ + (2x + 3y)³

(a) (3x – 5y) (5x – 2y) (2x + 3y)

(b) 3(3x – 5y) (5x – 2y) (2x + 3y)

(c) (3x – 5y) (2y – 5x) (2x + 3y)

(d) –3(3x – 5y) (5x – 2y) (2x + 3y)

2. If a + b + c = 9 and ab + bc + ca = 26, then the value of a³ + b³ + c³ – 3abc is:

(a) 27                  (b) 29                 (c) 495                (d) 729

3. If x³ + y³ + z³ = 3xyz then the relation between x, y and z is:

(a) x + y + z = 0

(b) x = y = z

(c) either x + y + z = 0 (or) x = y = z

(d) neither x + y + z = 0 nor x = y = z

4. If 0 < a < 1, then the value of is:

(a) greater than 2                         (b) less than 2

(c) greater than 4                         (d) less than 4

5. The value of is:

(a) 1                     (b) 10                  (c) 100                (d) None of these

6. If then the value of y is:

(a) 1                     (b) 0                    (c)                    (d) None of these

7. The value of is:

(a) 0                    (b) 0.1                 (c) 0.2                (d) 0.04

8. If 2x + y = 5 then 4x + 2y  is equal to:

(a) 5                    (b) 8                    (c) 9                    (d) 10

9. If x + y = 6 and 3x – y = 4 then x – y is equal to:

(a) –1                  (b) 0                    (c) 2                    (d) 4

10. If the product of two numbers is 10 and the sum is 7, then the larger of the two numbers is:

(a) –2                 (b) 2                    (c) 5                    (d)

11. The value of (55)³ – (75)³ + (20)³ is:

(a) –247500     (b) 251750         (c) 125320         (d) None of these

12. The value of the product at x = 1 is:

(a) 150                (b) 148               (c) 152                (d) None of these

13. _____.

(a) 0                    (b) a + b + c      (c) 1                     (d) None of these

14. The value of (x + 3)³ – (x – 3)³ is:

(a) 0                    (b) 1 – x³            (c) 3x² – 5         (d) 18x² + 54

Answer Key:

(1)-d; (2)-a; (3)-c; (4)-a; (5)-c; (6)-a; (7)-b; (8)-d; (9)-a; (10)-c; (11)-a; (12)-c; (13)-b; (14)-d