Maths I

OMTEX – CLASSES MATHS I

Total marks 40

IST PRELIMINARY EXAMINATION

Time: 3 hours

Code: OM2008

Q1. Attempt the following. (4 marks)

i. ii.

If A= 3214 and B= -1231 Prove that AB=AB. Find the value of x and y, if 4120213-213123820-1=xy

Q2. Attempt the following. (8 marks)

1. If A= 2110, find A-1. 2. If A= 122212221, prove that A2-4A is a scalar matrix. Q3. Attempt the following. (8 marks)

1. Evaluate: limx→0e8x-e5x-e3x+1cos4x-cos10x 2. If f is continuous at x=0, where fx= x2+a for x≥0 =2x2+1+ b for x<0 Find a, b given that f(1) = 2. Q4. Attempt the following. (4 marks)

1. Evaluate limx→π21-sin3xcos2x. 2. Discuss the continuity fo the function f defined as fx= x+8-3x3-1, x ≠1 =13 , x=1 at x=1. Q5. Attempt the following. (4 marks)

1. Finddydx, if y=xsinx 2. Finddydx, if y=sin-12x1+x2. Q6. Attempt the following. (4 marks)

1. Finddydx, if x=a cosθ, y=asinθ. 2. Finddydxif , y=x2+3xlogx. Q7. Attempt the following. (8 marks)

1. Finddydx, iftan-1x2a2-x2 2. Finddydx, ifcot-1(cosecx+cotx)

OMTEX

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