TNPSC GROUP I MAIN: GENERAL MENTAL ABILITY PRACTICE …appolosupport.com/wp-content/uploads/2019/07/ALPHA... · Page 1 PH: 044-24339436, 42867555 TNPSC GROUP I MAIN: GENERAL MENTAL

Page 1 www.appolotraining.com PH: 044-24339436, 42867555

TNPSC GROUP I MAIN: GENERAL MENTAL ABILITY

PRACTICE TEST - ALPHA

SECTION A: 3 MARKS

1. A sum 817 is divided among, A, B and C such that A receives 25% more than B and B received 25% less than C. What is the A share in the amount? &. 817 vd;w njhif A, B kw;Wk; C MfpNahhpilNa gq;fpl;L toq;fg;gLfpwJ. mjd;gb B-I tpl 25 rjtPjk; $Ljyhf A ngWfpwhh;> C-I tpl 25 rjtPjk; Fiwthf B ngWfpwhh;. me;jj; njhifapy;; A-d; gq;F vd;d?

2. Two dice are rolled and the product of the outcomes (numbers) are found. What is the probability that the product so found is a prime number? ,U gfilfs; xNu Neuj;jpy; cUl;lg;gLk;NghJ fpilf;Fk; Kf vz;fspd; ngUf;fw;gyd; xU gfh vz;zhf ,Ug;gjw;fhd epfo;jftpidf; fhz;f Solution: The sample space, S= {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6) (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6) (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6) (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6) (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6) (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} n(S) = 36 Let A be the event of product of outcomes of the prime number.

http://www.appolotraining.com/


Then A = {(1, 2), (1, 3) (1, 5), (2, 1), (3, 1), (5, 1)}

n(A) = 6

P(A) = ( ) 6 1

( ) 36 6

n A

n S

3. From a well shuffled pack of 52 playing cards, one card is drawn at random. Find the probability of getting (i) a black king (ii) a spade card (iii) a diamond 10. ed;F fiyj;J itf;fg;gl;l 52 rPl;Lfisf; nfhz;l rPl;Lf; fl;bypUe;J rktha;g;Gr; Nrhjid Kiwapy; xU rPl;L vLf;fg;gLfpwJ. me;jr; rPl;L gpd;tUtdthf ,Uf;f epfo;jfTfisf; fhz;f i. fUg;G ,uhrh ii. ];NgL iii. lakz;l; 10

4. A bicycle is sold at 10% profit. Had it been sold for ì 10 less, the profit

would have been 5% only. What is the cost price of the bicycle? xU kpjp tz;b 10 tpOf;fhL ,yhgj;jpw;F tpw;gid nra;ag;gLfpwJ. mJ 10 &gha; Fiwthf tpw;gid nra;ag;gl;bUe;jhy;> ,yhgk; ntWk; 5 tpOf;fhlhf kl;LNk ,Ue;jpUf;Fk;. me;j kpjp tz;bapd; nfhs;Kjy; tpiy vd;d? Solution:



Let, CP=100% 10% Profit then S.P = 110% 5% profit the S.P = 105% Difference 5% 10 Rs 100% 200 Rs

5. A can do a piece of work in 4 hours, B and C can do it in 3 hours, A and C can do it in 2 hours. How long will B alone take to do it?

‘A’ vd;gth; xU Ntiyia 4 kzp Neuj;jpYk;> mNj Ntiy BAk; CAk; Nrh;e;J 3 kzp Neuj;jpYk;> AAk; CAk; Nrh;e;J 2 kzp Neuj;jpYk; Kbf;fpd;wdh; vdpy;> „B‟ jdpahf Kbf;f vLj;Jf; nfhs;Sk; Neuk; vt;tsT?

6. If interest is calculated yearly and compound interest is ` 331 at the rate of interest of 10% for 3 years, then principal is xU njhifahdJ 3 Mz;Lfspy; 10% tl;b tPjj;jpy; $l;b tl;b &.331 fpilf;fpwJ. vdpy; me;j njhif ahJ? Solution:



7. Five years ago, the ratio of A‟s age of B‟s age was 3:2 and five years hence their ages will be in the ratio of 5:4. The present ages of A and B are respectively. 5 Mz;LfSf;F Kd;ghf A kw;Wk; B ,d; taJfs; 3:2 vd;w tpfpjj;jpy; ,Ue;jd. Ie;J Mz;Lfs; fopj;J mth;fspd; taJfs; 5:4 vd;w tpfpjj;jpy; ,Uf;Fk;. jw;NghJ A kw;Wk; B MfpNahhpd; taJfs; KiwNa: Solution: Five years ago A and B ages was 3x and 2x. Now A=3x+5 B=2x+5

After 5 years 3 5 5 5

12 40 10 50 2 10 52 5 5 4

xx x x x

x

Now A = 20 B=15 Required ratio 4 : 3

8. A wire in the shape of a rectangle of length 37 cm and width 29 cm is reshaped in the form of a circle. Find the radius and area of the circle.

37 nr.kP ePsKk;> 29 nr.kP mfyKk; cila nrt;tf tbtf; fk;gpahdJ tl;l tbtkhf khw;wp mikf;fg;gLfpd;wJ. tl;lj;jpd; Muk; kw;Wk; gug;gsitf; fhz;f.



9. What do you mean by an algorithm? nray;Kiw vd;why; vd;d?

Algorithm is defined as a step-by-step procedure or formula for solving a problem i.e. a set of instructions or procedures for solving a problem. It is also defined as a mathematical procedure that can usually be explicitly encoded in a set of computer language instructions that manipulate data.

10. What is open source software? jpw%y nkd;nghUs; vd;why; vd;d?

Open-source software (OSS) is computer software with its source code made available with a license in which the copyright holder provides the rights to study, change, and distribute the software to anyone and for any purpose. Open-source software may be developed in a collaborative public manner. According to scientists who studied it, open-source software is a prominent example of open collaboration. The term is often written without a hyphen as "open source software"

(open-source software) (Source code)

.


https://en.wikipedia.org/wiki/Computer_software

https://en.wikipedia.org/wiki/Source_code

https://en.wikipedia.org/wiki/Open-source_license

https://en.wikipedia.org/wiki/Copyright

https://en.wikipedia.org/wiki/Collaborative_software_development_model

https://en.wikipedia.org/wiki/Open_collaboration

https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AF%86%E0%AE%A9%E0%AF%8D%E0%AE%AA%E0%AF%8A%E0%AE%B0%E0%AF%81%E0%AE%B3%E0%AF%8D


(Software License)

, (Software License)

, ,

.

.

.

, .

11. What is IP addressing system?

,d;lh;nel; GNuhl;Nlhfhy; vd;why; vd;d? The Internet protocol (IP) addressing system is used to keep track of the million of users. This system uses the letter addressing system and number addressing systems. ,izaj;jpy; ,ize;j xU fzpg;nghwp Nritafk; host vdg;gLk;. ,izaj;jpy; xt;nthU fzpg;nghwpf;Fk; xU Kfthp cz;L. mijf; nfhz;Ljhd;> me;jf; fzpg;nghwpf;Fj; jfty; nry;Yk;. ,e;j Kfthpia vz;fspd; njhFg;ghf my;yJ nrhw;fspd; njhFg;ghff; nfhLf;fyhk;. ,izaj;jpy; jfty; mDg;g cjTk; newpKiw ,d;lh;nel; GNuhl;Nlhfhy; (Internet Protocol – IP) vdg;gLk;.

12. What is Sturges‟ Rule? ];l;u[]; tpjp vd;gJ ahJ?

The number of class intervals can be fixed arbitrarily keeping in view the nature of problem under study or it can be decided with the help of Sturges‟ Rule. According to him, the number of classes can be determined by the formula



13. What are broken bar diagrams? cile;j gl;il tpsf;fg;glq;fs; vd;why; vd;d?

Broken Bars: In certain series there may be wide variations in values – some values may be very small and others very large. In order to gain space for the smaller bars of the series, the largest bar may be broken.

