Sample PDF Of Std 11 And 12 Based MHT CET Triumph Maths .
Written in accordance with the latest MHT-CET Paper Pattern which includes topics based onStd. XII Sci. and relevant chapters of Std. XI Sci. (Maharashtra State Board)MHT-CETTRIUMPHontentMathematicsSalient FeaturesIncludes chapters of Std. XII and relevant chapters of Std. XI as per latest MHT-CET Syllabus. Exhaustive subtopic wise coverage of MCQs. ‘6240’ MCQs including questions from various competitive exams. Chapter at a glance, Shortcuts provided in each chapter. Includes MHT-CET 2020 Question Paper (14th October) along with Answer key. Various competitive examination questions updated till the latest year. Evaluation test provided at the end of each chapter. Two Model Question Papers with answer keys and solutions provided in the form of QR Code.eC Scan the adjacent QR code todownload Model Paper II andSolution.Scan the adjacent QR code todownload Hints for relevantquestions,SolutiontoEvaluation Test and MHTCET paper 2020 in PDFformat.SamplScan the adjacent QR code todownload Model Paper I andSolution.Printed at: Print to Print, Mumbai Target Publications Pvt. Ltd.No part of this book may be reproduced or transmitted in any form or by any means, C.D. ROM/Audio Video Cassettes or electronic, mechanicalincluding photocopying; recording or by any information storage and retrieval system without permission in writing from the Publisher.Balbharati Registration No.: 2018MH0022TEID: 1919P.O. No. 1696
PREFACE“Don’t follow your dreams; chase them!”- a quote by Richard Dumbrill is perhaps the most pertinent for onewho is aiming to crack entrance examinations held after std. XII. We are aware of an aggressive competition astudent appearing for such career defining examinations experiences and hence wanted to create books thatdevelop the necessary knowledge, tools and skills required to excel in these examinations.ontentFor the syllabus of MHT-CET 2021, 80% of the weightage is given to the syllabus for XIIth standardwhile only 20% is given to the syllabus for XIth standard (with inclusion of only selected chapters).Although the syllabus for Std. XI and XII and MHT-CET is aligned, the outlook to study the subjectshould be altered based on the nature of the examination. To score in MHT-CET, a student has to be notjust good with the concepts but also quick to complete the test successfully. Such ingenuity can bedeveloped through sincere learning and dedicated practice.Having thorough knowledge of mathematical concepts, formulae and their applications is a prerequisite forbeginning with MCQs on a given chapter in Mathematics. Students must know the required rules, formulae,functions and general equations involved in the chapter. Mathematics requires understanding and application ofbasic concepts, so students should also be familiar with concepts studied in the earlier standards. They shouldbefriend ideas like Mathematical logic, inverse functions, differential equations, integration and its applicationsand random variables to tackle the problems.CAs a first step to MCQ solving, students should start with elementary questions. Once a momentum is gained,complex MCQs with higher level of difficulty should be practised. Questions from previous years as well asfrom other similar competitive exams should be solved to obtain an insight about plausible questions.Competitive exams challenge the understanding of students about the subject by combining concepts fromdifferent chapters in a single question. To figure these questions out, cognitive understanding of subject isrequired. Therefore, students should put in extra effort to practise such questions.ePromptness being virtue in these exams, students should wear time saving short tricks and alternate methodsupon their sleeves and should be able to apply them with accuracy and precision as required.Such a holistic preparation is the key to succeed in the examination!To quote Dr. A.P.J. Abdul Kalam, “If you want to shine like a sun, first burn like a sun.”mplOur Triumph Mathematics book has been designed to achieve the above objectives. Commencing from basicMCQs, the book proceeds to develop competence to solve complex MCQs. It offers ample practice of recentquestions from various competitive examinations. While offering standard solutions in the form of concisehints, it also provides Shortcuts and Alternate Methods. Each chapter ends with an Evaluation test to allow selfassessment.Features of the book presented on the next page will explicate more about the same!We hope the book benefits the learner as we have envisioned.SaThe journey to create a complete book is strewn with triumphs, failures and near misses. If you think we’venearly missed something or want to applaud us for our triumphs, we’d love to hear from you.Please write to us on: mail@targetpublications.orgA book affects eternity; one can never tell where its influence stops.From,PublisherEdition: FirstBest of luck to all the aspirants!
