JEE Mathematics Linear Inequalities MCQs

Question. Given that x > 0, y > 0, x > y and z ≠ 0. The inequality which is not always correct is:
(a) xz > y > z
(b) x + z > y + z
(c) x – z > y – z
(d) None of these

Answer: A

Question. Solution of inequality log₁₀ (x -12x + 36) < 2 is
(a) (– 4, 16)
(b) (6, 16)
(c) (– 4, 6)
(d) None of these

Answer: A

Question. Number of integers satisfying either
log₃ | x | < 2 or | log₃ x | < 2 are –
(a) 16
(b) 23
(c) 18
(d) 20

Answer: A

Question. Solution set of (x + 1) (x – 1)² (x – 2) ≥ 0 is :
(a) [-1,2]
(b) (– 1, 2)
(c) Both
(d) none of these

Answer: D

Question. The inequalities y (– 1) ≥ – 4, y(1) ≤ 0 and y(3) ≥ 5 are known to hold for y = ax² + bx + c, then the least value of 'a' is
(a) 1/8
(b) – 1/3
(c) – 1/4
(d) 1/4

Answer: A

Question. The values of x satisfying the inequality | x³ – 1| ≥1 – x belong to
(1) (– ∞ , – 1]   (2) [0, 1]
(3) [1,∞ )          (4) (-∞, ∞)
(a) 1, 2 and 3 are correct
(b) 2 and 4 are correct
(c) 1 and 2 are correct
(d) 1 and 3 are correct

Answer: A

Question. Statement-1 : The set of all positive real nos. 'a' is such that a² + 2a, 2a + 3, a² + 3a + 8 are sides of a triangle in (5, ∞).
Statement-2 : In a triangle, sum of two sides is greater than third side and all sides are positive.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
(c) Statement -1 is False, Statement-2 is True.
(d) Statement -1 is True, Statement-2 is False.

Answer: A