Represent the data by a suitable diagram. Solution. Since the gap between the minimum and maximum figure is large, the broken bar diagram shall be more appropriate



cile;j gl;il tpsf;fg;glk;: (a) khwpfspd; kjpg;GfSf;fpilNa mjpf NtWghLfs; ,Ug;gpd;> mjhtJ rpy khwpfspd; kjpg;Gfs; kpfr; rpwpajhfTk; kw;Wk; rpy khwpfspd; kjpg;Gfs; kpfg; nghpajhfTk; ,Uf;Fk; nghOJ ,t;tifahd cile;j gl;il tpsf;fg;glq;fs; gad;gLj;jg; gLfpd;wd.

(b) fhuzk; rpW gl;ilfSf;fhd NghJkhd kw;Wk; epahakhd cUtj;ijf; nfhLg;gjw;fhf> nghpa gl;ilfs; cilf;fg;gl;L mjd; Nky; mjd; cz;ikahd kjpg;G vOjg;gLfpd;wJ.

14. What is the average female population in million?

ngz;fs; kf;fs;njhifapd; ruhrhp (kpy;ypadpy;) vt;tsT?

Solution: Total Population= 85 Male Population = 43.4 Female Population = 85 – 43.4 = 41.4

Average Female population = 41.4

8.325



SECTION B 15. Represent by a percentage bar diagram the following data on

investment for the First and Second Five-Year Plans: Kjy; kw;Wk; ,uz;lhk; Ie;jhz;L jpl;lq;fspy; KjyPL nra;ag;gl;l tptuq;fis nfhz;L rjtPj gl;il tpsf;fg;glk; xd;wpid mikj;Jf;fhl;Lf

Investment in the Public Sector / KjyPL nra;ag;gl;l nghJj;Jiwfs;

Sectors / Jiwfs;

The Five-Year Plan (in Crs) /

Kjy; Ie;jhz;L jpl;lk;

The Second Five Year Plan (in Crs) / ,uz;lhk; Ie;jhz;L

jpl;lk;

Agriculture / Ntshz;ik

357 76

Irrigation / ePh;g;ghrdk;

492 990

Industry / njhopw;rhiyfs;

261 909

Transport / Nghf;Ftuj;J

654 1485

Social services / r%f Nritfs;

306 945

Miscellaneous / kw;wit

90 300

Solution:



16. Write short notes on a. Class Limit b. Class Interval c. Range d. Mid-Point rpWFwpg;G tiuf a. gphpT vy;iyfs; b. gphpT ,ilntspfs; c. tPr;R d. ika kjpg;G

Class limits: The class limits are the lowest and the highest values that can be included in the class. For example, take the class 30-40.The lowest value of the class is 30 and highest class is 40. The two boundaries of class are known as the lower limits and the upper limit of the class. The lower limit of a class is the value below which there can be no item in the class. The upper limit of a class is the value above which there can be no item to that class. Of the class 60-79, 60 is the lower limit and 79 is the upper limit, i.e. in the case there can be no value which is less than 60 or more than 79. The way in which class limits are stated depends upon the nature of the data. In statistical calculations, lower class limit is denoted by L and upper class limit by U. Class Interval: The class interval may be defined as the size of each grouping of data. For example, 50-75, 75-100, 100-125… are class intervals. Each grouping begins



with the lower limit of a class interval and ends at the lower limit of the next succeeding class interval Range: The difference between largest and smallest value of the observation is called The Range and is denoted by „ R‟ ie R = Largest value – Smallest value R = L – S Mid-value or mid-point: The central point of a class interval is called the mid value or mid-point. It is found out by adding the upper and lower limits of a class and dividing the sum by 2.



17. What is piracy? Mention the types of piracy? How can it be prevented?

Software Piracy is about the copyright violation of software created originally by an individual or an institution. It includes stealing of codes / programs and other information illegally and creating duplicate copies by unauthorized means and utilizing this data either for one‟s own benefit or for commercial profit.

In simple words,Software Piracy is “unauthorized copying of software”. Figure shows a diagrammatical representation of software piracy.



Most of the commercial software is licensed for use at a single computer site or for use by only one user at any time. When a user buys any software, he becomes a licensed user for that software. He is allowed to make copies of the program for backup purposes, but it is against the law to distribute duplicate copies to others. Such illegal copying and distribution of commercial software should not be practiced.

An entirely different approach to software piracy is called shareware, acknowledges the futility of trying to stop people from copying software and instead relies on people‟s honesty. Shareware publishers encourage users to give copies of programs to friends and colleagues but ask everyone who uses that program regularly to pay a registration fee to the program‟s author directly. Commercial programs that are made available to the public illegally are often called warez.

Prevent Software Piracy Legal protection: Most companies make sure their software is protected legally by a user agreement. Letting consumers know that making unauthorized copies is against the law will help prevent people from unknowingly breaking piracy laws.

Product key The most popular anti-piracy system is a product key, a unique combination of letters and numbers used to differentiate copies of the software. A product key ensures that only one user can use the software per purchase.

Tamperproofing Some software programs have built-in protocols that cause the program to shut down and stop working if the source code is tampered with or modified. Tamperproofing prevents people from pirating the software through the manipulation of the program's code.

Watermarking Watermarks, company logos, or names are often placed on software interfaces to indicate that products are legitimately obtained, and are not illegal copies.


https://www.computerhope.com/jargon/e/eula.htm

https://www.computerhope.com/jargon/e/eula.htm

https://www.computerhope.com/jargon/c/cdkey.htm

https://www.computerhope.com/jargon/s/source.htm

https://www.computerhope.com/jargon/w/watermar.htm




18. How AND and OR can be realized using NAND and NOR gate.



19. A can do a piece of work in 120 days and B can do it in 150 days. They work together for 20 days. Then B leaves and A continues the work alone. 12 days after that C joins A and the work is completed in 48 days more. In how many days can C do it if he works alone? xU Fwpg;gpl;l Ntiyia A 120 ehl;fspYk; B 150 ehl;fspYk; nra;J Kbg;gh;. mth;fs; ,UtUk; Nrh;e;J 20 ehl;fs; Ntiy nra;fpd;wdh;. gpwF B mjpypUe;J tpyf> A kl;Lk; jdpahf njhlh;e;J Ntiy nra;fpwhh;. mjw;Fg; gpwF 12 ehl;fs; fle;j gpwF A cld; C me;j Ntiyapy; Nrh;fpwhh;. mijj; njhlh;e;J me;j NtiyahdJ NkYk; 48 ehl;fspy; nra;J Kbf;fg;gLfpwJ. me;j Ntiyia C kl;Lk; jdpahf nra;tjhdhy;> mijr; nra;J Kbf;f mth; vj;jid ehl;fis vLj;Jf; nfhs;thh;.





20. Answer the following questions gpd;tUk; tpdhf;fSf;F tpilasp

a. A man encashes a cheque for ` 600 from a bank. The bank pays him

money in 10-rupee notes and 5-rupee notes only, totaling 72. The ratio of the number of 10-rupess notes to that of 5 – rupee notes is: XU egh; xU tq;fpapy; ,Ue;J xU fhNrhiyia &.600f;F gzkhf;Ffpwhh;. me;j tq;fp mtUf;F gj;J &gha; kw;Wk; Ie;J &gha; Nehl;Lfshf kl;LNk nkhj;jk; 72 Nehl;Lfis nfhLf;fpwJ. gj;J &gha; Nehl;Lfs; kw;Wk; Ie;J &gha; Nehl;Lfspd; tpfpjk; vd;d? Solution: Let, 10 Rs notes = x numbers then 5 Rs notes = 72-x

10 72 5 600

10 360 5 600

5 240

48

x x

x x

x

x

10 Rs notes are 48 then 5 Rs notes = 72-48=24 Required ratio 72 : 48 3 : 2

b. 20 litres of a mixture contains milk and water in the ratio 5:3. If 4 litres

of this mixture are replaced by 4 litres of milk, the ratio of milk to water

in the new mixture will become 20 ypl;lh; fyitapy; ghy; kw;Wk; ePhpd; tpfpjk; Kiw 5 : 3. ,f;fyitapy; ,Ue;J 4 yp vLf;fg;gl;L gpwF 4 yp ghy; Nrh;f;fg;gLfpwJ vdpy; fyitapd; ghy; kw;Wk; ePhpd; jw;Nghija tpfpjk; vd;d?

