Eamcet - Maths - Differentiation Test

Test Instructions :

1. The Test is 1hr duration.
2. The Test Paper consists of 30 questions. The maximum marks are 30.
3. All the questions are multiple choice question type with three options for each question.
4. Out of the three options given for each question, only one option is the correct answer.
5. Each question is allotted 1 mark for each correct response.
6. 0.25 will be deducted for incorrect response of each question.
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If x

  

  

  

  

The derivative of (sin x)x w.r.to x is

  

  

  

  

If y=(x+√x2-1)m then (x2-1)y2+xy1=

  

  

  

  

If P(x)is a polynomial of 3rd degree and P’’(1)=0, P’’’(1)=6 then P’’(0)=

  

  

  

  

If x= sin t cos 2t, y= cos t sin 2t then (dy/dx)t=π/4

  

  

  

  

d/dx{Tan-1(acos x-bsin x/b cos x+a sin x)}=

  

  

  

  

If y2=4ax then 4a(1+y12)3/2+(y2+4a2)3/2y2=

  

  

  

  

If y=(1+x2)Tan-1x then y2=

  

  

  

  

If x= a(θ+sin θ), y=a(1-cosθ) then d2y/dx2 at θ=π/4 is

  

  

  

  

If f(x)=√(1-√(1-x2)), then

  

  

  

  

d/dx{(2x-3)/(3x+1)}=

  

  

  

  

d/dx{√(1+sin x/1-sin x)}=

  

  

  

  

If y=e-x cos x then y4=

  

  

  

  

If x= asin 2θ(1+ cos 2θ), y= bcos 2θ(1-cos 2θ), then dy/dx=

  

  

  

  

If y=(ax+b/cx+d) then 2y1y3=

  

  

  

  

If ay= sin(x+y) then y2+(1+y1)3 y=

  

  

  

  

If y= x log|x+√(1+x2)|-√(1+x2) then dy/dx=

  

  

  

  

d/dx{(√(a2+x2)+ √(a2-x2))/ (√(a2+x2)- √(a2-x2))}

  

  

  

  

If ay4=(x+b)5then 5yy2=1

  

  

  

  

If y= a cos x+(b+2x)sinx then y2+y=

  

  

  

  

If f(x)=x2sin(1/x) for x≠0, f(0)=0 then

  

  

  

  

If y=√(cos x+y) then dy/dx=

  

  

  

  

If x2-xy+y2=1 and y’’(1)=

  

  

  

  

If r2=x2+y2,x=et sin t,y=et cos t then dr/dt=

  

  

  

  

If x=e2tcos 3t, then d2x/dt2 at t=π/2 is

  

  

  

  

If x= acos3θ, y= asin3θ then d2y/dx2 at θ=π/4 is

  

  

  

  

d/dx{Sin-12x/1+x2+Sec-11+x2/1-x2}=

  

  

  

  

The derivative of Tan-1√(1+x2)-1/x w.r.to Tan-12x√(1-x2)/(1-2x2) at x=0 is

  

  

  

  

d/dx{Tan-1(x/1+√1-x2)}=

  

  

  

  

If (x+y)2=ax2 +by2 then dy/dx=

  

  

  

  

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