A trust fund has Rs. 30,000 that must be invested in two different types of bonds. first bond pays 5

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3 and 4 .Determinants and Matrices

hard

A trust fund has Rs. $30,000$ that must be invested in two different types of bonds. The first bond pays $5 \%$ interest per year, and the second bond pays $7 \%$ interest per year. Using matrix multiplication, determine how to divide Rs. $30,000$ among the two types of bonds. If the trust fund must obtain an annual total interest of Rs. $2000$.

$5000$ and $25000$

Solution

Let Rs $x$ be invested in the first bond. Then, the sum of money invested in the second bond will be Rs. $(30000-x)$.

Therefore, in order to obtain an annual total interest of Rs. $2000,$ we have:

$\left[ {x\,(30000 – x)} \right]\left[ {\begin{array}{*{20}{l}}
{\frac{5}{{100}}} \\
{\frac{7}{{100}}}
\end{array}} \right] = 2000$

$\Rightarrow \frac{5 x}{100}+\frac{7(30000-x)}{100}=2000$

$\Rightarrow 5 x+210000-7 x=200000$

$\Rightarrow 210000-2 x=200000$

$\Rightarrow 2 x=210000-200000$

$\Rightarrow 2 x=10000$

$\Rightarrow \quad x=5000$

Thus, in order to obtain an annual total interest of Rs. $2000$ , the trust fund should invest Rs. $5000 $ in the first bond and the remaining Rs. $25000$ in the second bond.

Standard 12

Mathematics

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normal

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medium

The order of $[x\,y\,z]\,\,\left[ {\begin{array}{*{20}{c}}a&h&g\\h&b&f\\g&f&c\end{array}} \right]\,\left[ \begin{array}{l}x\\y\\z\end{array} \right]$ is

easy

Let $A = \left( {\begin{array}{{20}{c}}
{\cos \,\alpha }&{ – \sin \,\alpha }\\
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hard

(JEE MAIN-2019)

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hard

(JEE MAIN-2013)

Solution

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