Solution:



SECTION – C


a. 2 men and 7 boys can do a piece of work in 14 days, 3 men and 8 boys

can do the same in 11 days. In how many days, 3 times the work can be completed by 8 men and 6 boys?

2 Mz;fs;> 7 rpWth;fs; Nrh;e;J xU Ntiyapid 14 ehl;fspy; Kbg;gh; 3 Mz;fs;> 8 rpWth;fs; Nrh;e;J> mNj Ntiyia 11 ehl;fspy; nra;J Kbg;gh;. vdpy;> mNj Nghy; %d;W klq;F Ntiyia> 8 Mz;fs;> 6 rpWth;fs; Nrh;e;J vj;jid ehl;fspy; nra;J Kbg;gh;? Solution:

2M+7B ×14= 3M+8B ×11

28M+98B=33M+88B

5M=10B

1M=2B

Equation (1) : 2M+7B or 4B + 7B = 11B completes in 14 days Required: 8M + 6B or 16B + 6B = 22B completes 3 times work in ? days

1 1 2 2 2

2

1 2

M D M D 2211 14= 21

W W 1 3

B DBD days

b. Two men undertake to do a piece of work for Rs.1000. One alone could

do it in 6 days, the other in 8 days. With the assistance of a boy they finish it in 3 days. How should the money be divided?

,uz;L Mz;fs; Nrh;e;J xU Fwpg;gpl;l Ntiyia &.1000-f;F nra;J Kbg;gjhf Vw;Wf; nfhs;fpd;wh;. ,e;j Ntiyia Kjyhk; eguhy; 6 ehl;fspYk;> ,uz;lhk; eguhy; 8 ehl;fspYk; nra;a KbAk;. xU rpWtdpd; cjtpiaf; nfhz;L mth;fs; ,e;j Ntiyia 3 ehl;fspy; nra;J Kbf;fpd;wdh;. me;jj; njhif vt;thW gphpf;fg;gl Ntz;Lk;?






a. In the adjoining figure M, N, P are the midpoints of the sides of the

rectangle ABCD. If the sides of the rectangle are 14 cm and 8 cm, then the area of the shaded portion is

14 nr.kP kw;Wk; 8 nr.kP vd;w gf;fq;fisf; nfhz;l ABCD nrt;tfj;jpy; M, N, P vd;w eLg;Gs;spfis ,izj;J cUthf;fg;gLk; cUtfj;jpd; epoyplg;gl;l gFjpapd; gug;G fhz;f

Solution:

b. A cuboid shaped slab of iron whose dimensions are 55 cm 40 cm 15 cm is melted and recast into a pipe. The outer diameter and thickness of the pipe are 8 cm and 1 cm respectively. Find the length of the pipe. 55 nr.kP 40 nr.kP. 15nr.kP vd;w msTfs; nfhz;l fdr;nrt;tf tbt jpz;k ,Uk;Gg; gyif cUf;fg;gl;L xU Fohahf thh;f;fg;gLfpwJ. mf;Fohapd; ntsp tpl;lk; kw;Wk; jbkd; KiwNa 8 nr.kP. kw;Wk; 1 nr.kP. vdpy;> mf;Fohapd; ePsj;ijf; fhz;f.



23. The educational qualifications of 100 teachers of a Government

higher secondary school are tabulated below

If a teacher is selected at random what is the probability that the chosen

teacher has

(i) Master degree only

(ii) M.Phil and age below 30

(iii) only a bachelor degree and age above 40

(iv) only a master degree and in age 30-40

(v) M.Phil and age above 40



fy;tp epiy taJ

Ma;tpay; epiwQh;

KJfiyg; gl;lk;

,sq;fiyg; gl;lk;

30-f;F fPo; 5 10 10 30-40 tiu 15 20 15 40-w;F Nky; 5 5 15 xU Mrphpaiu rktha;g;G Kiwapy; Njh;e;njLf;Fk; NghJ mth;

(i) KJfiyg; gl;lk; tiu ngw;wtuhf ,Uf;f

(ii) 30 tajpw;F FiwthdtUk; Ma;tpay; epiwQh; gl;lk; ngw;wtuhfTk; ,Uf;f

(iii) 40 tajpw;F Nkw;gl;ltuhfTk; ,sq;fiyg; gl;lk; ngw;wtuhfTk; ,Uf;f

(iv) 30 taJ Kjy; 40 tajpw;Fl;gl;ltuhfTk; KJfiyg; gl;lk; ngw;wtuhfTk; ,Uf;f

(v) 40 tajpw;F Nkw;gl;ltuhfTk; Ma;tpay; epiwQh;(M.Phil) gl;lk;

ngw;wtuhfTk; ,Uf;f epfo;jfT vd;d?

Solution; Total no. of teachers =n(S)=100 (i) No. of teachers having master degree only = n (A) = 10 + 20 + 5= 35





PRACTICE TEST - BETA Time: 1 ¼ Hrs Total Mark: 100

10 x 3 = 30

Answer all the questions not exceeding 30 words each 1. State De-Morgan‟s theorems.

bkhh;fd; Njhw;wq;fis vOJf. Solution:

Theorem 1: A+B A B

Theorem 2: A B A B

2. State the associative law.

njhlh;G tpjpapid tpsf;Ff. Solution:

A mathematical function is associative if its operands can be grouped in any order without affecting the result. In other words the order in which one does the OR operation does not affects then result. (A + B) +C = A+(B+C) = (A+C) +B Similarly the order in which one does the AND operation does not affect the result. (AB)C = A(BC) = (AC)B

xU ,af;fp mLj;jLj;J gy Kiw ,af;fg;gLk; NghJ> mtw;wpy; ve;j ,af;fp Kjypy; ,af;fg;gl;lhYk; xNu tpil fpilf;Fk; vd;why;> me;j ,af;fpf;F njhlh;G tpjp nghUe;Jk; vz;fisg; nghUj;jtiu $l;lYf;Fk;> ngUf;fYf;Fk; njhlh;G tpjpfs; nghUe;Jk; fopj;jYk;> tFj;jYk; nghUe;jhJ.

AND, OR ,af;fpfSf;F njhlh;G tpjp nghUe;Jk;.

