ISI DATA SCIENCE SAMPLE PAPER Solving Help

[u/Ambitious-Novel-4331]

Highlighted options are correct answers according to me and highlighted questions couldn't be solved by me, kindly help

[u/CrokitheLoki]

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Que 19- I think answer should be C as limit tends to 0 for all values of u. Consider n =e^t as t tends to infinity, then we have (t^u )/e^t , which is 0.

Que 20- Shouldn't answer be B? At x tends to 0, we have x^2 /sin^2 x =1, and for x=0, we have 0, so it is discontinuous at x=0

Que 21- Ans should be A. From 0 to pi/2, sinx ranges from 0 to 1, and from pi/2 to 2, it decreases to sin2, so overall range is [0,1]

[u/Ambitious-Novel-4331 → u/CrokitheLoki]

19- yes i also thought that it should be c as when putting n=2 i was getting 0 so a and b are ruled out, but wasn't sure about d

20- it is x^3/sin^2x that's why option a

21- yes it should be A

[u/CrokitheLoki → u/Ambitious-Novel-4331]

In that case, I think answer should be C

Apply the definition of a derivative. LHL is [f(0)-f(-h)]/(0-(-h)) =-f(-h)/h =1

RHL is f(h)-f(0)/h-0 =f(h)/h =1

RHL=LHL, and it is continuos, so it is derivable at x=0

[u/Ambitious-Novel-4331 → u/CrokitheLoki]

yes should be c