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# SOME ADDITIONALPROBLEMS ON DE and AUC(WA).pdf

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### SOME ADDITIONALPROBLEMS ON DE and AUC(WA).pdf

1. Select the correct alternatives : (More than one are correct) Q.71 Familyofcurveswhosetangentatapointwithitsintersectionwiththecurvexy=c2 formanangleof  4 is: (A) y2  2xy  x2 = k (B) y2 + 2xy  x2 = k (C) y = x - 2 c tan1 x c       + k (D) y = c ln c x c x    x + k where k is an arbitraryconstant . Q.72 The general solutionof the differential equation, x dy dx       = y. ln y x       is : (A) y = xe1  cx (B) y = xe1 + cx(C) y = ex . ecx (D) y = xecx where c is an arbitraryconstant. Q.73 Whichofthefollowingequation(s) is/are linear. (A) dy dx + y x = ln x (B) y dy dx       + 4x = 0 (C) dx + dy = 0 (D) d y dx 2 2 = cos x Q.74 The function f(x)satisfyingthe equation, f2(x) + 4 f(x) . f(x) + [f(x)]2 =0 . (A) f(x) = c .   e 2 3 - x (B) f(x) = c .   e 2+ 3 x (C) f(x) = c .   e 3  2 x (D) f(x) = c .   e 2+ 3  x where c is an arbitraryconstant . Q.75 Theequation ofthecurvepassingthrough (3 ,4)&satisfyingthedifferential equation, y 2 dx dy       + (x  y) dx dy – x = 0 can be (A) x  y + 1 = 0 (B) x2 + y2 = 25 (C) x2 + y2  5x  10 = 0 (D) x + y  7 = 0 Q.76 Theareaboundedbyacurve,theaxis ofco-ordinates&the ordinateofsomepoint ofthecurve is equal tothelengthofthecorrespondingarcofthecurve. Ifthecurvepasses throughthepoint P(0, 1)then the equation of this curve can be (A) y = 2 1 (ex  e – x + 2) (B) y = 2 1 (ex + ex) (C) y = 1 (D) y = x x e e 2   Q.77 Identifythestatement(s)whichis/areTrue. (A) f(x , y) = ey/x + tan y x is homogeneous of degree zero (B) x . ln y x dx + y x 2 sin1 y x dy= 0 is homogeneous differential equation (C) f(x , y) = x2 + sin x . cosy is not homogeneous (D) (x2 + y2) dx - (xy2  y3) dy= 0 is a homegeneous differential equation . Some Additional Problems on DE & AUC NUCLEUS
2. Q.78 Thegraphofthefunction y=f(x)passingthroughthepoint(0,1)andsatisfyingthedifferentialequation dx dy + y cos x = cos x is such that (A) itis aconstant function (B) it is periodic (C) it is neither an even nor an odd function (D) itis continuous &differentiableforall x . Q.79 A function y= f (x) satisfyingthe differential equation dx dy ·sin x – y cos x + 2 2 x x sin = 0 is such that, y  0 as x  then the statement which is correct is (A) 0 x Lim  f(x) = 1 (B) 0 2 /  f(x) dx is less than  2 (C) 0 2 /  f(x) dx is greater than unity (D) f(x)is an odd function Select the correct alternative : (Only one alternative is correct) Direction for Q.80 to Q.82 (3 question together) Considerthefunction f (x) = x3 – 8x2 + 20x – 13 Q.80 Numberof positiveintegers x forwhichf (x)is aprimenumber, is (A) 1 (B) 2 (C) 3 (D) 4 Q.81 Thefunction f(x)definedfor R R (A) is one one onto (B) is manyone onto (C) has 3 real roots (D) is such that f (x1) · f(x2) < 0 where x1 and x2 are the roots of f ' (x) = 0 Q.82 Area enclosed byy= f (x) and the co-ordinate axes is (A) 12 65 (B) 12 13 (C) 12 71 (D) none Answers Select the correct alternatives : (More than one are correct) Q.71 ABCD Q.72 ABC Q.73 ACD Q.74 CD Q.75 AB Q.76 BC Q.77 ABC Q.78 ABD Q.79 ABC Select the correct alternative : (Only one alternative is correct) Q.80 C Q.81 B Q.82 A
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