(A + B) +C = A+(B+C) = (A+C) +B

(AB)C = A(BC) = (AC)B

3. H.C.F of 81 729 6561, ,

576 288 144

kP.ng.t. fhz; 81 729 6561, ,

576 288 144 Solution:

HCF Numerator

LCMdenominatorHCF HCF= 81; LCM=576

81 9

576 64HCF

4. The greatest number of 4 digit which is divisible by 20,25,60 and 100 is vz;fs; 20> 25> 60 kw;Wk; 100 My; tFgLk; kpfg; nghpa ehd;F ,yf;f vz;



Solution: LCM (20, 25, 60, 100) =300 The greatest number of 4 digit = 9999. 9999 divisible by 300 get the remainder is 99 Required Number 9999-99=9900 Ans: 9900

5. If the price of sugar is increased from Rs.6 per kg to Rs. 7.50 per kg, then how much use of

sugar a person should reduce so that the expenditure on sugar does not change? xU fpNyh rh;f;fiuapd; tpiy &gha; 6ypUe;J &gha; 7.50 Mf cah;fpwJ vdpy;; rh;f;fiu cgNahfpf;Fk; msT vt;tsT rjtPjk; Fiwj;jhy; mjd; nrytpdj;jpy; vt;tpj khw;wKk; Vw;glhJ? Solution: Price Increased = 7.50 – 6 = 1.50

Percentage Increase = 1.5

100 25%6

Reduce the expenditure = 100 100 25

20%100 125

R

R

6. Two dice are thrown together. Find the probability that the two digit number formed with

the two numbers turning up is divisible by 3. ,U gfilfs; xU Nru cUl;lg;gLfpd;wd. Kf vz;fisf; nfhz;L mikf;fg;gLk; <hpyf;f vz; 3 My; tFgLk; vz;zhf ,Ug;gjw;fhd epfo;jfT fhz;f. Solution Two dice = { (1,1) (1,2) (1,3) (1,4) (1,5) (1, 6) (2,1) (2,2) (2,3) (2,4) (2,5) (2, 6) (3,1) (3,2) (3,3) (3,4) (3,5) (3, 6) (4,1) (4,2) (4,3) (4,4) (4,5) (4, 6) (5,1) (5,2) (5,3) (5,4) (5,5) (5, 6) (6,1) (6,2) (6,3) (6,4) (6,5) (6, 6) } n(S) = 36 Let A be the event of two digit number formed with two numbers turning up is divisible by 3. Then A = {12, 21, 24, 42, 33, 15, 51, 36, 63, 45, 54, 66 } n(E) = 12

Here ( ) 12 1

( )( ) 36 3

n AP A

n S

7. A die is thrown twice. Find the probability that at least one of the two throws comes up

with the number 5 (use addition theorem). xU gfil ,UKiw cUl;lg;gLfpwJ. Fiwe;jJ xU cUl;lypyhtJ vz; 5 fpilg;gjw;fhd epfo;jftpidf; fhz;f ($l;ly; Njw;wj;ijg; gad;gLj;Jf) Solution In rolling a die twice, the sample space, n(S) = 36



Let A be the event of getting 5 in the first throw. A = { (5,1) (5,2) (5, 3) (5,4) (5,5) (5,6)}

Then n(A) = 6, and P(A) 6

36

Let B be the event of getting 5 in the second throw B = { (1,5) (2,5) (3,5) (4,5) (5,5) (6,5) }

Then n(B) = 6, and P(B) 6

36

A and B are not mutually exclusive events, since 5,5A B

1

136

n A B and P A B

By addition theorem, ( ) ( ) ( )P A B P A P B P A B

6 6 1 11

36 36 36 36

8. Ram and Shyam can do a work in 8 days. Ram worked for 6 days and Shyam completed the remaining work in 10 days. In how many days can Shyam alone finish the work? xU Ntiyia uhKk; ~pahKk; Nrh;e;J 8 ehl;fspy; Kbg;gh;. mt;Ntiyia uhk; njhlq;fp 6 ehl;fSf;F gpd; tpyfp> kPjKs;s Ntiyia ~pahk; 10 ehl;fspy; Kbf;fpwhh; vdpy; ~pahk; jdpahf nkhj;j Ntiyia Kbf;f vj;jid ehl;fs; MFk;. Solution:

6 3Their workfor 6days

8 4

Work done by Shyam in (10-6) or 4 days 3 1

14 4

Shyam can do the work in 4 4 days = 16days

9. 4 men 3 boys can do a work in 5 days whereas 3 men and 4 boys can do the same work in 6 days. If daily wages of a man is ì 180, find the daily wages of a boy. 4 Mz;fs; kw;Wk; 3 rpWth;fs; Nrh;e;J xU Ntiyia 5 ehl;fspy; Kbg;gh;. mNj Ntiyia 3 Mz;fSk; kw;Wk; 4rpWth;fSk; Nrh;e;J 6 ehl;fspy; Kbg;gh;. xU Mzpd; jpdf;$yp &.180 vdpy; xU rpWtdpd; jpdf;$yp vt;tsT? Solution: (4M + 3B) 5=(3M + 4B) 6

20M+15B 18 24

2 9

9

2

9 180

2 40

M B

M B

M

B

Men unit

Boy Unit



10. A bag contains coins of ì 1, ì 2 and ì 5 denomination in the ratio 2: 3: 4. If the total amount is ì 280. Find the number of coins of ì 5 denominations. xU igapy; &.1> &.2 kw;Wk; &.5 ehzaq;fspd; vz;zpf;if tpfpjq;fs; KiwNa 2:3:4. ,itfspd; nkhj;j kjpg;G &.280. vdpy; &.5 ehzaj;jpd; vz;zpf;if vt;tsT?

Denomination of coins (in Rupees) are 1, 2 and 5. Ratio of number of coins = 2:3: 4

Value of coins (in rupees) = Denomination of coins Ratio of coins

= 12 : 23 : 54 = 2 : 6 : 20 Sum of ratios of value of coins = 2+6+20=28 28 unit = 280 Rs number of 5 rupee coins = 4 * 10 = 40 coins

5 x 8 = 40

Answer all the questions not exceeding 120 words each

11. Eight men and twelve boys can finish a piece of work in 10 days while six men and eight boys can finish the same work in 14 days. Find the number of days taken by one man alone to complete the work and also one boy alone to complete the work.

8 Mz;fs; kw;Wk; 12 rpWth;fs; Nrh;e;J xU Ntiyia 10 ehl;fspy; nra;J Kbg;gh;. mNj Ntiyia 6 Mz;fs; kw;Wk; 8 rpWth;fs; Nrh;e;J 14 ehl;fspy; nra;J Kbg;gh;. xU Mz; jdpahf mt;Ntiyia vj;jid ehl;fspy; nra;J Kbg;ghh;? xU rpWtd; jdpahf mt;Ntiyia vj;jid ehl;fspy; nra;J Kbg;ghd;?

1 1 2 2

8 12 10

6 8 14

(8 12 ) 10 (6 8 ) 14

M B days

M B days

M D M D

M B M B

40 60 42 56

2 4

2

M B M B

M B

M B

(1) 16 12 28

28 10

1 ?

Eqn B B B

B days

B

28 10280

1

(1) 1 2 6 12

8 6 14 10

1 ? 140

days

Eqn M B M B

M M M days

M days

1 Boy Complete a work in 280 days 1 Men Complete a work in 140 days



12. Give an account on Boolean Algebra.

G+ypad; fzpjj;ij tpthp:

Boolean algebra is a mathematical discipline that is used for designing digital circuits in a digital computer. It describes the relation between inputs and outputs of a digital circuit. The name Boolean algebra has been given in honor of an English mathematician George Boole who proposed the basic principles of this algebra. As with any algebra Boolean algebra makes use of variables and operations (functions). A Boolean variable is a variable having only two possible values such as true or false or as 1 or 0. The basic logical operations are AND, OR and NOT which are symbolically represented by dot plus sign and by overbar/single apostrophe. Example: A AND B = A.B A OR B = A+B NOT A = A‟ (orA) A Boolean expression is a combination of Boolean variables and the logical operators. All possible operations in Boolean algebra can be created from basic logical operators. There are no negative or fractional numbers in Boolean algebra. The operation AND yields true (binary value 1) if and only if both of its operands are true. The operation OR yields true if either or both of its operands are true. The unary operation NOT inverts the value of its operand. The basic logical operations can be defined in a form known as Truth Table which is a list of all possible input values and the output response for each input combination.

[hh;[; G+y; vd;Dk; Mq;fpNyauhy; Njhw;W tpf;fg;gl;l fzpjk; ,J. fzpg;nghwpapy; ,Uepiy Kiwpay; fzpg;Gfisr; nra;aj; Njitahd Rw;Wfis tbtikg;gjpd; mbg;gilj; jj;Jtk; ,e;j G+ypad; fzpjk; jhd;. ,J xU Rw;wpd; cs;sPl;bw;Fk;> ntspaPl;bw;Fk; cs;s njhlh;gpidf; $w cjTfpwJ.

