Two stations due south of a leaning tower which leans towards the north are at distances a and b from its foot if α and β be elevation of these station from the tower, Prove that its inclination θ to be Horizontal is given by Cot θ = (b cot α  acot β)/ba
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Q.Find the sum of 20 terms of the series: 1222+3242+52... In Triangle ABC, <ACB = 900 Þ <BCP = 900
So, In Triangle BPC: BC2 = BP2 – CP2 Now, In Triangle ABC, AB2 = AC2 + BC2 Þ AB2 = AC2 + BP2 – CP2 AB2 = AC2 – CP2 + BP2 AB2 = (AC  CP) (AC + CP) + BP2 AB2 = (AC  CP) (AP) + BP2 AB2 = (AC x AP  CP x AP) + BP2 AB2 = AC x AP + BP2  CP x AP But, AP x CP = BP x PD (D APB ~ D CPB) AB2 = AC x AP + BP2  BP x PD AB2 = AC x AP + BP(BP – PD) AB2 = AC x AP + BP x BD Given: In D ABC where D is the midpoint of BC, E is the midpoint AD.
BE produced meets AC at X. To Prove: BE : EX = 3:1 Solution:
The distance covered by the policeman in 12 sec s = ut + 1/2 at2 = 0 x12 + 0.5 x3 x 12x12 = 216m v = u + at = 0 + 12x3 = 36m/s The distance covered by the robber in 12 sec s = 20 x 12 = 240m Suppose he over takes in 12 + t sec, in which he travels = 216 + 36 * t r robbers will travel in the same time 20 * ( 12+t) m 216 + 36 t = 240 + 20 t t = 24 / 16 = 1.5 s Distance travelled by policeman in 12 + 1.5 = 13.5 s = 216 + 36 x 1.5 = 270 m Show that there is no positive integer n which + is rational.
Solution: Suppose there exists a positive integer p/q for which n is a rational number. q ≠ 0. 
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