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August 2015 V62/T63/T07032/T04032/EE/20150819 APPLIED MATHEMATICS-2 Instructions Marks-80 Time: 3 Hrs 1. All questions are compulsory. 2. “Long Answer type Question (LAQ)” is a supply type question of 15 marks which required a typical answer of about 60-80 lines in bout 32-40 minutes. 3. “Sort Answer type Question (SAQ)” is a supply type question of 5 marks which required a typical answer of about 15-20 lines in bout 08-10 minutes. 4. Figures to the right indicate marks allotted to the questions. 5. Assume suitable data if necessary 6. Use a nonprogrammable type of scientific calculator is allowed Marks SECTION-A Q.1 A)Evaluate:- ∫ B)Evaluate:- ∫ 10 dx . 5 dx OR Q.1 A) Evaluate:- B)Evaluate: ∫ ∫ √ √ √ 10 dx dx 5 Q.2 A)Solve the differential equation: 2 + =y 10 B)Find the order and degree of differential equation : 5 = . OR Q.2 A) Find the C.G. of an area enclosed by the parabola y=x2-2x and the x-axis. 10 5 B)Calculate the area enclosed by curve y2=8x and the line x=2 Q.3 Evaluate:- 5 + 4 + 25 Q.4 Solve: x. dy - y.dx=0. 5 SECTION-B Q.5 A) 2 10 The acceleration of a particle is given by =3t -6t+8. Find the distance covered in 2 second given that v=0,s=0 at t=0 B) Solve using Jacobi's method; 2x+y+z=4, x+2y+z=-4 and x+y+2z=4. 5 (three iteration only) OR Q.5 A) Using Newton's Raphson method evaluate, upto three iteration only. √10 B) A body is released from a height of 490m.Find the time taken by the body to reach the ground(g=9.8 m/sec2). Q.6 A)In 200 sets of tosses of 5 fair coins, In how many ways you can expect: i) at least two heads ii) at most two heads. B) A coin is tossed 5 times. What is the probability of getting exactly 3 heads? 10 05 10 5 OR Q.6 A) In a certain examination 500 students appeared.Mean score is 68 with S.D 8. Find the number of students scoring. 1)less than 50 2)more than 60 10 (Given that area between z=0 to z=2.25 is 0.4878 and area between z=0 to z=1 is 0.3413) B) From a class of 12 students,5 are boys and rest are girls.Find the probability a student selected is a girl. 5 Q.7 A particle moves with acceleration (3-t) m/s2 with initial velocity 2m/sec.Find the velocity of particle at the end of 5 sec. 5 Q.8 Using Poissondistribution, Find the probability that the king of diamond will be drawn from a pack of well shuffled card at least one in 156 consecutive trial.(Given e3= 20) 5