,e;jf; fzpjj;jpy; khwp (Variable), khwpyp(constant), rhh;G(function) kw;Wk; ,af;fpfs;

(operators) cz;L. ,q;F 0> 1 my;yJ nka;> ngha; vd ,uz;L khwpypfs; kl;LNk

cs;sd.

khwp kw;Wk; khwpypfis ,izf;Fk; %d;W ,af;fpfs; cs;sd. mit. AND, OR

kw;Wk; NOT, ,it KiwNa ‘mJTk; ,JTk;;> ‘my;yJ’ kw;Wk; ‘,y;iy’ vd;w nghUs;gLk;

nray;fisr; nra;Ak;. ,tw;iw KiwNa Gs;sp> $l;ly; Fwp> mgh];l;u/gp Fwp my;yJ Nky; NfhL vd;gtw;why; Fwpg;gplyhk;. vLj;Jf;fhl;L:

A AND B = A.B

B OR B = A + B

NOT A = A‟ (or A )



G+ypad; khwpfs;> khwpypfs; kw;Wk; ,af;fpfisf; nfhz;L vOjg;gLk; njhlh;. G+ypad; njhlh; vdg;gLk;.

AND kw;Wk; OR ,af;fpfSf;F ,U tpid Vw;gpfs; Njit. ,uz;Lk; 1 vd;w kjpg;G

nfhz;bUe;jhy; kl;LNk. AND vd;w ,af;fp 1 vd;w tpiliaf; nfhLf;Fk;. kw;w rkaq;fspy; 0 vd;w tpiliaf; nfhLf;Fk;.

VjhtJ xd;wpd; kjpg;G 1 vd;whNyNa OR ,af;fp 1 vd;w tpil nfhLf;Fk;. ,uz;LNk

0 vd;why; tpilAk; 0.

‘,y;iy’ vd;Dk; ,af;fp xNu xU tpid Vw;gpapd; kPJjhd; nray;gLk;. me;j tpid Vw;gpapd; kjpg;ig khw;wpf; nfhLf;Fk;. 1 vd;why; 0 vdTk;> 0 vd;why; 1 vdTk; khw;wp tpLk;. ,e;j %d;W ,af;fpfspd; nray;ghLfisAk; tiuaWf;Fk; gl;baiy vspjhfj; jahhpf;fyhk;. mJ nka;g;gl;bay; vdg;gLk;.

13. To win an election, a candidate needs 3

4of the vote cast. If after

2

3of the vote have been

counted, a candidate has 5

6of what he needs, then what part of the remaining

xU Ntl;ghsh; ntw;wp ngw gjpthd thf;Ffspy; 3

4ghfk; Njitg;gLfpwJ.

2

3gFjp

Xl;Lfs; vz;zg;gl;l gpd;dh;> Njitapy; 5

6gFjp thf;Ffs; ngw;wpUe;jhy;. ,d;Dk;

kPjKs;s thf;Ffspy; vj;jid gFjp mtUf;F ,d;Dk; Njitg;gLfpwJ.



14. Answer the following questions

gpd;tUk; tpdhf;fSf;F tpilasp a) When teams of the same size are formed from three groups of 512, 430 and 489 students

separately 8, 10 and 9 students respectively are left out. What could be the largest size of the team? 512> 430 kw;Wk; 489 vd;w khzth;fspd; vz;zpf;if cila %d;W FOf;fspypUe;J xNu rk vz;zpf;ifapyhd FOf;fis Njh;T nra;Ak; NghJ KiwNa 8> 10 kw;Wk; 9 khzth;fs; ntspNaWfpd;wdh;. vdpy; ,k;%d;W FOf;fspy; mjpfgl;r FOtpd; vz;zpf;if vt;tsT.

b) The product of two 2 digit numbers is 2028 and their GCM is 13. The numbers are. ,uz;L vz;fspd; ngUf;fw;gyd; 2028 kw;Wk; ,itfspd; kP.ng.t. 13. vdpy; me;j vz;fs; ahJ?


a) A man and his wife appear in an interview for two vacancies in the same post. The

probability of husband's selection is (1/7) and the probability of wife's selection is (1/5). What is the probability that only one of them is selected?



xU fztDk; kidtpAk; xNu gjtpf;fhd> ,uz;L fhypaplq;fSf;fhd Neh;Kfj; Njh;tpy; fztd; ntw;wp ngw epfo;jfT 1/7 kw;Wk; kidtp ntw;wp ngw epfo;jfT 1/5 vdpy; ,t;tpUtupy; xUtUf;F mg;gjtp fpilf;f epfo;jfT ahJ?

b) A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability

that it will be a spade or a king. ed;F fiyj;J mLf;fp itf;fg;gl;l 52 rPl;Lfisf; nfhz;l rPl;Lf; fl;bypUe;J rktha;g;G Kiwapy; xU rPl;L vLf;fg;gLfpwJ. me;jr; rPl;L ];NglhfNth (Spade) my;yJ ,uhrhthfNth (King) ,Ug;gjw;fhd epfo;jftpidf; fhz;f Solution Let A be the event of drawing a spade card. Then n(A) = 13

( ) 13

( )( ) 52

n AP A

n S

Let B be the event of drawing a king card n(B) = 4

( ) 4

( )( ) 52

n BP B

n S

Then A B is the event of drawing a spade king. n( A B )=1

P( A B )1

52

P(A or B) = P( A B ) = P(A) + P(B) - P( A B )

13 4 1

52 52 52

16 4

52 13



2 x 15 = 30 Answer all the questions not exceeding 250 words each


gpd;tUk; tpdhf;fSf;F tpilasp a. Give an account on ASCII code. ASCII code vd;gJ vd;d?

Different types of coding schemes are used to represent the character set and numbers. The most commonly used coding scheme is the American Standard Code for Information Interchange (ASCII). Each binary value between 0 and 127 is used to represent a specific character. The ASCII value for a blank character (blank space) is 32 and the ASCII value of numeric 0 is 48. The range of ASCII values for lower case alphabets is from 97 to 122 and the range of ASCII values for the upper case alphabets is 65 to 90.

ciuapy; cs;s Mq;fpy vOj;Jf;fs;> gjpd;k ,yf;fq;fs; kw;Wk; rpwg;Gf; FwpaPLfisAk;> xU

igl;ilf; nfhz;L Fwpg;gplyhk;. ,jw;fhd xU Kiw M];fp FwpaPL (American Standard Code for

Information interchange – ASCII) ,J fzpg;nghwpfspy; ,d;W ngUksT gad;gLfpwJ. ,jpy; 0

Kjy; 127 tiuapy; cs;s kjpg;Gfs; gad;gLfpd;wd. Mq;fpy vOj;Jfspy; fPo;epiy vOj;Jf;fs; 26I M];fp FwpaPLfs; 65 Kjy; 57 tiuAk;. Fwpg;gpLfpd;wd. ,ilntspf;fhd FwpaPL 32.

b. Distinguish between MSB and LSB.

tiuaW: MSB kw;Wk; LSB

The leftmost bit in the binary number is called the most significant bit (MSB) and it has the largest positional weight. The rightmost bit is the least significant bit (LSB) and has the smallest positional weight.

To write the binary equivalent of the decimal number, read the remainders from the bottom upward as (23)10 = (10111)2

vy;v];gp (LSB – Least Significant Bit) vd;gJ rpW kjpg;G gpl; vd;gijAk; vk;v];gp (MSB – Most

Significant Bit) vd;gJ ngU kjpg;G gpl; vd;gijAk; Fwpf;Fk;.



vLj;Jf;fhl;L:

2310 vd;gij ,Uepiy Kiwf;F khw;Wf.

<T kPjp

23/2 11 1 (LSB)

11/2 5 1

5/2 2 1

2/2 1 0

1/2 0 1 (MSB) nfhLj;j vz;iz ,UepiyKiw vz;zhf khw;w> ,e;j kPjpfis fPopUe;J Nkyhf vLj;J> ,lkpUe;J tykhf vOjTk;.