FEATURES1.Elementary Transformations:SymbolRi RjontentChapter at a glanceMeaningInterchange of ith and jth rowsInterchange of ith and jth columnsMultiplying the ith row by nonzero scalar kMultiplying the ith column bynon-zero scalar kAdding k times the elements ofjth row to the correspondingelements of ith rowAdding k times the elements ofjth column to the correspondingelements of ith columnCi CjRi kRiCi kCiRi Ri kRjChapter at a glance includes short andprecise summary along with Tables andKey formulae in the chapter.This is our attempt to make tools offormulae accessible at a glance for thestudents while solving problems.CCi Ci kCjChapter at a glanceShortcutseShortcutsplShortcuts to help students save timewhile dealing with questions.This is our attempt to highlightcontent that would come handywhile solving questions.1.f ( x ) f ( x ) dxf ( x)dx 2 f ( x) cf ( x) 3. [f(x)]n f (x) dx Sam2.Classical Thinking5.11. f( x) c, n 1 n 1 n 1Classical ThinkingArea under the curveArea bounded by the curve y x3, X-axis andordinates x 1 and x 4 is(A) 64 sq. units(B) 27 sq. units(C) log f(x) c127sq. units4(D)255sq. units4Classical Thinking section encompassesstraight forward questions includingknowledge based questions.This is our attempt to revise chapter inits basic form and warm up the studentsto deal with complex MCQs.
FEATURESontentCritical ThinkingCritical Thinking3.1Competitive Thinking2.6satisfying the equation tan (A)(C)If f(x) x3 – 3x has minimum value at x a, then a [MHT CET 2019](A) –1(B) –3(C) 1(D) 3mple94.Maxima and MinimaSaSubtopic wise segregationEvery section is segregated sub-topicwise.This is our attempt to cater toindividualistic pace and preferences ofstudying a chapter and enabling easyassimilation of questions based on thespecific concept.equationsandtheThe values of in between 0 and 360 and1. 150 and 300 (B) 60 and 240 (D)CCritical Thinking section encompasseschallenging questions which testunderstanding, rational thinking andapplication skills of the students.This is our attempt to take the studentsfrom beginner to proficient level insmooth steps.Trigonometricsolutions1 0 is equal to3 120 and 300 150 and 330 Competitive ThinkingCompetitiveThinkingsectionencompasses questions from variouscompetitiveexaminationslikeMHT CET, JEE, etc.This is our attempt to give the studentspractice of competitive questions andadvance them to acquire knack essentialto solve such questions.Subtopics1.11.21.31.41.51.6Derivative of Composite functionsDerivative of Inverse functionsLogarithmic DifferentiationDerivative of Implicit functionsDerivative of Parametric functionsHigher Order derivatives
ous section incorporatesMCQswhosesolutionsrequireknowledge of concepts covered indifferent sub-topics of the samechapter or from different chapters.This is our attempt to develop cognitivethinking in the students which isessential to solve questions involvingfusion of multiple key concepts.The distance from the origin to the orthocentre of thetriangle formed by the lines x y – 1 0 and6x2 – 13xy 5y2 0 is[AP EAMCET 2019](A)11 22(B)13(C)11(D)11 224C39.Evaluation TestEvaluation test1.SampleEvaluation Test covers questions fromchapter for self-evaluation purpose.This is our attempt to provide thestudents with a practice test and helpthem assess their range of preparationof the chapter.If f(x) is a polynomial of degree 2, such that2f(0) 3, f (0) 7, f (0) 8, then f ( x)dx 1(A)(C)116176(B)(D)136196
