Q. \( 11 \operatorname{Sin}(\mathrm{~A}+\mathrm{B})= \) Q. 12 The slope of line which is parallel to other line whose slope is 5 is SECTION-C Note: Short answer type questions. Attempt any eight questions out of ten questions. Q. 13 Find the multiplicative inverse of \( (5-7)^{2} \). Q. 14 Solve \( \log 3+\log (x+1)=\log 8 \) Q. 15 Expand the binomial up to 4 terms \( \left(1-x^{2}\right)^{4} \) Q. 16 Solve \( \mathrm{X}+2 \mathrm{Y}=2,2 \mathrm{X}+3 \mathrm{Y}=3 \) by Cramer's rule Q. 17 Find the value of Sin \( 105^{\circ} \). Q. 18 Express the following as product : Sin140 + Sin \( 2 \theta \). Q. 19 Prove that the line joining \( (6,-4) \&(-3,2) \) is parallel to the line joining \( (1,3) \&(-2,5) \) Q. 20 Find the length of perpendicular from the point (4,1) on the \( 3 \mathrm{X}-4 \mathrm{Y}+12=0 \)

### Q. 11: \( 11 \operatorname{Sin}(\mathrm{~A}+\mathrm{B}) \) Cannot determine the value without specific values for \( A \) and \( B \). ### Q. 12: Slope of a parallel line The slope is 5. ### Q. 13: Multiplicative inverse of \( (5-7)^{2} \) The multiplicative inverse is \( \frac{1}{4} \). ### Q. 14: Solve \( \log 3 + \log (x+1) = \log 8 \) \( x = \frac{5}{3} \). ### Q. 15: Expand \( (1 - x^{2})^{4} \) up to 4 terms \( 1 - 4x^{2} + 6x^{4} - 4x^{6} \). ### Q. 16: Solve \( X + 2Y = 2 \) and \( 2X + 3Y = 3 \) by Cramer's rule \( X = 0 \), \( Y = 1 \). ### Q. 17: Find \( \sin 105^{\circ} \) \( \sin 105^{\circ} = \frac{\sqrt{6} + \sqrt{2}}{4} \). ### Q. 18: Express \( \sin 140^{\circ} + \sin 2\theta \) as a product \( 2 \sin\left(\frac{140^{\circ} + 2\theta}{2}\right) \cos\left(\frac{140^{\circ} - 2\theta}{2}\right) \). ### Q. 19: Prove lines are parallel Calculate slopes and show they are equal. ### Q. 20: Find the length of the perpendicular from (4,1) to \( 3X - 4Y + 12 = 0 \) Length is \( \frac{|3(4) - 4(1) + 12|}{\sqrt{3^{2} + (-4)^{2}}} = \frac{20}{5} = 4 \).