Inserting the Missing Number
In this chapter questions contain a figure, a set of figures, an arrangement or a matrix, each of which bears certain characters, be it numbers, letters or group/combination of Setters numbers which follow a particular pattern. You are required to identify and decipher this pattern and accordingly find the missing character in the figure.
Example: No. (1 to 6)
Direction: Find the missing character from among the given alternatives.
1.
(a) 45 (b) 35
(c) 25 (d) 15
(e) None of these
Ans. (c)
Explanation: The pattern is \[\to \text{ }{{\left( 16\text{ }-\text{ }6 \right)}^{2}}+\text{ }{{\left( 5\text{ }-\text{ }2 \right)}^{2}}=\text{ }100\text{ }+\text{ }9\text{ }=\text{ }109\]
\[\to \,\,\,{{\left( 22\text{ }-\text{ }15 \right)}^{2}}+\text{ }{{\left( 21\text{ }-\text{ }19 \right)}^{2}}=\text{ }49\text{ }+\text{ }4\text{ }=\text{ }53\]
\[\to \,\,\,{{\left( 17\text{ }-\text{ }13 \right)}^{2}}+\text{ }{{\left( 51\text{ }-\text{ }48 \right)}^{2}}=\text{ }16\text{ }+\text{ }9\text{ }=\text{ }\]
2.
(a) 50 (b) 39
(c) 26 (d) 1
(e) None of these
Ans. (b)
Explanation: The pattern is: \[\to \,\,\,3\,\times \,2-1=5\]
\[\to \,\,5\,\,\times \,\,2\,\,-\,\,2\,\,=\,\,8\]
\[\to \,\,8\,\,\times \,\,2\,\,-\,\,3\,\,=\,\,13\]
\[\to 13\,\,\times \,\,2\,\,-\,\,4\,\,=\,\,22\]
So, \[So,\,\,\,\to \,\,\,22\,\,\times \,\,2\,\,-\,\,5\,\,=\,\,39\]
3.
(a) 18 (b) 36
(c) 135 (d) 175
(e) None of these
Ans. (c)
Explanation: The pattern is: \[15\times \,2=30\]
\[2\,\,\times \,\,7\,\,=\,\,63\]
So, the missing number is: \[9\times 15=135.\]
4.
(a) 860 (b) 1140
(c) 2880 (d) 3240
(e) None of these
Ans. (c)
Explanation: Clearly, moving clockwise, we observe the following pattern:
\[4\times 1=4;\text{ }4\times 2=8;\text{ }8\times 3=24;\text{ }24\times 4=96;\text{ }96\times 5=480\]
So required number = \[\left( 480\times 6 \right)=2880\]
Hence, the answer is (c).
5.
(a) 5 (b) 4
(c) 3 (d) 2
(e) None of these
Ans. (c)
Explanation: In the first column, \[12\,\,\times \,\,(18\,\,\div \,\,3)\,\,=\,\,72\]
In the third column, \[16\,\,\times \,\,(32\,\,\div \,\,4)\,\,=\,\,128\]
Let the missing number be x. Then, in the second column, we have
\[14\times \left( 24\text{ }\div \text{ }x \right)\text{ }=112\text{ }\Rightarrow \text{ }24\div x\,=8\text{ }\Rightarrow \,\text{ }x=3\]
Hence, the answer is (c).
6.
(a) P (b) R
(c) S (d) V
(e) None of these
Ans. (b).
Explanation: Putting \[A\,\,=\,\,1,\,\,B\,\,=\,\,2,\,\,C\,\,=\,\,3,\,\,........,\,\,M\,\,=\,\,13,.......,\,\,X\,\,=\,\,24,\,\,Y\,\,=\,\,25,\,\,Z\,\,=\,\,26,\]
we have:
In the first row, \[F\,\,+\,\,I\,\,=\,\,6\,\,+\,\,9\,\,=\,\,15\,\,=\,\,O\]
In the second row, \[A\,\,+\,\,J\,\,=\,\,1\,\,+\,\,10\,\,=\,\,11\,\,=\,\,K\]
So, in the third row, missing letter \[=E\,\,+\,\,M\,\,=\,\,5\,\,+\,\,13\,\,=\,\,18\,\,=\,\,R\]
Hence, the answer is (b)
So number of boys in the row \[=\text{ }\left( 15+1+3+1+4+1+15 \right)=40\]
Hence, the answer is (b).
Fig. 2.1: Most Populous Countries
DENSITY OF POPULATION
Each unit of land has limited capacity to support people living on it. Hence, it is necessary to understand the ratio between the numbers of people to the size of land. This ratio is the density of population. It is usually measured in persons per sq. km
Population
\[Density\text{ }of\text{ }Population\text{ }=\frac{Population}{Area}\]
For example, area of Region X is 100 sq. km and the population is 1,50,000 persons. The density of population is calculated as:
\[Density\,\,=\,\,\frac{1,50,000}{100}\]
= 1,500 person/sq. km
What does this tell you about Region X?
Look at the map given below:
Do you observe that some areas are really crowded? These are the densely populated parts of the world with more than 200 persons on every sq. km. These are the North –Eastern part of U.S.A., North-Western part of Europe, South, South-East and East Asia.
Other areas like those near the North and South Poles, the hot and the cold deserts and high rainfall zones near the Equator have very low density of population. These are the sparsely populated regions of the world with less than 01 person per sq. km.
Do you know that cities can also grow negatively? Look at the photographs of this tsunami affected city. Are natural disasters the only reasons for negative growth in a city’s size?
This meant that the bigger the economy of the country, the more developed it was considered, even though this growth did not really mean much change in the lives of most people.
The idea that the quality of life people enjoy in a country, the opportunities they have and freedoms they enjoy, are important aspects of development, is not new.
These ideas were clearly spelt out for the first time in the late eighties and early nineties. The works of two South Asian economists, Mahbub-ul-Haq and Amartya Sen are important in this regard.
The concept of human development was introduced by Dr. Mahbub-ul-Haq. Dr. Haq has described human development as development that enlarges people’s choices and improves their lives. People are central to all development under this concept. These choices are not fixed but keep on changing. The basic goal of development is to create conditions where people can live