MHT-CET PAPER PATTERN There will be three papers of Multiple Choice Questions (MCQs) in ‘Mathematics’, ‘Physics andChemistry’ and ‘Biology’ of 100 marks each.Duration of each paper will be 90 minutes. Questions will be based on the syllabus prescribed by Maharashtra State Board of Secondary andontent Higher Secondary Education with approximately 20% weightage given to Std. XI and 80% weightagewill be given to Std. XII curriculum. Difficulty level of questions will be at par with JEE (Main) for Mathematics, Physics, Chemistry and atpar with NEET for Biology. There will be no negative marking. Questions will be mainly application based. Details of the papers are as given below:SubjectPaper IMathematicsPhysicsChemistryBiologyPaper IIPaper III CPaperApproximate No. of MultipleChoice Questions (MCQs) based onStd. XIStd. XII1040104010402080Mark(s) PerQuestionTotalMarks210011001100i.eQuestions will be set onthe entire syllabus of Std. XII of 2020-21 of Physics, Chemistry, Mathematics and Biologyplsubjects excluding portion which is deleted by Maharashtra State Bureau of Textbook Productionand Curriculum Research, Pune, andii.SubjectmSr. No.chapters / units from Std. XI curriculum as mentioned ters / Units of Std. XIMotion in a plane, Laws of motion, Gravitation, Thermal properties ofmatter, Sound, Optics, Electrostatics, SemiconductorsSome Basic Concepts of Chemistry, Structure of Atom, ChemicalBonding, Redox Reactions, Elements of Group 1 and Group 2, States ofMatter: Gaseous and Liquid States, Basic Principles and techniques ofChemistry, Adsorption and Colloids, HydrocarbonsTrigonometry - II, Straight Line, Circle, Measures of Dispersion,Probability, Complex Numbers, Permutations and Combinations,Functions, Limits, ContinuityBiomolecules, Respiration and Energy Transfer, Human Nutrition,Excretion and osmoregulation
CONTENTSSr.No.TextbookChapter No.Chapter NamePage No.Std. XI3Trigonometry - II125Straight Line2536Circle4848Measures of Dispersion6359Probability7061Complex Numbers9373Permutations and Content1148166Std. XII1Mathematical Logic183122Matrices200133Trigonometric Functions214144Pair of Straight Lines242155Vectors255166Line and Plane288177Linear Programming320181Differentiation338192Applications of Derivatives366203Indefinite Integration3934Definite Integration4345Application of Definite Integration4576Differential Equations46822m23pl21e1124Sa252678Probability DistributionBinomial DistributionMHT-CET 2020 Question Paper494505513Note: Questions of Standard XI are indicated by ‘*’ in each Model Question Paper.DisclaimerThis reference book is transformative work based on XIth std. textbook Mathematics; First edition: 2019 and XIIth std. textbook Mathematics;First edition: 2020 published by the Maharashtra State Bureau of Textbook Production and Curriculum Research, Pune. We the publishers are makingthis reference book which constitutes as fair use of textual contents which are transformed by adding and elaborating, with a view to simplify the sameto enable the students to understand, memorize and reproduce the same in examinations.This work is purely inspired upon the course work as prescribed by the Maharashtra State Bureau of Textbook Production and Curriculum Research, Pune.Every care has been taken in the publication of this reference book by the Authors while creating the contents. The Authors and the Publishers shall not beresponsible for any loss or damages caused to any person on account of errors or omissions which might have crept in or disagreement of any third party onthe point of view expressed in the reference book. reserved with the Publisher for all the contents created by our Authors.No copyright is claimed in the textual contents which are presented as part of fair dealing with a view to provide best supplementary study material forthe benefit of students.
