Exercise 2.13: Choose the correct or the most suitable answer

CHAPTER: Basic Algebra

Choose the correct or the most suitable answer.

1. If |x + 2| ≤  9, then x belongs to

(1) (-∞,-7)

(2) [-11, 7]

(3) (-∞,-7) ∪ [11, ∞)

(4) (-11, 7)

Solution

2. Given that x, y and b are real numbers x < y, b > 0, then

(1) xb < yb

(2) xb > yb

(3) xb ≤ yb

(4) x/b ≥ y/b

Solution

3. If |x – 2| / (x – 2) ≥ 0, then x belongs to

(1) [2, ∞)

(2) (2, ∞)

(3) (-∞, 2)

(4) (-2, ∞)

Solution

4. The solution of 5x - 1 < 24 and 5x + 1 > -24 is

(1) (4, 5)

(2) (-5,-4)

(3) (-5, 5)

(4) (-5, 4)

Solution

5. The solution set of the following inequality |x - 1| ≥ |x – 3| is

(1) [0, 2]

(2) [2,∞)

(3) (0, 2)

(4) (-∞, 2)

Solution

6. The value of log_√2 512 is

(1) 16

(2) 18

(3) 9

(4) 12

Solution

7. The value of log₃1/81 is

(1) -2

(2) -8

(3) -4

(4) -9

Solution

8. If log_√x 0:25 = 4, then the value of x is

(1) 0:5

(2) 2:5

(3) 1:5

(4) 1:25

Solution

9. The value of log_a b log_b c logc a is

(1) 2

(2) 1

(3) 3

(4) 4

Solution

10. If 3 is the logarithm of 343, then the base is

(1) 5

(2) 7

(3) 6

(4) 9

Solution

11. Find a so that the sum and product of the roots of the equation 2x² + (a - 3)x + 3a - 5 = 0 are equal is

(1) 1

(2) 2

(3) 0

(4) 4

Solution

12. If a and b are the roots of the equation x² - kx + 16 = 0 and satisfy a² + b² = 32, then the value

of k is

(1) 10

(2) -8

(3) -8, 8

(4) 6

Solution

13. The number of solutions of x² + |x – 1| = 1 is

(1) 1

(2) 0

(3) 2

(4) 3

Solution

14. The equation whose roots are numerically equal but opposite in sign to the roots of 3x² - 5x - 7 = 0 is

(1) 3x² - 5x - 7 = 0

(2) 3x² + 5x - 7 = 0

(3) 3x² - 5x + 7 = 0

(4) 3x² + x - 7

Solution

15. If 8 and 2 are the roots of x² +ax+c = 0 and 3, 3 are the roots of x² +dx+b = 0, then the roots

of the equation x² + ax + b = 0 are

(1) 1, 2

(2) -1, 1

(3) 9, 1

(4) -1, 2

Solution

16. If a and b are the real roots of the equation x² - kx + c = 0, then the distance between the points (a, 0) and (b, 0) is

(1) √(k² - 4c)

(2) √(4k² – c)

(3) √(4c - k²)

(4) √(k - 8c)

Solution

17. If , then the value of k is

(1) 1

(2) 2

(3) 3

(4) 4

Solution

18. If , then the value of A + B is

(1) -1/2

(2) -2/3

(3) 1/2

(4) 2/3

Solution

19. The number of roots of (x + 3)⁴ + (x + 5)⁴ = 16 is

(1) 4

(2) 2

(3) 3

(4) 0

Solution

20. The value of log₃ 11. log₁₁ 13. log₁₃ 15.log₁₅ 27.log27 81 is

(1) 1

(2) 2

(3) 3

(4) 4

Solution