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Question

Consider the following statements
S1: If x3+y2=5(xy1), then dydx at (1,3) is equal to 12
S2: If xe=ey, then dydx at x=1 is equal to e
S3: If f(x) is a linear polynomial, then f(sinx)+f(sinx) is constant.
Which of the following is/are correct about the truth value of above statements

A
S1 is false and S3 is true
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B
S2 and S3 both are true
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C
S1 and S3 both are true
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D
S1 is true and S2 is false
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Solution

The correct option is C S1 and S3 both are true
S1:3x2+2yy=5(y+xy)
at (1,3); 3+6y=5(3+y)
y=12

S2:xe=ey
elnx=y
y=ex
at x=1,y=e

S3:f(x)=ax+bf(sinx)=asinx+b
f(sinx)cosx=acosxf(sinx)=a
f(sinx)=0
f(sinx)+f(sinx)=a (constant)

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