A cliff on the bank of a river is 300 meter high. if the angle of depression of a point on the opposite side of the river is \(60^\circ\), find the width of...

A student spent \( \frac{1}{5} \) of his allowances on books, \( \frac{1}{3} \) of the remainder on food and kept the rest for contingences. What fraction wa...

A binary operation \(plus\) defined on the set of integers is such that m \(plus\) n = n + mn for all integers m and n. Find the inverse of -5 under this ope...

A polynomial in x whose roots are \( \frac{4}{3} \) and \( -\frac{2}{5} \) is

If \( Q = \begin{pmatrix} 9 & -2 \\ -7 & 4 \end{pmatrix} \), then \( |Q| \) is

Find the infinity, the sum of the sequence \(1, \frac{9}{10}, \left(\frac{9}{10}\right)^2, \left(\frac{9}{10}\right)^3, ...\)

Solve 52(x - 1) x 5x + 1 = 0.04

If \(m * n = n-(m + 2)\) for any real numbers m and n, find the value of \(3 * (-5)\)

i. \(S \cap T \cap W = S\) ii. \(S \cup T \cup W = W\) ii. \(T \cap W = S\) If \(S \subset T \subset W\). Which of the above statements are true?