TextbookChapter No.08Binomial DistributionSubtopicsBernoulli Trial, Binomial Distribution,Mean & Variance of BinomialDistributionChapter at a glanceShortcutsBinomial distribution:Let a random variable X denote the number ofsuccesses in n trials. Let p and q be theprobabilities of success and failure. Then in then independent trials, the probability that therewill be r successes and n r failures isnP(X r) Cr pr qn r, r 0, 1, 2, ., nThe probability distribution of the randomvariable X is given by1.The mean of binomial distribution is greaterthan the variance.2.Probability of occurrence of the event exactlyr times: P(X r) nCrqn r pr.3.Probability of occurrence of the event at leastr times:XC 0q1nn1 n 1C1p q2n2 n 2C2 p q R n n Cr pr q n r n Cn pnplP(x)0neC1.The binomial distribution for throwing3 dice is given by 3 Cr pr q3 r.ontent8.1When 3 dice are thrown .4.5.Sa8.1X B(n, p) denotes that X follows BinomialDistribution with parameters n and p.2.nnx 0x 0 P( x) nnC x p x q n x (q p) 1Mean and Variance of Binomial distribution:For the binomial distribution,nP(X r) Cr prqn r, r 0, 1, 2, ., nMean ( ) E(X) npVariance ( 2) npqStandard deviation ( ) npqIf the probability of happening of an event in onetrial be p, then the probability of successivehappening of that event in r trials is pr.Classical Thinking n C x p x q n x , x 0,1,2,.,n 0 p 1,q 1 p 0,otherwise Note:Probability of occurrence of the event at mostr times:P(0 X r) qn nC1qn 1 p . nCrqn r pr.mHence, the probability distribution is called thebinomial distribution.A discrete r.v. X taking values 0, 1, 2, , n issaid to follow binomial distribution with n and pas parameters if its p.m.f. is given byP(X x) p(x)P(X r) nCrqn r pr . nCn pn.Bernoulli Trial, Binomial Distribution,Mean & Variance of BinomialDistribution1.If there are n independent trials, p and q theprobability of success and failure respectively,then probability of exactly r successes is(B) nCn pr–1 qr 1(A) nCn r pr qn–r(C) nCr pr qn–r(D) nCr pr 1 qr–12.Let X B (n 10, p 0.2). Then P (X 1) is(A) 0.2684(B) 0.3684(C) 0.4684(D) 0.5684505
MHT-CET Triumph Maths (MCQs)(A)9128(B)(C)12(D)74 1 5 C4 6 6 4(C)(B)7(D)(A)5163 1 5 C4 6 6 1 5 6 6 (B)(C)316(D)12324(C)(B)(D)A coin is tossed 3 times. The probability ofobtaining at least two heads is31(A)(B)8812(D)(C)23m10.(C)8345(B)(D)38544 4 1 C1 5 5 4 1 5 5 (B)45 4 1 C1 5 5 45(D) 4 1 5 5 5 A man makes attempts to hit the target. The3. Then the5probability that a man hits the target exactly2 times in 5 attempts, is(A)(C)3.4.5.144625216625(B)723125(D)323125The probability that a bulb produced by afactory will fuse after 150 days of use is 0.05.The probability that out of 5 such bulbs nonewill fuse after 150 days of use is(A)191 – (C) 3 4 20 55(B) 19 20 (D)190 455 A contest consists of predicting the results aswin, draw or defeat of 7 football matches.A person sent his entry by predicting at random.The probability that his entry will containexactly 4 correct predictions is816(B)(A)7337(C)A die is thrown 5 times. Getting an odd numberis considered as a success. Then the variance ofdistribution of success is5probability of hitting the target isFor a binomial distribution,(A) Mean variance(B) Mean variance(C) Mean variance(D) Mean 1 variance(A)5062.3414Sa9.(C)4A die is thrown two times. If getting an oddnumber is considered as a success, then theprobability of two successes is12231, then the probability that out of 5 students5(A)33If the probability that a student is not a swimmerisA die is thrown 5 times, then the probability thatan even number will come up exactly 3 times is(A)8. 1 5 6 6 3Bernoulli Trial, Binomial Distribution,Mean & Variance ofBinomialDistributionone is swimmer ispl7.1.If a die is thrown 7 times, then the probability ofobtaining 5 exactly 4 times is(A)6.632561932568.1ontent5.In tossing 10 coins, the probability of gettingexactly 5 heads isCritical ThinkingC4.In a simultaneous toss of four coins, theprobability of getting exactly three heads is11(B)(A)2311(D)(C)45e3.28037(D)56037A coin is tossed successively three times. Theprobability of getting exactly one head or2 heads is(A)14(B)12(C)34(D)32
