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MULTIPLE CHOICE QUESTIONS, CHAPTER –5, DIFFERENTIATION, Q1. If f (1)=4, f (1)=2, the value of derivative of log f (e* )w.r.t. xat.x=0is:, (a) 1, (b) 2, (c), (p), Q2. If y=sin, 1, dy is:, -1, + cos, the value of, dx, 2, 4, (a) 0, (b) 1, 1+x, 1+x, dy., Q3. If y=2*, then, -is:, dx, (a) x(2* '), 2*, (b), log 2, (c) 2* log 2, (d) none of these, dy is:, Q4. If y=sin(x*), then, dx, (a) x* cos(x*), (b) x* cos(x*)[1+logx], (c) x* cos (x* ) log x (d) none of these, dy, Q5. If e*** =xy, then, -is:, dx, *(1-y), y(1-x), х- ху, (c), ху — у, (a), (b), (d) none of these, y(x-1), x(у-1), Q6. If Vx+ y =Va , then, dy, is:, dx, 1 y, (b), (a), (c), (d) none of these, 2, Q7. If x'-y* = 0, then is:, dx, y-xlog y, y(y-xlog y), y(y+xlog y), (a), (b), (c), (d) none of these, x- y log x, x(x-ylog x), x(x+ y log x)

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dy is:, a² ), then, dx, Q8. If y=log(x+Vx² +, 1, 1, 1, (a), (b), (c), Vr +a?, (d) none of these, x+/x +a, cos x+sin x, dy, then, is:, dx, -1, Q9. If y=tan, cos x-sin x, (a) 1, (b) -1, (c) 1/2, (d) -1/2, Q10. If y=log, V1+x +x, dy is:, then, dx, 2/1+x, (a), (b), (c), (d) none of these, dy is:, then, sec x-1, Q11. If y=,, sec x+1, dx, 1, (a) sec? x, (», sec, cos ec, (d) none of these, a cos x-bsinx, -1, Q12. If y=tan, then, is:, bcos x+asin x, dx, (a), b, (b), (c) 1, (d) -1, a, dy, Q13. If, y=tan, 1-Vax, is:, then, dx, 1, 1, 1, (a), 1+x, (d), 2Vx(1+x), (b), Vx (1+x), (r+1)x, x -1, dy, is:, then, dx, Q14. If y=cos, 2, x +1, (a), 1+x?, (b), 1+x?, 2x, (c), 1+ x², (d) none of these

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dy, Q15. If y=tan (sec x+tan x), then is:, dx, (a) 1/2, (b) -1/2, (c) 1, (d) none of these, 1-x, -1, Q16. If y=cot, is:, then, dx, 1+x, 1, 1, (b), 1+x?, 1, (d) none of these, (a), 1+x, (c), 3/2, (1+x)*, Q17. If x=at?, y = 2at , then, -is:, dx, (a), t, (b), (d) none of these, t, dy is:, Q18. If x=acos 0, y = bsin? 0 ,then, dx, a, cot 0, (a), b., (b), (d) none of these, dy is:, Q19. If x=a(cos0+0sin 0), y = a(sin 0-O cos 0), then, dx, (a) cot 0, (b) tan 0, (c) a cot 0, (d) a tan O, VI+x+/1-x, dy, Q20. If y = sin, then is:, dx, 1, 1, (b), 2/1-x, 1, (a), 2/1-x?, (d) none of these, 2(1+x*), dy, is:, then, dx, COS X, Q21. If y = tan, 1+sin x, 1, (b), 2, (c) 1, (a), (d) -1, dy, -then, is:, dx, -1, -1, Q22. If y=tanx+tan, (a) 0, (b) 1, 1+x²

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3-2х, dy, Q23. If y=tan, then, is:, 1+6x, dx, 1, (a), 1+4x, (b), 1+4x, (c), 1+4x2, (d) none of these, dy js., Q24. If y=tan (V1+x² - x),, dx, 1, 1, (a), 2(1+x*), (b), 2(1+x*), 1, (c), 1+x, (d), 1+x?, dy is:, Q25. If y=xe', then, dx, y, y, (a), 1- y, (b), x(1-y), (c), 1- y, (d), y(1-y), Q26. If /1-x -/1-y² = a(x+y), then, dy, -is:, dx, Vi-x, (b), Vi-x, (d) -, VI-y², Q27. If log, -is:, then, dx, (c)., y, (d) 2, (а) х, (b) y, dy, -is:, Q28. If sin y=xsin (a+y), then, dx, sin (a+y), sin (a+y), (b), sin (a+y), (c), sin (a+y), (d), cos a, (а), sin a, sin a, sin a, dy, Q29. If x* Y + ys x = 1, then the value of, -at (1,1) is:, dx, (a) -1, (b) 0, (c) 1, (d) none of these, Q30. If x' y' = (x+y), then, dy, is:, dx, (b), y, (c) 2, (d), y, (а)

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a, Q31. If x=-, 1+m, dy is:, then, am, , y =, 1+m, dx, 1-2m, (b), 3m2, 2m -1, 1+2m³, (a), 3m?, (d) 1, Зт?, Q32. Derivative of f (sin x)w.r1.g(x² +x) at x = 0 if f (0) = 2g° (0) is:, %3D, (a) 1, (b) 2, (с) -1, (d) 0, Q33. The derivative of f(x)=|x-1|+x-4 at x 3is:, (a) 3, (b) -3, (c) 0, (d) 1, V1+x -1, 2x, is:, -1, Q34. Derivative of tan, w.r.t. sin, 1+x?, (a) 1/2, (b) 2, (c) 1/4, (d) 1, dy is:, Q35. If y=100", then, dx, (a) 1010*, log 10, (b) 100 (log 10), (c) 100.10 (log10)ʻ (d) 10".10* (log10), dy is:, then, x+, +a?, Q36. If y=e, dx, +a", (a), (b) 1+, (d) none of these, e, +, Q37. If y=log (log x), then value of xy, +y, +xy, is:, (a) 1, (b) 0, (c) -1, (d) 2, Q38. If y=(sinx), then the value of (1-x)y, -xy, is:, (b) 1 N, (c) -2, (a) 2, (d) 0, -is:, Q39. If sin (x+y) = log (x+y), then, dx, (a) 2, (b) -2, (c) 1, (d) -1, Q40. The derivative of cos (2x -1) w.rt. cos xis:, COS, (a) 2, 1, (b), (d) 1-x