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Solve the inequality 3x + 2 > – 16, 2x – 3 ≤ 11.

1) (- 6, 7] 2) [ -6, 7) 3) (- 6, 7) 4) [- 6, 7] Solution: (1) (- 6,... View Article

Solve the inequality 2x – 5 ≤ (4x – 7)/3

1) x ∈ (- ∞ , 4) 2) x ∈ (- ∞ , 4] 3) x ∈ (- ∞ ,... View Article

The number of solutions of the inequation |x – 2| + |x + 2|< 4 is

1) 1 2) 2 3) 4 4) 0 5) 3 Solution: (4) 0 It is given that |x – 2|... View Article

If x³ / [(2x – 1) (x + 2) (x – 3)] = A + B / (2x – 1) + C / (x + 2) + D / (x – 3), then A =

1) 1/2 2) -1/50 3) -8/25 4) 27/25 Solution: (1) 1 / 2 x3 / [(2x – 1) (x +... View Article

If [3x + 2] / [(x + 1) (2x² + 3)] = A / (x + 1) + {Bx + C} / (2x² + 3)}, then A + C – B =

1) 0 2) 2 3) 3 4) 5 Solution: (2) 2 [3x + 2] / [(x + 1) (2x2 +... View Article

The partial fraction of [3x³ – 8x² + 10] / [x – 1]⁴ is

1) 3 / (x – 1) + 1 / (x – 1)2 + 7 / (x – 1)3 + 5... View Article

[3x² + 1] / [x² – 6x + 8] =

1) 3 – [49] / [2 (x – 4)] – [13] / [2 (x – 2)] 2) [49] / [2... View Article

If [x² + x + 1] / [x² + 2x + 1] = A + B / (x + 1) + C / (x + 1)², then A – B =

1) 4 2) 4C + 1 3) 3C 4) 2 Solution: (4) 2 [x2 + x + 1] / [x... View Article

If a real value of fraction f of a real variable x is such that 1 / [(1 + x²) (1 + x²)] = A / [1 + x] + f (x) / (1 + x²) then f (x) =

1) [1 – x] / 2 2) [x2 + 1] / 2 3) 1 – x 4) None of these... View Article

If x is real, then the value of [x + 2] / [2x² + 3x + 6] is

1) (1 / 13, 1 / 3) 2) (- 1 / 13, 1 / 3) 3) (- 1 / 3,... View Article

If x is real, then the minimum value of [x² – x + 1] / [x² + x + 1] is

1) 1/3 2) 3 3) 1/2 4) 1 Solution: (1) 1 / 3 y = [x2 – x + 1]... View Article

If the both the root of the quadratic equation x² – 2kx + k² + k – 5 = 0 are less than 5, then k lies in the interval

1) (4, 5) 2) (- ∞, 4) 3) (6, ∞) 4) (5, 6) Solution: (2) (- ∞, 4) Let f... View Article

The values of k, for which the equations x² – kx – 21 = 0 and x² – 3kx + 35 = 0 will have a common roots, is

1) K = ± 4 2) K = ± 1 3) K = ± 3 4) K = 0 Solution:... View Article

All the values of m for which both roots of the equation x² – 2mx + m² – 1 = 0 are greater than – 2 but less than 4 lie in the interval

1) m > 3 2) – 1 < m < 3 3) 1 < m < 4 4) – 2... View Article

Let a, b and c be real. If ax² + bx + c = 0 has two real roots α and β where α < - 1 and β > 1 , then 1 + (c / a) + |b / a| =

1) < 0 2) > 0 3) ≤ 0 4) None of these Solution: (1) < 0 The roots are... View Article

The quadratic equations x² – 6x + a = 0, x² – cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then, the common root is

1) 2 2) 1 3) 4 4) 3 Solution: (1) 2 Let ɑ and 4β be the root of x2... View Article

If x is complex, then the expression [x² + 34x – 71] / [x² + 2x – 7] takes all values which lie in the interval (a, b), where

1) a = -1, b =1 2) a = 1, b = – 1 3) a = 5, b =... View Article

If ax² + bx + c = 0 and 2x² + 3x + 4 = 0 have a common root, where a, b, c ∈ N (set of natural numbers), then the least value of a + b + c is

1) 13 2) 11 3) 7 4) 9 Solution: (4) 9 Since 2x2 + 3x + 4 = 0 has... View Article

If a, b and c are in GP, then the equation ax² + 2bx + c = 0 and dx² + 2ex + f = 0 have a common root, if d / a, e / b and f / c are in

1) AP 2) HP 3) GP 4) None of these Solution: (1) AP Since a, b, c are in GP,... View Article

If the roots of the equation bx² + cx + a = 0 is imaginary, then for all real values of x, the expression 3b² x² + 6bcx + 2c² is

1) greater than 4ab 2) less than 4ab 3) greater than – 4ab 4) less than – 4ab Solution: (3)... View Article

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