Maths 1a Imp Qstns - 3281 Words

WWW.PAPERSHUNT.COM MATHS - FIRST YEAR 1 A VERY IMPORTANT QUESTIONS BY WWW.PAPERSHUNT.COM AND HUNT FOR SUCCESS PUBLICATIONS. LONG ANSWER QUESTIONS Functions : 01. Let f : A ï‚ ® B , g : B ï‚ ® C be bijections. Then gof : A ï‚ ® C is a bijection. 02. Let f : A ï‚ ® B , g : B ï‚ ® C be bijection. Then ( gof ) ï€ ­1 ï€ ½ f ï€ ­1og ï€ ­1 03. Let f : A ï‚ ® B , I A and I B be identify functions on A and B respectively. Then foI A ï€ ½ f ï€ ½ I B of 04. Let f : A ï‚ ® B be a bijection. Then fof 05. Let f : A ï‚ ® B be a function. Then f is a bijection if and only if there exists a function g : B ï‚ ® A such that fog ï€ ½ I B and gof ï€ ½ I A and, in this case, g ï€ ½ f ï€ ­1 Mathematical Inductions : 06. Show that 49n ï€ « 16n ï€ ­ 1 is divisible by 64 for all positive integers n. n(n 2 ï€ « 6n ï€ « 11)†¦show more content†¦The angle of elevation of the top of a tower from the foot of the building is twice the angle of its elevation from the top of the building. The height of the building is 50 meters and the height of the tower is 75 meters. Find the angle of elevation of the top of the tower from the foot of the building. 29. From a point on the slope of a hill, the angle of elevation of the top of the hill is 45 °. After walking 200 meters from that point on a slope which makes 15 ° angle with the horizontal, the same point on the top of the hill, makes an angle of elevation of 60 °. Show that the height of the hill is 100 HUNT FOR SUCCESS ï€ ¨ 6 ï€ « 2 meters ï€ © 30. A pillar is leaning towards East and ï  ¡ and ï  ¢ are the angles of elevation of the top of pillar from two points due West of the pillar at distance a and b respectively. Show that the angle between the pillar and the horizontal is Tan ïÆ' § ï€ ­1 ïÆ' ¦ ïÆ' ¶ bï€ ­a ïÆ' · ïÆ' ¨ b cot ï  ¡ ï€ ­ a cot ï  ¢ ïÆ' ¸ Demoviers Theorem : 2n 2n n ï€ «1 31. If n is an integer then show that (1 ï€ « i) ï€ « (1 ï€ « i ) ï€ ½ 2 cos nï  ° 2 32. If cos ï  ¡ ï€ « cos ï  ¢ ï€ « cos ï  § ï€ ½ 0 ï€ ½ sin ï  ¡ ï€ « sin ï  ¢ ï€ « sin ï  § then show that (i) cos 3ï  ¡ ï€ « cos 3ï  ¢ ï€ « cos 3ï  § ï€ ½ 3cos(ï  ¡ ï€ « ï  ¢ ï€ « ï  § ) (ii) sin 3ï  ¡ ï€ « sin 3ï  ¢ ï€ « sin 3ï  § ï€ ½ 3sin(ï  ¡ ï€ « ï  ¢ ï€ « ï  § ) (iii) cos(ï  ¡ ï€ « ï  ¢ ) ï€ « cos( ï  ¢ ï€ « ï  § ) ï€ « cos(ï  § ï€ « ï  ¡ ) ï€ ½ 0 33. Find all the roots of the equation x11 ï€ ­ x 7 ï€ « x 4 ï€ ­ 1 ï€ ½ 0 34. If n is a positive integer, show that :3: mail us @ huntforsuccess@gmail.com , cell: 798 3699 456 , Our books are available in selected book shops in andhra