2310 = 101112

c. Write a basic concepts of flip –flop. /gpspg;/g;shg;Gfspd; mbg;gil epiyiaf; $Wf?

A flip-flop circuit can be constructed using either two NOR gates or two NAND gates. A common example of a circuit employing sequential logic is the flip-flop, also called a bi-stable gate.

Thus a basic flip-flop has two useful states. When Q=1 and Q =0, it is called as set state. When

Q=0 and Q =1, it is called as reset state.

,uz;L ehz;l; my;yJ ,uz;L ehh; thapy;fis itj;J xU /gpshg;/g;shg;gpid mikf;fyhk;. njhlh;r; Rw;Wf;F ,J Xh; vLj;Jf;fhl;L Xh; vspa /gpspg;/g;shg;gpy; ,U jplkhdd epiyfs; (0>1) cz;L. ,ijj; njhe;juT nra;ahj tiuapy; mNj epiyapy; ePbf;Fk;. xU kpd; Jbg;gpid cs;Ns nrYj;jpdhy;jhd; ,Uf;Fk; epiyia ntspapLk; gpd;dh; cs;sPl;bw;Nfw;g jd; epiyia khw;wpf; nfhs;Sk;.


gpd;tUk; tpdhf;fSf;F tpilasp

a) A and B can complete a piece of work in 12 and 18 days respectively. A begins to do the work and they work alternatively one at a time for one day each. The whole work will be completed in: xU Ntiyia A-vd;gth; 12 ehl;fspYk; B-vd;gth; mNj Ntiyia 18 ehl;fspYk; Kbj;jdh;. Ntiyia ,t;tpUtUk; xU ehs; tpl;L xU ehs; nra;Ak; NghJ KjyhtJ ehspy; A Ntiyia njhlq;Ffpwhh; vdpy; Ntiyia Kbf;f vt;tsT ehl;fs; MFk;?



b) A started a work and left after working for 2 days. Then B finished the remaining work in 9 days. Had A left the work after working for 3 days, B would have finished the remaining work in 6 days. In how many days B alone can finish the work? xU Ntiyia A njhlq;fp ,uz;L ehl;fSf;F gpwF tpyfp> kPjKs;s Ntiyia B 9 ehl;fspy; Kbf;fpd;whh;. khw;whf ,t;Ntiyia A Jtq;fp 3 ehl;fSf;Fg;gpwF tpyfp kPjKs;s Ntiyia B 6 ehl;fspy; Kbg;ghh; vdpy;> nkhj;j Ntiyia B Kbf;f vj;jid ehl;fs; MFk;?



PRACTICE TEST – GAMMA Time: 1 Hrs Total Mark: 90

10 x 3 = 30


1. What is a Boolean expression? G+ypad; njhlh;fs; vd;why; vd;d? A Boolean expression is a combination of Boolean variables and the logical operators. All possible operations in Boolean algebra can be created from basic logical operators. There are no negative or fractional numbers in Boolean algebra. G+ypad; khwpfs;> khwpypfs; kw;Wk; ,af;fpfisf; nfhz;L vOjg;gLk; njhlh;. G+ypad; njhlh; vdg;gLk;.

AND kw;Wk; OR ,af;fpfSf;F ,U tpid Vw;gpfs; Njit. ,uz;Lk; 1 vd;w kjpg;G

nfhz;bUe;jhy; kl;LNk. AND vd;w ,af;fp 1 vd;w tpiliaf; nfhLf;Fk;. kw;w rkaq;fspy; 0 vd;w tpiliaf; nfhLf;Fk;.

2. State the commutative law ,lkhw;w tpjp vd;why; vd;d? A mathematical operation is commutative if it can be applied to its operands in any order without affecting the result. Addition and multiplication operations are commutative. Example : A+B = B+A AB = BA ,U tpid Vw;gpfis Vw;Fk; ,af;fp. me;j tpid Vw;gpfs; tUk; thpir vJthf ,Ue;jhYk;> xNu tpiliaf; nfhLj;jhy;> mJ ,lkhw;w tpjpf;F cl;gLfpwJ vdg;gLk;. vLj;Jf;fhl;lhf ,U vz;fisf; $l;Lk;NghJ> ve;j vz; Kjypy; tUfpwJ vd;gJ Kf;fpakpy;iy.

Example: A+B = B+A

AB = BA

3. Find Least Common Multiple of 4 3

,5 10

and 7

15.

4 3,

5 10 kw;Wk;

7

15Mfpatw;wpd; kPr;rpW nghJ klq;if fhz;:

Solution

min

LCM NumerotorsLCM

HCF Deno ators

LCM (4, 3, 7) = 84 HCF (5, 10, 15) = 5

84

5LCM



4. The least number of 4 digit which is divisible by 8, 10 and 12 is

vz;fs; 8, 10 kw;Wk; 12 My; tFgLk; kpfr; rpwpa ehd;F ,yf;f vz; Solution LCM (8, 10, 12) = 120 1000 divisible by 120 get the remainder 40 Required Number = 1000 – 40 + 120 = 1080

5. The price of a cloth is increased by 60%. How many percent should a family reduce its expenditure of cloth so as not to increase its monthly expenditure? Jzpapd; tpiy 60% cah;e;Js;s epiyapy;> xU FLk;gj;jpd; khjr; nrytpdk; mjpfhpf;fhky; ,Ug;gjw;F> mth;fs;; Jzpf;fhf nrytpy; vt;tsT rjtPjk; Fiwf;f Ntz;Lk;?

Solution 100 100 60

37.5%100 160

R

R

6. Two dice are thrown together. Find the probability that the two digit number formed with the two numbers turning up is divisible by 3. ,U gfilfs; xU Nru cUl;lg;gLfpd;wd. Kf vz;fisf; nfhz;L mikf;fg;gLk; <hpyf;f vz; 3 My; tFgLk; vz;zhf ,Ug;gjw;fhd epfo;jfT fhz;f. Solution Two dice = { (1,1) (1,2) (1,3) (1,4) (1,5) (1, 6) (2,1) (2,2) (2,3) (2,4) (2,5) (2, 6) (3,1) (3,2) (3,3) (3,4) (3,5) (3, 6) (4,1) (4,2) (4,3) (4,4) (4,5) (4, 6) (5,1) (5,2) (5,3) (5,4) (5,5) (5, 6) (6,1) (6,2) (6,3) (6,4) (6,5) (6, 6) } n(S) = 36 Let A be the event of two digit number formed with two numbers turning up is divisible by 3. Then A = { 12, 21, 24, 42, 33, 15,51, 36, 63, 45, 54, 66 } n(E) = 12

Here ( ) 12 1

( )( ) 36 3

n AP A

n S

7. Three dice are thrown simultaneously. Find the probability of getting the same

number on all the three dice. %d;W gfilfs; xNu Neuj;jpy; cUl;lg;gLk;NghJ> %d;W gfilfspYk; xNu vz; fpilg;gjw;fhd epfo;r;rpapd; epfo;jftpidf; fhz;f Solution: Total Events = 216 (1, 1, 1) (2, 2, 2), (3, 3, 3) (4, 4, 4) (5, 5, 5) (6, 6, 6)

Probability = 6 1

216 36



8. A did three-fourth of a work in 15 days. With the help of B, he finished the remaining work in 3 days. Find the ratio in which the wages earned by them, is to be distributed? A 4y; 3 gq;F Ntiyia 15 ehl;fspYk;> mth; B apd; cjtpAld; kPjKs;s Ntiyia 3 ehl;fspy; Kbj;jhh; vdpy;. mth;fs; nra;j Ntiyapd; tpfpjk; ahJ? Solution:

9. A is twice as good as workman as B and together they finish a piece of work in 18 days. In how many days will B alone finish the work. A-d; Ntiy nra;Ak; jpwdhdJ B-I Nghy; ,uz;L klq;F. ,t;tpUtUk; xU Ntiyia 18 ehl;fspy; Kbf;fpd;wdh; vdpy; B jdpahf mt;Ntiyia Kbf;f vj;jid ehl;fs; MFk;?

