JEE Mathematics Linear Inequalities MCQs

Question: If a² + b² + c² = 1, then ab + bc + ca lies in the interval:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

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: xz > y > z

Question:

• a) x < y < z
• b) x > y > z
• c) x < y > z
• d) x > y < z

Answer: x < y < z

Question:

• a)

  

• b)

  

• c)

  

• d) none of these

Answer:

Question:

• a) y = 1 and x = 0
• b) none of these
• c)

  

• d)

  

Answer: y = 1 and x = 0

Question: Solution of inequality log₁₀ (x -12x + 36) < 2 is

• a) (– 4, 16)
• b) (6, 16)
• c) (– 4, 6)
• d) None of these

Answer: (– 4, 16)

Question: Number of integers satisfying either

log₃ | x | < 2 or | log₃ x | < 2 are –

• a) 16
• b) 23
• c) 18
• d) 20

Answer: 16

Question: The solution set of the inequality

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

More Questions..............................

Question: Solution set of (x + 1) (x – 1)² (x – 2) ≥ 0 is :

• a) none of these
• b) (– 1, 2)
• c) [-1,2]
• d) Both

Answer: none of these

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If x satisfies | 3 x – 2 | + | 3x – 4 | + | 3x – 6 | ≥12, then

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

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: 1/8

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d) none of these

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: The largest interval for which x¹² – x⁹ + x⁴ – x + 1 > 0 is

• a)

  

• b) None of these
• c) –100 < x< 100
• d) – 4 < x ≤ 0

Answer:

Question:

• a) 0
• b) 2
• c) 2
• d) Infinitely many

Answer: 0

Question: All real values of x which satisfy x² - 3x + 2 > 0 and x² - 2x - 4 ≤ 0 lie in

• a)

  

• b) (–5, 0)
• c) [3, 6]
• d) [1, 6]

Answer:

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: 1, 2 and 3 are correct

Question:

• a) 1 and 2 are correct
• b) 1 and 3 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 2 are correct

Question:

• 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: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

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: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

• a) Statement -1 is False, Statement-2 is True.
• b) Statement -1 is True, Statement-2 is False.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is False, Statement-2 is True.