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Maths Case study (4 Marks)

Determinants · Uttarakhand Board (UBSE) STD 12 Science (Uttarakhand - English Medium). 2 questions.

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Case study (4 Marks)

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2 questions · self-marked practice — reveal the answer and mark yourself.

Question 14 Marks
A tin can manufacturer designs a cylindrical tin can for a company making sanitizer and disinfectors. The tin can is made to hold 3 litres of sanitizer or disinfector. The cost of material used to manufacture the tin can is $₹ 100 / \mathrm{m}^2$.

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(i) If $\mathrm{r} \mathrm{cm}$ be the radius and $\mathrm{h} \mathrm{cm}$ be the height of the cylindrical tin can, then express the surface area as a function of radius (r)

(ii) Find the radius of the can that will minimize the cost of tin used for making can?

(iii) Find the height that will minimize the cost of tin used for making can ?

OR

Find the minimum cost of material used to manufacture the tin can.

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Question 24 Marks
A trust fund has $₹ 35000$ that must be invested in two different types of bonds, say $\mathrm{X}$ and $\mathrm{Y}$. The first bond pays $10 \%$ interest p.a. which will be given to an old age home and second one pays $8 \%$ interest p.a. which will be given to WWA (Women Welfare Association). Let A be a $1 \times 2$ matrix and B be a $2 \times 1$ matrix, representing the investment and interest rate on each bond respectively.

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(i) Represent the given information in matrix algebra.

(ii) If ₹ 15000 is invested in bond $\mathrm{X}$, then find total amount of interest received on both bonds?

(iii) If the trust fund obtains an annual total interest of ₹ 3200 , then find the investment in two bonds.

OR

If the amount of interest given to old age home is ₹500, then find the amount of investment in bond Y.

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