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Each fir.ll question carries 15 marks.)UNn-Iill (a) Evaluate lim / x3 - 6a \*-4 [*r- 16 7'(b) If v = log (secx + tarx), prove that I = secx.dx(c) If y = xsinx, prove that yll + y = 2go.*.On IV (a) If x = a Cos3t, y=b sin3t, *o # . 5(b) If x3 + f = 3a:rY, fitd d,Y .&5(c) If y= a oos (ogx) +b sin (Iogl(), show that x2 yll +xyr +y= g. 5Urrr - IIV (a) Find lhe values ofx for which the tangent to the curve y= * will be parallelto the y-axis. 5(b) A particle moves such that the displacernent from a fixed point '0' is alwaysgiven by S = 5 cosnt + 4 sirmt, where 'n' is a constant. Prove that theacceleration varies as its displacement S at the instant. 5(c) A spherical balloon is inflated by pumping 25cc of gas per second Find trc rateat which tre radius of the balloon is increasing when the radius is 15 crn 5.on VI (a) Find the velocity and acceleration at time t = 4 secs of a body whose displacementS metres related to time t seconds is given by the equation S=Zf +fi 5 (b) The deflechon of a beam is given by y:2x3 -gx2 + l2x. Find the maximumdeflection. 5(c) An open box is to be made out of a square sheet of side 18 cm by cutting offequal squares at each comer and tuming up the sides. 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No.Signatule DIPLOMA EXAMINATION IN ENGINEERING/TECHNOLOGY/MANAGEMENT/COMMERCIAL PRACTICE - OCTOBER, 2OI8TECHNICAL MATIIEMATICS - [[?irze : 3 houn(Maximum marks : 100)PART - A(Mayimum marks : l0)MarksI Amwer a// questions. Each question carries 2 marks.i. Evaluate lun (2x + 3).x)22. Find the derivative of 3 Cosx - 4tanx wittr respect to ,x'.3. Find the rate of change of area of a circle with respect to iS radius.4. lntegrate (3x2 + 2) with respect to x.5. Find the order and clegree of the differential equation 4 + 5y = 0. (5 x 2 = l0)PART - B(Maximum marks : 30)II Answer arry five of the following questions. Each question carries 6 marks.I . Differentiate -xn by the method of first principle.2. lf x=a(e-Sine),andy=a(l-Cose), find 9.&3. Find the equation to the tangent and normal to the curve y = 3x2 +x-2 at (1,2).4. Integrate x2 e-x with respect to x.5. Evaluate [n ----!- a*.* I +Siu6. Find the area bounded by the curve y = x2 and y = 3a.7. 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