Express each of the following in standard form: |
(a) The mass of a proton in gram is \[\frac{1673}{1000000000000000000000000000}\] |
(b) A Helium atom has a diameter of 0.000000022 cm. |
The population of a place increased to 54,000 in 2003 at a rate of 5% per annum |
(a) Find the population in 2001. |
(b) What would be its population in 2005? |
(a) \[-13~~\] |
(b) \[\frac{-13}{19}\] |
(c) \[\frac{1}{5}\] |
(d) \[\frac{-5}{8}\times \frac{-3}{7}\] |
Simplify: |
(a) \[-\text{ }pcr\text{ }\left( {{p}^{2}}+{{q}^{2}}+{{r}^{2}} \right)\] |
(b) \[(px+qy)(ax-by)\] |
(a) Construct a quadrilateral BLUE in which BL = 5.3 cm, BE = 2.9 cm, \[\angle B=70{}^\circ ,\] \[\angle L=95{}^\circ\] and \[\angle U=85{}^\circ .\] |
(b) A student attempted to draw a quadrilateral PLAY, where PL = 3 cm, LA = 4 cm, AY = 4.5 cm, PY = 2 cm, LY = 6 cm, but could not draw it. What is the reason? |
(a) In a lottery, there are 10 prizes and 20 blanks. A ticket is chosen at random, what is the probability of getting a prize? |
(b) Study the following pictograph and answer the questions given below it. |
(i) How many cars were produced in the month of July? |
(ii) In which month were maximum number of cars produced? |
(a) \[{{(-9)}^{3}}\div {{(-9)}^{8}}\] |
(b) \[\frac{{{3}^{-5}}\times {{10}^{-5}}\times 125}{{{5}^{-7}}\times {{6}^{-5}}}\] |
(a) \[{{x}^{2}}+\text{ }xy+8x+8y~\] |
(b) \[15xy-6x+5y-2\] |
(c) \[ax+bx-ayby\] |
(a) \[{{(b-7)}^{2}}\] |
(b) \[{{(xy+3z)}^{2}}\] |
(c) \[{{(6{{x}^{2}}-5y)}^{2}}\] |
(d) \[{{\left( \frac{2}{3}m+\frac{3}{2}n \right)}^{2}}\] |
(e) \[{{(0.4p-0.5q)}^{2}}\] |
(f) \[{{(2xy+5y)}^{2}}\] |
(a) Water is poured into a cuboidal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 find the number of hours it will take to fill the reservoir. |
(b) If the radius and height of the cylindrical tank are 7 m and 10 m, find the capacity of the tank. |
In a hypothetical sample of 20 people, the amount of money (in thousands of rupees) with each was found to be as follows : |
114,108,100,98,101,109,117,119,126,131,136,143,156,169,182,195, 207, 219,235,118. |
Draw a histogram of the frequency distribution, taking one of the class interval as 50 - 100 |
(a) \[\left\{ \frac{7}{5}\times \left( \frac{-3}{12} \right) \right\}+\left\{ \frac{7}{5}\times \frac{5}{12} \right\}\] |
(b) \[\left\{ \frac{9}{16}\times \frac{4}{12} \right\}+\left\{ \frac{9}{16}\times \frac{-3}{9} \right\}\] |
(a) \[{{71}^{2}}\] |
(b) \[{{99}^{2}}\] |
(c) \[{{102}^{2}}\] |
(d) \[{{998}^{2}}\] |
(e) \[{{5.2}^{2}}\] |
(f) \[297\times 303\] |
(g) \[78\times 82\] |
(h) \[{{8.9}^{2}}\] |
In a primary school, the parents were asked about the number of hours they spend per day in helping their children to do homework. There were 90 parents who help for \[\frac{1}{2}\]hr to\[1\frac{1}{2}\]hr. The distribution of parents according to the time for which, they said they helped is given in the adjoining figure, 20% helped for more than 1-hr per day. 30% helped for \[1\frac{1}{2}\] hr to \[1\frac{1}{2}\]hr; 50% did not help at all Using this, answer the following : |
(a) How many parents were surveyed? |
(b) How many said that did not help? |
(c) How many said that they helped for more than \[1\frac{1}{2}\] hours? |
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