Mathematics>Algebra>Sets, Relations and Functions>Functions

Functions

IMPORTANT

Functions: Overview

This topic covers concepts, such as, Graph of a Function, Properties of Modulus Function, Graph of Simple Functions & Shifting of Graphs etc.

Important Questions on Functions

MEDIUM

IMPORTANT

Mathematics>Sets, Relations and Functions>Functions> Q 1

Study the following table and answer the question.

Population of a locality from $1988 - 1992$

Year	Men	Women	Children	Total	Increase $(+)$ or decrease $(-)$ over preceding year
$1988$	$65104$	$60387$	-	$146947$	-
$1989$	$70391$	$62516$	-	-	$(+) 11630$
$1990$	-	$63143$	$20314$	$153922$	-
$1991$	$6995$	-	$21560$	-	$(-) 5337$
$1992$	$71274$	$65935$	$23789$	$160998$	-

The total population in

1989

is ______

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Mathematics>Sets, Relations and Functions>Functions> Q 2

The table given below shows the income (in $₹$ ) together with their sources, received by $5$ employees of a company during the last month of a particular year.

Study the table carefully and answer the question.

Employee Source of Income	A	B	C	D	E
Salary	$₹ 12000$	$₹ 6000$	$₹ 21000$	$₹ 9000$	$₹ 12000$
Bonus	$₹ 2400$	$₹ 1200$	$₹ 4500$	$₹ 2400$	$₹ 3000$
Overtime	$₹ 5400$	$₹ 2100$	$₹ 6000$	$₹ 5100$	$₹ 6000$
Arrears	$₹ 6000$	$₹ 5400$	$₹ 12000$	$₹ 4200$	$₹ 7500$
Miscellaneous	$₹ 1200$	$₹ 300$	$₹ 1500$	$₹ 300$	$₹ 1500$
Total	$₹ 27000$	$₹ 15000$	$₹ 45000$	$₹ 21000$	$₹ 30000$

What is the average overtime allowance given to employees

A

,

B

,

C

,

D

and

E

?

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IMPORTANT

Mathematics>Sets, Relations and Functions>Functions> Q 3

DIRECTIONS : Read the following table and answer the question.

Internet owners in our country(Approximate)

Year	Government	Private
$2007 - 08$	$3900$	$-$
$2008 - 09$	$29400$	$-$
$2009 - 10$	$90000$	$-$
$2010 - 11$	$230000$	$12000$
$2011 - 12$	$520000$	$120000$
$2012 - 13$	$1060000$	$450000$
$2013 - 14$	$1550000$	$950000$

What is the approximate percentage increase in the Private internet owners in the period $2013 - 14$ over that in the period $2010 - 11 ?$

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IMPORTANT

Mathematics>Sets, Relations and Functions>Functions> Q 4

Refer the table below and answer the following questions related to the table
A survey of movie goers from cities $A, B, C, D$ and $E$ is summarised below. The first column gives the percentage of viewers in each city who watch less than one movie a week . The second column gives the total number of viewers who view one or more movies per week

City	I	II
$A$	$60$	$2400$
$B$	$20$	$3000$
$C$	$85$	$2400$
$D$	$55$	$2700$
$E$	$75$	$8000$

The highest number of movie watchers in any given city is equal to_____.

EASY

IMPORTANT

Mathematics>Sets, Relations and Functions>Functions> Q 5

DIRECTIONS : Study the following table to answer the given questions:

Production (in Crore units) of six companies over the year

Company	Years						Total
TP	$2009$	$2010$	$2011$	$2012$	$2013$	$2014$
TP	$103$	$150$	$105$	$107$	$110$	$132$	$707$
ZIR	$75$	$80$	$83$	$86$	$90$	$91$	$505$
AVC	$300$	$300$	$300$	$360$	$370$	$340$	$1970$
CTU	$275$	$280$	$281$	$280$	$285$	$287$	$1688$
PEN	$25$	$30$	$35$	$40$	$42$	$45$	$217$
SIO	$85$	$87$	$89$	$91$	$92$	$96$	$540$
Total	$863$	$927$	$893$	$964$	$989$	$991$	$5627$

For ZIR, which of the following is the difference between production in $2014$ and that in $2013$ ?

EASY

IMPORTANT

Mathematics>Sets, Relations and Functions>Functions> Q 6

DIRECTIONS : Study the following table to answer the given questions:

Production (in crore units) of six companies over the year

Company	Years							Total
	2009	2010	2011	2012	2013	2014
TP	103	150	105	107	110	132		707
ZIR	75	80	83	86	90	91		505
AVC	300	300	300	360	370	340		1970
CTU	275	280	281	280	285	287		1688
PEN	25	30	35	40	42	45		217
SIO	85	87	89	91	92	96		540
Total	863	927	893	964	989	991		5627

For how many companies did the production increase every year from that of the previous year?

