| Factorise the following: |
| (a) \[\frac{{{x}^{2}}}{4}+2x+4\] |
| (b) \[16{{x}^{2}}+40x+25\] |
| (a) Find the area of rectangular park which is \[36\frac{3}{5}\]m long and \[16\frac{2}{3}\]m broad. |
| (b) Write the name of property for any rational numbers \[\frac{a}{b}\] and \[\frac{c}{d}\], we have \[\left( \frac{a}{b}\times \frac{c}{d} \right)=\left( \frac{c}{d}\times \frac{a}{b} \right)\] |
| (a) \[{{a}^{3}}-4{{a}^{2}}+12-3a\] |
| (b) \[4{{x}^{2}}-20x+25\] |
| Factorise and divide the following: |
| (a)\[\left( {{x}^{2}}-22x+117 \right)\div \left( x-13 \right)~~~~\] |
| (b) \[\left( 9{{x}^{2}}-4 \right)\div \left( 3x+2 \right)\] |
| It is given that I varies directly as m. |
| (a) Write an equation which relates 1 and m. |
| (b) Find the constant of proportion (k), when 1 is 6 then m is 18. |
| (c) Find 1, when m is 33. |
| (d) Find m when 1 is 18. |
| (a) A cylindrical tank has a capacity of 5632\[{{m}^{3}}\]. If the diameter of its base is 16 m. Find its depth. |
| (b) If side of square is 14 cm, then find the area of semi-circle as shown in the figure. |
 |
| Prove that \[\angle COD=\frac{1}{2}[\angle A+\angle B].\] |
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