The inequality x - y is same as -Consider x and y are positive integers-A- X - yB- 1-v-D- x-y-C- 1-x-y-7D- 1-x-1-y

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Standard VII

Mathematics

Inverting the Terms of an Inequation

The inequalit...

Question

The inequality $x \leq y$ is same as ___ .(Consider x and y are positive integers.)

$x \geq y$

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$\frac{1}{x} \geq \frac{1}{y}$

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$\frac{1}{x} \geq \frac{y}{1}$

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$\frac{1}{x} \leq \frac{1}{y}$

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Solution

The correct option is B
$\frac{1}{x} \geq \frac{1}{y}$

When a positive number is multiplied by both sides of an inequation, the sign of the inequation remains same.
$x \leq y$
$\frac{1}{x y}$ is a positive number.
When we multiply both sides by $\frac{1}{x y}$ , we get
$\frac{1}{x} \geq \frac{1}{y}$

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When simplified $(x^{- 1} + y^{- 1})^{- 1}$ is equal to

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\frac{d y}{d x} = y \tan x, y (0) = 1

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(iii)

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(iv)

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Q. (i)

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(ii)

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(iii)

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(iv)

\cos y \frac{d y}{d x} = e^{x}, y (0) = \frac{π}{2}

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x y \frac{d y}{d x} = (x + 2) (y + 2), y (1) = - 1

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when y = 0, x = 0 [NCERT EXEMPLAR]
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\frac{d y}{d x} = \frac{y (x + 2 y)}{x (2 x + y)}, y (1) = 2

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\{x \sin^{2} (\frac{y}{x}) - y\} d x + x d y = 0, y (1) = \frac{π}{4}

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x \frac{d y}{d x} - y + x \sin (\frac{y}{x}) = 0, y (2) = x

Q. The positive integral solution of the equation

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The inequality x≤y is same as ___ .(Consider x and y are positive integers.)

The correct option is B 1x≥1y When a positive number is multiplied by both sides of an inequation, the sign of the inequation remains same. x≤y 1xy is a positive number. When we multiply both sides by 1xy, we get 1x≥1y

The inequality $x \leq y$ is same as ___ .(Consider x and y are positive integers.)