Diploma(engineering- All) Year Ist (applied Mathematics-i) 4m366v

EIILM UNIVERSITY, SIKKIM EXAMINATIONS, FEBEURARY -2011 DIPLOMA ENGINEERING (ALL), YEAR – I APPLIED MATHEMATICS-I

Time: 3 Hours

Max. Marks: 60

Note: 1-Attempt any five questions. 2-All questions carry equal marks. 01.

Solve the following equations by the formula method: (a) 9x2 +10x+3=0 (b) 3x2-7x+5=0

02. 03.

Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120. The 3rd term of a G.P. is 24 and 6th term is 192. Find the 10th term.

04.

Resolve the following fractions into partial fractions: (a) x/1+x3 (b) x/x3+x2+x+1 Show that 26 ! is divisible by 210.What is the largest natural numbers n such that 26 ! is divisible by 2n ? Find the term independent of x in the expansion of (3x2/2 - 1/3x)9.

05. 06. 07. 08. 09.

Prove the following identities: (a) cosec6A – cot6 A= 1+3 cot2A+3 cot4 A (b) cos4A – sin4 A = 1-2 sin2 A (a) If the area of a triangle is 75 sq. cm and two of its sides are 20 cm and 15 cm, find the angle between these sides. (b) In the triangle ABC, A =450, B=75, C=60, show that a+c√2=2b. Which of the following points lie on the locus of x2+y2=16: (a) (4,1) (b) (4,0)