Chapter 08: Binomial Distribution7.8. 1 C4 2 4 1 C4 2 8(A)10(C)10 1 C4 2 (B)10(D)1013.8coinsaretossedsimultaneously.The probability of getting at least 6 heads is(A)6(C)10 1 C6 2 14.The records of a hospital show that 10% of thecases of a certain disease are fatal. If 6 patientsare suffering from the disease, then theprobability that only three will die is(B) 1458 10–6(A) 1458 10–5–6(D) 8748 10–5(C) 41 10If X denotes the number of sixes in fourconsecutive throws of a dice, then P(X 4) is14(A)(B)129661295(C) 1(D)1296In a box of 10 electric bulbs, two are defective.Two bulbs are selected at random one after theother from the box. The first bulb after selectionbeing put back in the box before making thesecond selection. The probability that both thebulbs are without defect 727(D)527The probability that a man can hit a target is18.Sahit the target at least three times is291371(B)(A)364464(C)471502(D)459512If three dice are thrown together, then theprobability of getting 5 on at least one of them is125215(B)(A)216216(C)1216(D)91216(B)(D)27 19 20 20 (C)153202292563725682724277 1 20 (B)533 19 400 20 (D)35 1 16 20 766If X follows a binomial distribution withparameters n 6 and p. If 9P(X 4) P(X 2),then p 1314(B)12(D)1If X follows a binomial distribution withparameters n 6 and p. If4 P(X 4) P (X 2), then p (A)12(B)(C)16(D)1413A fair coin is tossed a fixed number of times. Ifthe probability of getting 7 heads is equal to thatof getting 9 heads, then the probability ofgetting 3 heads is(A)(C)19.4271627(A)(C)3. He tries 5 times. The probability that he will412.(B)The items produced by a firm are supposed tocontain 5% defective items. The probability thata sample of 8 items will contain less than2 defective items is(A)plA die is thrown three times. Getting a 3 or 6 onthe top face is considered success. Then theprobability of at least two successes is(A)11.(D)e(C)10.5764764An experiment succeeds twice as often as itfails. The probability that in 4 trials there will beat least three successes isC9.A die is thrown ten times. If getting an evennumber is considered as a success, then theprobability of four successes isontent6.352127212(B)(D)352147214Let X be the number of successes in ‘n’independent Bernoulli trials with probability ofsuccess p 3. The least value of ‘n’ so that4P(X 1) 0.9375 is(A) 1(C) 3(B)(D)24507
MHT-CET Triumph Maths (MCQs)20.21.Minimum number of times a fair coin must betossed so that the probability of getting at leastone head is more than 99% is(A) 6(B) 7(C) 8(D) 51The probability of hitting a target is . Then327.If X B(16, p) and E(X) 12.8, then thestandard deviation of X is(A) 256(B) 16(C) 2.56(D) 1.628.If the mean and variance of a binomial variateX are 2 and 1 respectively, then the probabilitythat X takes a value greater than or equal to 1 isgreater than(A)(C)(C)1 1,2 125 1,6 2(B)(D)51251289e(D)34m1,(D)3,14n k p.k 1 qn 1 q.k p(B)(D)n k 1 p.kqn 1 q.k 1 pTwo cards are drawn successively withreplacement from a well shuffled deck of 52cards, then the mean of the number of aces is(A)(C)23(B)(C)78(D)113213(B)(D)313413451516The mean and variance of a binomialdistribution are 4 and 3 respectively, then theprobability of getting exactly six successes inthis distribution is10(A)16 1 3 (C)12 1 3 6C6 4 4 101016 1 3 (D)12 1 3 6C6 4 4 6(B)C6 4 4 66C6 4 4 Competitive ThinkingC13Sa(C)5081,61,28.11.Bernoulli Trial, Binomial Distribution,Mean & Variance ofBinomialDistribution 1 3 If r.v. X B n 5, p , then P (2 X 4) [MH CET 2016](A)80243(B)40243(C)40343(D)803432.A coin is tossed 10 times. The probability ofgetting exactly six heads is[Kerala (Engg.) 2002]512105(A)(B)513512100(C)(D) 10C61533.In a box containing 100 eggs, 