Solution:

Let B be x and A be 2x (A+B)'s 18 days' work=1 (A+B)'s 1 days' work=1/18 This can also be written as x+2x=1/18 3x=1/18 x=1/54 Thus, B alone can do a piece of work in 54 days.

10. A bag contains ì 114 in the form of 1 rupee, 50 paisa and 10 paisa coins in the ratio 3: 4: 10. What is the number of 50 paisa coins? xU igapy; &.1> 50 igrh kw;Wk; 10 igrh ehzaq;fspd; vz;zpf;if tpfpjq;fs; KiwNa 3:4:10. ,itfspd; nkhj;j kjpg;G &. 114. vdpy; 50 igrh ehzaj;jpd; vz;zpf;if vt;tsT?

Solution

Denomination of coins 100p 50p 10p Ratio of coins 3 4 10 Value of coins 300 200 100 Total value = 300+200+100=600paise =Rs.6

Number of 50 paise coins 114

4 766

3 x 10 = 30



Answer all the questions not exceeding 120 words each 11. Eight men and twelve boys can finish a piece of work in 10 days while six men and

eight boys can finish the same work in 14 days. Find the number of days taken by one man alone to complete the work and also one boy alone to complete the work. 8 Mz;fs; kw;Wk; 12 rpWth;fs; Nrh;e;J xU Ntiyia 10 ehl;fspy; nra;J Kbg;gh;. mNj Ntiyia 6 Mz;fs; kw;Wk; 8 rpWth;fs; Nrh;e;J 14 ehl;fspy; nra;J Kbg;gh;. xU Mz; jdpahf mt;Ntiyia vj;jid ehl;fspy; nra;J Kbg;ghh;? xU rpWtd; jdpahf mt;Ntiyia vj;jid ehl;fspy; nra;J Kbg;ghd;?

1 1 2 2

8 12 10

6 8 14

(8 12 ) 10 (6 8 ) 14

M B days

M B days

M D M D

M B M B

40 60 42 56

2 4

2

M B M B

M B

M B

(1) 16 12 28

28 10

1 ?

Eqn B B B

B days

B

28 10280

1

(1) 1 2 6 12

8 6 14 10

1 ?

140

days

Eqn M B M B

M M M days

M

days

1 Boy Complete a work in 280 days 1 Men Complete a work in 140 days

12. What are logical operations? How are they represented? G+ypad; fzpjj;jpy; gad;gLk; ,af;fpfs; ahit? mit vt;thW Fwpf;fg;gLfpd;wd. The basic logical operations are AND, OR and NOT which are symbolically represented by dot plus sign and by over bar/ single apostrophe. Example: A AND B = A.B A OR B = A + B NOT A = A‟ (or A) AND GATE



OR operator

NOT OPERATOR


a) Two dice are rolled simultaneously. Find the probability that the sum of the numbers on the faces is neither divisible by 3 nor by 4.

,U gfilfs; xNu Neuj;jpy; Nru cUl;lg;gLk; NghJ fpilf;Fk; Kf vz;fspd; $Ljy; 3 My; kw;Wk; 4 My; tFglhkypUf;f epfo;jfT fhz;f Solution:



b) A committee of 5 Students is to be chosen from 6 boys and 4 girls. Find the probability that the committee contains exactly 2 girls.

6 rpWth;fs; kw;Wk; 4 rpWkpfs; nfhz;l FOtpy; ,Ue;J VNjDk; 5 egh;fis Njh;e;njLf;Fk; NghJ mjpy; ,uz;L rpWkpfs; fz;bg;ghf ,Uf;f epfo;jfT ahJ? Solution: No of ways of choosing 5 students from 10 = 10C5 = 10*9*8*7*6/5*4*3*2 = 2*3*7*6 No ways of choosing 2 girls from 4 = 4c2 = 6 no of ways of choosing 2 boys from 6 = 6C3 = 20 Probability = 6 * 20/2*3*7*6 = 10/21





a) Mention the different kinds of Flip –flop circuits. What is the use of flip-flop

circuits? /gpsg;/g;shg;Gfspy; cs;s tiffis vOJf? fzpg;nghwpapd; xUq;fik Rw;Wfspy; Kf;fpa gq;fhw;WtJ vJ? Solution:

There are several kinds of flip-flop circuits, with designators such as D, T, J-K, and R-S. Flip- flop circuits are interconnected to form the logic gates that comprise digital integrated circuits (ICs) such as memory chips and microprocessors.

/gpspg;/g;shg;Gfspy;> R-S, J-K, D, Tvd gy tiffs; cz;L kw;w Rw;WfSld; ,it ,ize;J

nrayhw;Wk;. njhlh; Rw;Wfspy; xU Neuf;$wpy; tUk; ntspaPl;bid epidtpy; itj;J mLj;J Neuf;$wpy; nfhLf;Fk; epidtfkhf ,J nray;gLfpwJ. vdNt fzpg;nghwpapd; xUq;fik Rw;Wfspy; ,J xU Kf;fpa gq;fhw;WfpwJ.

b) Tabulate the different memory sizes in which the computer memory is measured. ntt;NtW epidtf msTfs; nfhz;l fzpdp epidtf msTfis gl;baypLf. Solution:

The different memory sizes in which the computer memory is measured are:

Name Abbreviation Size (Bytes)

Kilo K 2^10

Mega M 2^20

Giga G 2^30

Tera T 2^40

Peta P 2^50

Exa E 2^60

Zetta Z 2^70

Yotta Y 2^80


a) Two pipes A and B can fill a cistern in 6 and 8 minutes respectively. If they be turned on alternatively for one minute each, how long will it take to fill the cistern? xU njhl;bia A kw;Wk; B Foha;fs; KiwNa 6 kw;Wk; 8 epkplq;fspy; epug;Gfpd;wd. ,t;tpUtUk; Foha;fSk; xU epkplk; tpl;L xU epkplk; epug;Gk; NghJ KjyhtJ epkplj;jpy; A Foha; epug;g njhlq;FfpwJ. vdpy; mj;njhl;bia KOtJkhf epug;g vt;tsT epkplq;fs; MFk;?



b) A and B can separately do a piece of work in 45 days and 40 days respectively. They worked together for some time, and then B completed the remaining work in 23 days. Find the number of days A had worked for: A kw;Wk; B xU Ntiyia KiwNa 45 ehl;fs; kw;Wk; 40 ehl;fspy; Kbg;gh;. ,t;Ntiyia ,t;tpUtUk; njhlq;fp rpy ehl;fSf;Fg; gpwF A tpyfpa gpd;G kPjKs;s Ntiyia B 23 ehl;fspy; Kbf;fpwhh;. vdpy; ,t;Ntiyia A vj;jid ehl;fspy; gzpGhpe;jhh;. Solution

1 23B's work for last 23days= ×23=

40 40

23 17Remaining work=1- = isdone by A and Btogether

40 40

17 45×40Time taken by them = × =9days

40 85

A worked for 9 days.



PRACTICE TEST – DELTA

Time: 45 Minutes 6 x 3 = 18 Answer all the questions not exceeding 30 words each

1. Find the rate percent at which a sum of money becomes 7

6times in 3 years.

xU mryhdJ 3 tUlj;jpy; 7

6klq;fhf MFnkdpy; mjd; tl;b tpfpjk; vt;tsT?

