Question Library

Identity(e) : a \(\ast\) e = a m \(\ast\) e = m...(i) m \(\ast\) e = me + m + e Because m \(\ast\) e = m : m = me + m + e m - m = e(m + 1) e = \(\frac{0}{m + 1}\) e = 0

Let x represent total vol. 2 : 3 = 2 + 3 = 5 \(\frac{3}{5}\)x = 351 x = \(\frac{351 \times 5}{3}\) = 585 Volume of smaller block = \(\frac{2}{5}\) x 585 = 234.00cm\(^3\)

The diagonal of a rhombus is a line segment that joins any two non-adjacent vertices. A rhombus has two diagonals that bisect each other at right angles. i.e this splits 6cm into 3cm each AND 8cm to 4cm Using Hyp\(^2\) = adj\(^2\) + opp\(^2\) Hyp\(^2\) = 3\(^2\) + 4\(^2\) Hyp\(^2\) = 25 Hyp = 5 ∴ Length (L) is 5cm because a rhombus is a quadrilateral with 4 equal lengths

Area of Trapezium = 1/2(sum of parallel sides) * h 91 = \(\frac{1}{2}\) (5 + 9)h cross multiply 91 = 7h h = \(\frac{91}{7}\) h = 13cm

Length of Arc AB = \(\frac{\theta}{360}\) 2\(\pi\)r = \(\frac{48}{360}\) x 2\(\frac{22}{7}\) x \(\frac{21}{2}\) = \(\frac{4 \times 22 \times \times 3}{30}\) \(\frac{88}{10}\) = 8.8cm Perimeter = 8.8 + 2r = 8.8 + 2(10.5) = 8.8 + 21 = 29.8cm

Volume of a cylinder = \pir\(^2\)h First convert 3m to cm by multiplying by 100 Volume of External cylinder = \(\pi \times 13^2 \times 300\) Volume of Internal cylinder = \(\pi \times 10^2 \times 300\) Hence; Volume of External cylinder - Volume of Internal cylinder Total volume (v) = \(\pi (169 - 100) \times 300\) V = \(\pi \times 69 \times 300\) V = 20700\picm\(^3\)

Each interior angle = \(\frac{(n - 2)180}{n}\) 140 = \(\frac{(n - 2)180}{n}\) Cross multiply: 140n = 180n - 360 40n = 360 n = 9 sides ( A Nonagon)

Sum of all 4 angles of a quadrilateral = 360^\circ (5x-30) + (3x + 61) + (60-x) + (4x+ 60) = 360^\circ 11x + 151 = 360^\circ 11x = 360 - 151 = 209 x = 209/11 = 19^\circ Each angles is : 5x - 30 = 65^\circ 4x+ 60 = 136^\circ 60 - x =41^\circ 3x + 61 = 118^\circ Smallest of these angles is 41^\circ

Line: 2y+8x-17=0 recall y = mx + c 2y = -8x + 17 y = -4x + \(\frac{17}{2}\) Slope m\(_1\) = 4 parallel lines: m\(_1\). m\(_2\) = -4 where Slope ( -4) = \(\frac{y_2 - y_1}{x_2 - x_1}\) at points (-1, -p) and (-2,2) -4( \(x_2 - x_1\) ) = \(y_2 - y_1\) -4 ( -2 - -1) = 2 - -p p = 4 - 2 = 2

The required locus is angle bisector of the two lines

Sin\theta = \(\frac{6}{12}\) Sin\theta = \(\frac{1}{2}\) \theta = Sin\(^0.5\) \theta = 30^\circ Bearing of Z from X, (270 - 30)^\circ = 240^\circ

y = 2x\(^2\)(2x - 1) y = 4x\(^3\) - 2x\(^2\) dy/dx = 12x\(^2\) - 4x at x = -1 dy/dx = 12(-1)\(^2\) - 4(-1) = 12 + 4 = 16

Mean of 10 numbers = 16 The total sum of numbers = 16 x 10 = 160 Mean of 11 numbers = 18 Total sum of numbers = 11 x 18 = 198 The 11th no. = 198 - 160 = 38

Given that 4, 16, 30, 20, 10, 14 and 26 Adding up = 120 nos \(\geq\) 16 are 16 + 30 + 20 + 26 = 92 The requires sum of angles = \(\frac{92}{120}\) x \(\frac{360^o}{1}\) = 276o

Given from 41 to 56 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56 The nos multiple of 9 are: 45, 54 P(multiple of 9) = \(\frac{2}{16}\) = \(\frac{1}{8}\)