Solve the given two equations and select the correct option.
$I. 13x - 8y + 81 = 0$
$II. 15x - 5y + 65 = 0$

  • A
    if $x > y$
  • B
    if $x < y$
  • C
    if $x \ge y$
  • D
    if $x \le y$

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The number of real roots of the equation ${e^{\sin x}} - {e^{-\sin x}} - 4 = 0$ is:

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Solve the given two equations and select the correct option.
$I.$ $42x - 17y = -67$
$II.$ $7x - 12y = -26$

The equation $x^{2}-p x+q=0, p, q \in R$ has no real root if:

Solve the given two equations and select the correct answer from the given options.
$I.$ $(17)^{2} + 144 \div 18 = x$
$II.$ $(26)^{2} - 18 \times 21 = y$

If the roots of the equation $\frac{1}{x + p} + \frac{1}{x + q} = \frac{1}{r}$ are equal in magnitude but opposite in sign,then the product of the roots will be

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