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12th Standard English Medium Maths Subject Application of Differential Calculus Book Back 5 Mark Questions with Solution Part - II

12th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 25

    5 Marks

    5 x 5 = 25
  1. A hollow cone with base radius a cm and, height b em is placed on a table. Show that the volume of the largest cylinder that can be hidden underneath is \(\frac { 4 }{ 9 } \) times volume of the cone.

  2. Write the Maclaurin series expansion of the following function
    tan-1(x); -1 ≤ x ≤ 1

  3. Find the asymptotes of the following curve \(f(x)=\frac { { x }^{ 2 } }{ { x }^{ 2 }-1 } \)

  4. Evaluate the following limit, if necessary use l ’Hôpital Rule 
    \(\underset { x\rightarrow { \frac { \pi }{ 2 } } }{ lim } { \left( sinx \right) }^{ tanx }\)

  5. A steel plant is capable of producing x tonnes per day of a low-grade steel and y tonnes per day of a high-grade steel, where \(y=\frac { 40-5x }{ 10-x } \). If the fixed market price of low-grade steel is half that of high-grade steel, then what should be optimal productions in low-grade steel and high-grade steel in order to have maximum receipts.

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