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 loga b logb
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
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