Home
Class 12
MATHS
If Q denotes the set of all rational num...

If Q denotes the set of all rational numbers and f(p/q) = `sqrt(p^(2) -q^(2))` for any `(p)/(q) in Q` then observe the following Statements
Statement-I : `f ((p)/(q))` is real for each `(p)/(q) in Q`
Statement -II : `f ((p)/(q))` is a complex number for each `(p)/(q) in Q`

A

Both I and II are true

B

I is true , II is false

C

I is false , II is true

D

Both I and II are false

Text Solution

Verified by Experts

The correct Answer is:
C
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • COMPLEX NUMBERS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|93 Videos

  • COMPLEX NUMBERS

    AAKASH SERIES|Exercise EXERCISE - I|49 Videos

  • CIRCLES

    AAKASH SERIES|Exercise PRACTICE EXERCISE|164 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Exercise (Level-2)|38 Videos

Similar Questions

Explore conceptually related problems

Statement -1 : ~(P harr ~q) is equivalent to p harr q Statement - 2 : ~(P harr ~q) is a tautology.

(p + q) ( p^2 - pq + q^2 ) = ____

Knowledge Check

  • The statement ~p vv q is equivalent is

    A
    `p rarr q`
    B
    `~p rarr q`
    C
    `~p rarr ~q`
    D
    `p rarr ~q`

  • Statement - I : (p ^^ ~ q) ^^ (~ p ^^ q) is a fallacy. Statement - II : (p rarr q) harr (~q rarr ~ p) is a tautology.

    A
    Statement - I is true, statement-II is false
    B
    Statement - I is false, Statement - II is true.
    C
    Statement - I is true, Statement - II is true, Statement - II is a correct explanation for Statement - I
    D
    Statement-I is true, Statement-II is true, Statement-II is not a correct explanation for statement-I

  • The statement ~(p ^^ q) vv q

    A
    is a tautology
    B
    is equivalent to `(p ^^ q) vv ~q`
    C
    is equivalent to `p vv q`
    D
    is a contradiction

    • Similar Questions

    Explore conceptually related problems

    Statement p rarr (q rarr p) is equivalent to

    The resultant of two vectors of magnitudes (P+Q) and (P-Q) is sqrt(P^(2) + Q^(2)) . THn the angle between the vectors is

    Let p and q be any two propositons Statement 1 : (p rarr q) harr q vv ~p is a tautology Statement 2 : ~(~p ^^ q) ^^ (p vv q) harr p is fallacy

    The statement ~(p harr ~q) is

    The statement p rarr (q rarr p) is equivalent is

    Home
    Profile