Solution

N= 3year P = x A = 7

6x SI =

1

6x

1 3

6 100

50 55 %

9 9

x Rx

R

2. A shopkeeper mixes 20 kgs of rice which cost Rs.5per kg with 35kg of rice which cost Rs.7per kg. Then he sells the mixture at Rs.6.50 per kg. Find his profit percentage. xU filf;fhuh; jd;dplk; ,Ue;j &.5 mlf;f tpiyAs;s 20fp mhprpiaAk;. &.7 mlf;f tpiyAs;s 35 fpNyh mhprpiaAk; xd;whf fye;J fpNyh &.6.50f;F tpw;why; mtUf;F fpilf;Fk; yhgj;jpd; rjtPjk; vd;d? Solution

Cost price of 55 kg rice = [20 5] + [35 7 ]= 345

Selling price of 55 kg rice = 55 6.50 = 375.50 Profit = SP – CP = 375.50 – 345 = 12.50

Pr 12.50 250 43100 100 3 %

345 69 69

ofitGain

CP

3. A sector containing an angle of 180 is cut off from a circle of radius 7 cm and folded into a

cone. Find the curved surface area of the cone

7nr.kP MuKs;s xU tl;lj;jpypUe;J 180ika Nfhzk; nfhz;l xU tl;lf; Nfhzg;gFjpia ntl;bnaLj;J. mjd; Muq;fis xd;wpizj;J xU $k;ghf;fpdhy; fpilf;Fk; $k;gpd; tisgug;ig fhz;f Solution: Area of sector = Curved Surface Area of Cone

CSA = 2

360r

=

180 227 7

360 7 = 77cm

4. Traffic lights at three different junctions change simultaneously at morning 8.00 am. The first light changes once in 30 seconds, the second once in 72 seconds, the third once in 45 seconds. After 8.00am which is the next time they change simultaneously? Kt;NtW rhiy re;jpg;Gfspy; cs;s rhiy ghJfhg;G tpsf;Ffs; fhiy 8.00 kzpf;F xNu Neuj;jpy; khw;wkilfpd;wd. %d;Wk; KiwNa 30 tpdhbf;F xU juk;> 72 tpdhbf;F xU



juk;> 45 tpdhbf;F xU juk; khWfpd;wd. 8.00 Kg.gpd;G kPz;Lk; ,k;%d;Wk; vg;nghOJ xNu rkaj;jpy; khWk;? Solution: LCM of (30, 72, 45) = 360sec = 6 min Next time they change simultaneously at 8.06 AM

5. What is Lorenz curve? Mention its important. yhud;]; tistiu vd;why; vd;d? mjd; Kf;fpaj;Jtj;ij Fwpg;gpLf.

Lorenz curve is a graphical method of studying dispersion. It was introduced by Max.O.Lorenz, a great Economist and a statistician, to study the distribution of wealth and income. It is also used to study the variability in the distribution of profits, wages, revenue, etc.

6. What is a word processor software? Give Examples. nrhy; nrayp vd;why; vd;d? ,jw;F vLj;Jf;fhl;Lfs; jUf.





gpd;tUk; tpdhf;fSf;F tpilasp

a. Rs. 50 is divided among 6 men, 12 women and 17 boys so that 2 men get as much as 5

boys and 2 women as much as 3 boys. Find the share of each. &.50 I 6 Mz;fs;> 12 ngz;fs; kw;Wk; 17 rpWth;fSf;F gphpj;jspf;fg;gLfpwJ. 2 Mz;fSf;F fpilf;fg;ngWk; njhifahdJ 5 rpWth;fSf;F fpilf;Fk; njhiff;F rkk;. kw;Wk; 2 ngz;fSf;F fpilf;Fk; njhifahdJ 3 rpWth;fSf;F fpilf;Fk; njhiff;F rkk; vdpy; xt;nthUthpd; gq;F vt;tsT.

Solution: Given: 6M + 12W + 17B = Rs. 50 ----- (1) 2M = 5B and 2W = 3B 6M = 15B and 12W = 18B (1) 15B + 18B + 17B = 50 50B = 50 B = 1 Each Boy gets = Re.1 Totally 17 Boys gets = Rs. 17 Each Men gets = Rs. 2.50 Totally 6 Men gets = Rs. 15 Each women gets = Rs. 1.50 Totally 12 women gets = Rs. 18

b. The range of the first 10 prime numbers Kjy; 10 gfh vz;fspd; tPr;R Solution:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Range = L – S = 29 – 2 = 27.


a. From a well shuffled pack of 52 playing cards, one card is drawn at random. Find the probability of getting (i) a king (ii) a black king (iii) a spade card (iv) a diamond 10. ed;F fiyj;J itf;fg;gl;l 52 rPl;Lfisf; nfhz;l rPl;Lf; fl;bypUe;J rktha;g;Gr; Nrhjid Kiwapy; xU rPl;L vLf;fg;gLfpwJ. me;jr; rPl;L gpd;tUtdthf ,Uf;f epfo;jfTfisf; fhz;f (i) ,uhrh (ii) fUg;G ,uhrh (iii) ];NgL (iv) lakz;l; 10



b. A card is drawn from a deck of 52 cards. Find the probability of getting a King or a Heart or a Red card. 52 rPl;Lfisf; nfhz;l xU rPl;Lf;fl;bypUe;J rktha;g;G Kiwapy; xU rPl;L vLf;fg;gLk; NghJ> mr;rPl;L xU ,uhrh (King) my;yJ xU `hh;l; (Heart) my;yJ xU rptg;G epwr; rPl;lhff; fpilg;gjw;fhd epfo;jftpidf; fhz;f



9. A lead pencil is in the shape of right circular cylinder. The pencil is 28 cm long and its radius is 3 mm. If the lead is of radius 1 mm, then find the volume of the wood used in the pencil. xU ngd;rpyhdJ xU Neh; tl;l cUis tbtpy; cs;sJ. ngd;rpypd; ePsk; 28 nr.kP kw;Wk; mjd; Muk; 3 kp.kP. ngd;rpypDs; mike;j ikapd; (fpuh/igl;) –d; Muk; 1kp.kP vdpy;> ngd;rpy; jahhpf;f gad;gLj;jg;gl;l kug;gyifapd; fd msitf; fhz;f.



1 x 15 = 15



a. If 5 men and 3 boys can reap 23 acres in 4 days, and 3 men and 2 boys can reap 7 acres in 2 days, how many boys must assist 7 men in order that they may reap 45 acres in 6 days? 5 Mz;fs; kw;Wk; 3 rpWth;fs; Nrh;e;J 23 Vf;fh; epyj;ij mWtil nra;a 4 ehl;fs; Mfpd;wJ. 3 Mz;fs; kw;Wk; 2 rpWth;fs; Nrh;e;J 7 Vf;fh; epyj;ij mWtil nra;a 2 ehl;fshFk; vdpy; 45 Vf;fh; epyj;ij 6 ehl;fspy; mWtil nra;a 7 Mz;fSld; vj;jid rpWth;fs; Njitg;gLth;? (10 Marks) Solution:

Formulae: 1 1 2 2

1 2

M ×D M ×D=

W W

5M+3B 4 3M+2B 2

23 7

5M+3B 2 3M+2B

23 7

70 42 69 46

1 4

M B M B

M B

5 M + 3 B = 20B + 3B = 23B can reap 23 acres in 4 days ? can reap 45 acres in 6 days

2

2

M ×623×4=

23 45

M =30 boys

=30 -7×4=2boysassist them

b. Represent the following by a suitable diagram (5 Marks) fPNo nfhLf;fg;gl;Ls;s jfty;fSf;F rhpahd tpsf;fg;glk; tiuf.

Profits for 2014 (2014 k; Mz;bd; %d;W epWtdq;fspd; yhgk;)

Company A (epWtdk; A) Rs. 125000

Company B (epWtdk; B) Rs. 64000

Company C (epWtdk; C) Rs. 27000




Documents

TNPSC GROUP I MAIN: GENERAL MENTAL ABILITY PRACTICE …appolosupport.com/wp-content/uploads/2019/07/ALPHA... · Page 1 PH: 044-24339436, 42867555 TNPSC GROUP I MAIN: GENERAL MENTAL