EASY

IMPORTANT

Mathematics>Sets, Relations and Functions>Functions> Q 7

Refer to the table below and answer the following questions related to the table.
Mr. X has a concern where he manufactures shirts of $5$ qualities- (H) High, (HM) High Medium (M) Medium, (LM) Low Medium, (L) Low from $3$ types of fabrics High, Medium and Low. Each of these fabrics could be woven from $3$ types of yarn Cotton, Polyester, and Nylon. Each shirt requires $1.5$ m of fabric. Answer the following question that Mr. X faces if the table indicates the true position.

Fabric Usage (%)

	High	Medium	Low
H	$70$	$30$
HM	$20$	$60$	$20$
M	$10$	$50$	$40$
ML		$40$	$60$
L		$20$	$80$

Production

Shirt Type	Nos in millions
H	$20$
HM	$30$
M	$30$
ML	$10$
L	$10$

Yarn Usage(%)

	Cotton	Polyster	Nylon
High	$80$	$10$	$10$
medium	$70$	$20$	$10$
Low	$60$	$30$

How many number of shirt of type (H), will be made from High quality fabric ?

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IMPORTANT

Mathematics>Sets, Relations and Functions>Functions> Q 8

Read the following table carefully and answer the question given below. Marks obtained by four students in five different subjects in class $VIII, IX and X .$

Student	Amit	Amit	Amit	Jyoti	Jyoti	Jyoti	Nitin	Nitin	Nitin	Ekta	Ekta	Ekta
Subject	$VIII$	$IX$	$X$	$VIII$	$IX$	$X$	$VIII$	$IX$	$X$	$VIII$	$IX$	$X$
Hindi	$550$	$245$	$650$	$650$	$746$	$636$	$480$	$468$	$355$	$323$	$300$	$234$
English	$327$	$465$	$354$	$645$	$656$	$842$	$654$	$354$	$353$	$256$	$134$	$342$
Sanskrit	$245$	$635$	$657$	$683$	$725$	$754$	$336$	$345$	$645$	$454$	$234$	$445$
Maths	$646$	$534$	$565$	$766$	$675$	$522$	$643$	$324$	$543$	$442$	$120$	$454$
Science	$465$	$724$	$564$	$446$	$635$	$634$	$435$	$532$	$343$	$346$	$323$	$213$

What is the difference between total marks obtained by Jyoti in Sanskrit in all the three classes and marks obtained by Amit in Maths in class $X ?$

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IMPORTANT

Mathematics>Sets, Relations and Functions>Functions> Q 9

Refer to the table below and answer the following question related to the table:

The following table shows the number of institution and enrolments for various years,

INSTITUTION (Figures in Number)	$1970$	$1980$	$1990$
Primary	$1060$	$1470$	$1980$
Middle	$620$	$750$	$840$
Higher	$580$	$650$	$760$
College & University	$32$	$52$	$67$
ENROLMENTS (Figures in Thousands)	$1970$	$1980$	$1990$
Primary	$35000$	$39000$	$41000$
Middle	$9000$	$13000$	$15000$
Higher	$6500$	$7200$	$8100$
College $ University	$120$	$150$	$190$

In

1990

, what is the number of higher-level school as a fraction of primary schools?

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Mathematics>Sets, Relations and Functions>Functions> Q 10

Study the table carefully to answer the questions give below.
Number of candidates (in lakh) appearing in an entrance examination from six different cities and the ratio of candidates passing and failing in the same.

City	A	B	C	D	E	F
Number of candidates	1.25	3.14	1.08	2.27	1.85	2.73

RATIO OF CANDIDATES PASSING AND FAILING WITHIN THE CITY.

CITY	PASSING	FAILING
A	7	3
B	5	3
C	4	5
D	1	3
E	3	2
F	7	5

What is the ratio of the number of candidates failed the exam from city D to that of those failed the exam from city A?

EASY

IMPORTANT

Mathematics>Sets, Relations and Functions>Functions> Q 11

Directions (Q. Nos. 91-95) Answer these questions on the basis of the data given in the following table giving the trend in sales of four companies. The amounts given in lakhs of rupees.

Which company recorded the lowest growth rate in sales in l99O over its previous year ?

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Mathematics>Sets, Relations and Functions>Functions> Q 12

Study the following table and answer the question based on it. Expenditures of a Company (in Pesetas) per Annum Over the given Years.

Years	Salary	Fuel and Transport	Bonus	Interest in Loans	Taxes
$1998$	$288$	$98$	$3.0$	$23.4$	$83$
$1999$	$342$	$112$	$2.52$	$32.5$	$108$
$2000$	$324$	$101$	$3.84$	$41.6$	$74$
$2001$	$336$	$133$	$3.68$	$36.4$	$88$
$2002$	$420$	$142$	$3.96$	$49.4$	$98$

The total expenditure of the company over these items during the year $2000$ is _______.

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IMPORTANT

Mathematics>Sets, Relations and Functions>Functions> Q 13

Study the following table carefully to answer the question that follow:

Number of medals won by five different countries in six different year

Year	$A$	$B$	$C$	$D$	$E$
$2005$	$120$	$45$	$135$	$65$	$64$
$2006$	$160$	$60$	$70$	$46$	$28$
$2007$	$142$	$102$	$46$	$43$	$110$
$2008$	$172$	$28$	$108$	$39$	$58$
$2009$	$90$	$64$	$56$	$25$	$64$
$2010$	$64$	$36$	$85$	$19$	$83$

Which country won second highest number of medals over all the years together?

