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Set 6 of 6 · Questions 151-171 of 171

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JEE Main Mathematics · Mathematical Logic & Miscellaneous Algebra · Set 6 (Q151-171)

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  1. 151.
    The negation of the statement "All continuous functions are differentiable" is
    1. (1)All continuous functions are not differentiable
    2. (2)Some continuous functions are not differentiable
    3. (3)Some continuous functions are differentiable
    4. (4)All differentiable functions are continuous
  2. 152.
    If x = 198 !, then value of the expression equals
    1. (1)–1
    2. (2)0
    3. (3)1
    4. (4)198
  3. 153.
    Which of the following is NOT equivalent to .
    1. (1) only if
    2. (2) is necessary for
    3. (3) only if
    4. (4) is sufficient for
  4. 154.
    If , and are in A.P., then is equal to
    1. (1)5/2
    2. (2)log25
    3. (3)log23
    4. (4)log32
  5. 155.
    Which of the following quantified statement is true?
    1. (1)The square of every real number is positive
    2. (2)There exists a real number whose square is negative
    3. (3)There exists a real number whose square is not positive
    4. (4)Every real number is rational
  6. 156.
    Which of the following statement is contingency?
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  7. 157.
    The roots of the equation log2(x2 – 4x + 5) = (x – 2) are
    1. (1)4, 5
    2. (2)2, – 3
    3. (3)2, 3
    4. (4)3, 5
  8. 158.
    If the statement is false, then true statement/statement pattern is
    1. (1)
    2. (2)
    3. (3)
    4. (4)
  9. 159.
    If the truth value of the Boolean expression ((p ∨ q) ∧ (q → r) ∧ (∼ r)) → (p ∧q) is false then the truth values of the statements p,q,r respectively can be:
    1. (1)TFT
    2. (2)FFT
    3. (3)TFF
    4. (4)FTF
  10. 160.
    The compound statement (P ∨ Q) ∧ (∼ P) ⇒ Q is equivalent to:
    1. (1)P ∨ Q
    2. (2)P∧∼ Q
    3. (3)∼ (P ⇒ Q)
    4. (4)∼ (P ⇒ Q) ⇔ P∧∼ Q
  11. 161.
    If x satisfies |x – 1| + |x – 2| + |x – 3| ≥ 6, then
    1. (1)0 ≤ x ≤ 4
    2. (2)x ≤ –2 or x ≥ 4
    3. (3)x ≤ 0 or x ≥ 4
    4. (4)None of these
  12. 162.
    Let ∗,□∈ {∧, ∨} be such that the Boolean expression (p∗∼ q) ⇒ (p□q) is a tautology. Then :
    1. (1)∗ = ∨,□= ∨
    2. (2)∗ = ∧,□ = ∧
    3. (3)∗ = ∧,□ = ∨
    4. (4)∗ = ∨,□ = ∧
  13. 163.
    of the following is equivalent to the Boolean expression p∧∼ q?
    1. (1)∼ (q → p)
    2. (2)∼ p →∼ q
    3. (3)∼ (p →∼ q)
    4. (4)∼ (p → q)
  14. 164.
    If logxa, ax/2 and logbx are in G.P. Then x is equal to
    1. (1)loga (logba)
    2. (2)loga(logea)+ loga logbb
    3. (3)– loga(logab)
    4. (4)none of these
  15. 165.
    The number log27 is
    1. (1)an integer
    2. (2)a rational
    3. (3)an irrational
    4. (4)a prime number
  16. 166.
    If logx 256 = 8/5, then x is equal to
    1. (1)64
    2. (2)16
    3. (3)32
    4. (4)8
  17. 167.
    Which of the following is NOT true ?
    1. (1) is a tautology
    2. (2) is a tautology
    3. (3)
    4. (4)
  18. 168.
    The number is :
    1. (1)an integer
    2. (2)a rational number
    3. (3)an irrational number
    4. (4)a prime number
  19. 169.
    Let f(x) = |x – 1|. Then
    1. (1)f(x2) = (f(x))2
    2. (2)f(x + y) = f(x) + f(y)
    3. (3)f(|x|) = |f(x)|
    4. (4)None of these
  20. 170.
    The value of is ___________
  21. 171.
    The value of is ___________.