(a) If ABCD is a square of side 14 cm and APB and DPC are semi-circles, then find the area of shaded region as shown in the figure. |
(b) If area of a trapezium is 44 cm2, whose parallel sides are 10 cm and 12 cm and height is 4 cm, then verify that Area of trapezium \[=\frac{1}{2}\] [sum of parallel sides] \[\times \]height. |
Find five rational number between. |
(a)\[\frac{2}{3}\,\,and\,\,\frac{4}{5}~\] |
(b)\[\frac{-3}{2}\,\,and\,\,\frac{5}{3}~\] |
(c) \[\frac{1}{4}\,\,and\,\,\frac{1}{2}~\] |
(a) Subtract \[4a\text{ }-\text{ }7ab\text{ }+\text{ }3b\text{ }+\text{ }12\]from |
\[12a\text{ }-\text{ }9ab\text{ }+\text{ }5b\text{ }-\text{ }3\] |
(b) Subtract \[3xy+\text{ }5yz-7zx\]from |
\[5xy-\text{ }2yz-2zx+10xyz\] |
(c) Subtract \[4{{p}^{2}}q-3pq+5p{{q}^{2}}-8p+7q-10\] |
From \[18-3p-11q+5pq-2p{{q}^{2}}+5{{p}^{2}}q\] |
The students of Anju's class sold posters to raise money. Anju wanted to create a ratio for finding the amount of money her class would make for different numbers of posters sold. She knew they could raise Rs. 250 for every 60 posters sold. |
(a) How much money would Anju's class make for selling 102 posters? |
(b) Could Anju's class raise exactly T 2,000? If so, how many posters would they need to sell? |
(a) The sum of the digits of a two-digit number is 15. If the number formed by reversing the digits is less than the original number by 27, find the original number. |
(b) Verify that \[x=2\]is a solution of the equation |
\[2\left( x+1 \right)=3\left( x+1 \right)-3.\] |
Show that: |
(a) \[{{(3x+7)}^{2}}-84x={{(3x-7)}^{2}}\] |
(b) \[{{\left( 9p-5q \right)}^{2}}+180\text{ }pq={{\left( 9p+5q \right)}^{2}}\] |
(c) \[{{\left( \frac{4}{3}m-\frac{3}{4}n \right)}^{2}}+2mn=\frac{16}{9}{{m}^{2}}+\frac{9}{16}{{n}^{2}}\] |
(d) \[\,{{(4pq+3q)}^{2}}-{{(4pq-3q)}^{2}}=48p{{q}^{2}}\] |
Construct a pie chart for the data. | |
A | 130 |
B | 120 |
C | 90 |
D | 40 |
E | 20 |
Factorise the expressions and divide them as directed. |
(a) \[\left( {{y}^{2}}+7y+10 \right)\div \left( y+5 \right)\] |
(b) \[\left( {{m}^{2}}-14m-32 \right)\div \left( \text{m}+2 \right)\] |
(c) \[\left( 5{{p}^{2\text{ }}}-25p+20 \right)\div \left( p-1 \right)\] |
(d) \[4yz\left( {{z}^{2}}+\text{ }6z-16 \right)\div \text{ }2y\text{ }\left( z+8 \right)\] |
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