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Derivative from First Principle

If x and ...

Question

If $x$ and $y$ are negative, then which of the following statements is/are always true?
I. $x + y$ is positive II. $x \times y$ is positive III. $x - y$ is positive

A

I only

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B

II only

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C

III only

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D

I and III only

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Solution

The correct option is B II only
$G i v e n x a n d y a r e n e g a t i v e . L e t u s t a k e x = - a y = - b (w h e n a a n d b a r e p o s i t i v e)$
$O p t i o n (1) x + y = - a - b = - (a + b) \Rightarrow x + y i s n e g a t i v e s i n c e (a + b) i s p o s i t i v e . ∴ - (a + b) i s n e g a t i v e . ∴ O p t i o n (1) i s n o t c o r r e c t .$
$O p t i o n (2) x . y = (- a) \times (- b) = a b ∵ a, b a r e p o s i t i v e, ∴ a b i s p o s i t i v e . ∴ x y i s p o s i t i v e . ∴ O p t i o n (2) i s c o r r e c t .$
$O p t i o n (3) x - y = a - b (a) I f v a l u e o f x i . e a i s g r e a t e r t h a n t h e v a l u e o f y i . e b t h e n a - b i s p o s i t i v e .$
$(b) I f v a l u e o f x i . e a i s l e s s t h a n t h a t o f y i . e b, t h e n a - b i s n e g a t i v e .$
$∴ x - y i s p o s i t i v e o r n e g a t i v e .$
$∴ O p t i o n (3) i s n o t c o r r e c t .$

$A n s w e r - O p t i o n (2) i s c o r r e c t .$

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Similar questions

Q. If x and y are negative, then which of the following statements is/are always true?
I. x + y is positive II. xy is positive III. x y is positive

Q. Q. If x and y are negative, then which of the following statements is/are true?
I. x+ y is positive
II. xy is positive
III. x - y is positive

Q. If x and y are negative then which of the following statements is/are always true?
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II.

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x, y, z

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H C F (x, y, z) = 1

x^{2} + y^{2} = 2 z^{2}

. Which of the following statements are true?
I.

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x

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y

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x + y

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In which quadrant are the following points ?

(i) whose both co-ordinates are positive.

(ii) whose both co-ordinates are negative.

(iii) whose x co-ordinate is positive, and the y co-ordinate is negative.

(iv) whose x co-ordinate is negative and y co-ordinate is positive.

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