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Mathematics>Sets, Relations and Functions>Functions> Q 14

Study the following table to answer the given question.
Number of students of different classes of a school playing different games

Class	VI	VII	VIII	IX	X
Games
Chess	$12$	$10$	$22$	$02$	$12$
Cricket	$16$	$12$	$24$	$22$	$08$
Basket Ball	$18$	$16$	$14$	$24$	$14$
Table Tennis	$05$	$08$	$18$	$12$	$18$
Football	$09$	$12$	$02$	$06$	$16$
Tennis	$03$	$10$	$08$	$06$	$18$

Approximately what percent of Xth class students play table tennis out of the total Xth class students playing different games?

MEDIUM

IMPORTANT

Mathematics>Sets, Relations and Functions>Functions> Q 15

DIRECTIONS : Study the following table to answer the given question:

Percentage of marks obtained by seven students in six subjects

(Maximum marks $= 100$ )

Student/Subject	English	History	Commerce	Maths	Science	Economics
Meenu	$100$	$80$	$50$	$90$	$90$	$60$
Subodh	$80$	$70$	$80$	$100$	$80$	$40$
Kunal	$90$	$70$	$60$	$90$	$70$	$70$
Soni	$60$	$60$	$65$	$80$	$80$	$80$
Richu	$50$	$90$	$62$	$80$	$85$	$95$
Irene	$40$	$60$	$64$	$70$	$65$	$85$
Vgay	$80$	$80$	$35$	$65$	$50$	$75$

In which subject is the overall percentage the best ?

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Mathematics>Sets, Relations and Functions>Functions> Q 16

Study the following table to answer these questions.
PLAN-WISE PUBLIC SECTOR OUTLAYS AND EXPENDITURE ( $1974 - 79$ TO $1985 - 90$ )
(in Rs. Crores)

Five Years Plans	Period	Approved Outlay	Actual Expenditure
Fifth Plan	$1974 - 79$	$39, 303$	$39, 426$
Sixth Plan	$1980 - 85$	$97, 500$	$1, 09, 292$
Seventh Plan	$1985 - 90$	$1, 80, 000$	-----

Sixth Plan outlay exceeded the Fifth Plan outlay by almost

EASY

IMPORTANT

Mathematics>Sets, Relations and Functions>Functions> Q 17

Refer the table below and answer the following questions related to the table
The following table shows the number of institution and enrollments for various years

INSTITUTION (Figures in Number)	1970	1980	1990
Primary	1060	1470	1980
Middle	620	750	840
Higher	580	650	760
College & University	32	52	67
ENROLLMENTS (Figures in Thousands)	1970	1980	1990
Primary	35000	39000	41000
Middle	9000	13000	15000
Higher	6500	7200	8100
College $ University	120	150	190

What is the increase in average enrolment in middle schools between

1980

and

1990 ?

HARD

IMPORTANT

Mathematics>Sets, Relations and Functions>Functions> Q 18

Refer to the table below and answer the following questions related to the table:

The institute placement cell conducted a survey to determine the preferences of students in the various areas of specialisation. The two areas tested were Finance and Marketing. The following table indicates the number of students who preferred one or both specialisations.

Prior work experience (years)	Specialisation preferred						Total no. of students surveyed including those who did not prefer either specialisation
	Marketing		Finance		Both
	Male	Female	Male	Female	Male	Female	Male	Female
$0$ to $1$	$180$	$60$	$240$	$180$	$90$	$45$	$420$	$270$
$2$ to $3$	$150$	$120$	$120$	$150$	$90$	$60$	$600$	$480$
$4$ or more	$120$	$90$	$90$	$60$	$30$	$45$	$300$	$360$

How many students who preferred at least one specialisation had more than

4 years

of work experience?

EASY

IMPORTANT

Mathematics>Sets, Relations and Functions>Functions> Q 19

This table gives us information about the North, east, west, and south zone-wise survey report of the people of a country who consumes coffee.

Take Coffee	Zone
	North	East	West	South
More than $3$ times a day	$410$	$310$	$700$	$1450$
$1$ to $3$ times a day	$1220$	$830$	$1250$	$1120$
Twice a week	$1640$	$710$	$950$	$420$
Only once a week	$620$	$540$	$530$	$350$
Never	$950$	$430$	$620$	$50$

What is the percentage of people of south zone who take coffee at least once a day ?

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Mathematics>Sets, Relations and Functions>Functions> Q 20

Study the following table to answer the given questions:

Production (in crore units) of six companies over the year

Company	Years						Total
	2009	2010	2011	2012	2013	2014
TP	103	150	105	107	110	132	707
ZIR	75	80	83	86	90	91	505
AVC	300	300	300	360	370	340	1970
CTU	275	280	281	280	285	287	1688
PEN	25	30	35	40	42	45	217
SIO	85	87	89	91	92	96	540
Total	863	927	893	964	989	991	5627

Which company has less average production in the last three years compared to that of first three years?