10 eggs are rotten.The probability that out of a sample of 5 eggsnone are rotten, if the sampling is withreplacement, is[UPSEAT 2000]If X has binomial distribution with mean npP(X k)isand variance npq, thenP(X k 1)(A)26.29.A card is drawn at random 4 times, withreplacement, from a pack of 52 playing cards. Ifgetting a red card is considered as success, thenthe mean and variance of the distribution arerespectively(A) 1, 2(B) 2, 1(C)25.4None of theseA die is tossed twice. Getting a number greaterthan 4 is considered a success. Then thevariance of the distribution of the number ofsuccesses is24(B)(A)99(C)24.(B)(D)A die is thrown thrice. If getting a four isconsidered a success, then the mean and variance ofthe distribution of the number of successes are(A)23.35pl22.5is6(A)ontentminimum number of times the target should behit so that probability of at least one success is(A) 1 10 (C) 9 5 55(B) 1 5 (D) 9 10 55
Chapter 08: Binomial Distribution4.5.Probability that a person will develop immunityafter vaccination is 0.8. If 8 people are given thevaccine then probability that all developimmunity is[MHT CET 2017](B) (0.8)8(A) (0.2)8(C) 1(D) 8C6 (0.2)6 (0.8)2The probabilitydistribution isfunctionofa 6 (C)11.binomial(A)(C)6.(B)(D)1415A fair coin is tossed n times. If the probability thathead occurs 6 times is equal to the probability thathead occurs 8 times, then n is equal to[AMU 2000](A) 15(B) 14(C) 12(D) 7One hundred identical coins each withprobability p of showing up heads are tossedonce. If 0 p 1 and the probability of headsshowing on 50 coins is equal to that of headsshowing on 51 coins, then the value of p is[MP PET 1(D)(C)(2n!) 1.(n!)2 4n(D)The probability that an event A occurs in asingle trial of an experiment is 0.6. In the firstthree independent trials of the experiment, theprobability that A occurs at least once is[GUJ CET 2019](A) 0.930(B) 0.936(C) 0.925(D) 0.92713.A die is thrown four times. The probability ofgetting perfect square in at least one throw is[MHT CET 2018]14.(A)1681(B)(C)2381(D)10.If a die is thrown twice, the probability ofoccurrence of 4 at least once is[UPSEAT 2003]117(A)(B)361235(C)(D) None of these36A bag contains 2 white and 4 black balls. A ballis drawn 5 times with replacement.The probability that at least 4 of the balls drawnare white is[AMU 2001](A)8141(B)(C)15.1024365815881Probability of guessing correctly at least 7 out of10 answers in a “True” or “False” test is[MH CET 2016](A)11641116(B)(D)11322732If in a certain experiment the probability ofsuccess in each trial is3times the proabability4of failure, then the probability of at least onesuccess in 5 trials is[MHT CET 2019]None of theseSa9.1–181658112.eplA coin is tossed 2n times. The chance that thenumber of times one gets head is not equal to thenumber of times one gets tail is[DCE 2002]2n(2n!) 1 (2n!)(B) 1 –(A) 2 (n!) 2 (n!)2m8.841An unbiased die with faces marked 1, 2, 3, 4, 5and 6 is rolled four times. Out of four facevalues obtained, the probability that theminimum face value is not less than 2 and themaximum face value is not greater than 5, is[Roorkee 2000]C7.1312(D)ontentP(x) px q6 – x, x 0, 1, 2, , 6. x If 2P(2) 3P(3), then p [Gujrat CET 2017]1124316. 3 (A)1– 7 (C) 4 7 55(B) 3 7 (D)1– 7 5 4 5If getting a head on a coin when it is tossed isconsidered as success, then the probability ofhaving more number of failures when ten faircoins are tossed simultaneously, is[TS EAMCET 2019](A)(C)1052819329(B)(D)7327638210509
MHT-CET Triumph Maths (MCQs)17.In a workshop, there are five machines and theprobability of any one of them to be out ofservice on a day is24.1. If the probability that at4The mean and variance of a random variable Xhaving a binomial distribution are 4 and2 respectively, then P(X 1) is [AIEEE 2003](A)most two machines will be out of service on the33same day is k, then k is equal to4(C) (C)174(D)178In order to get a head at least onceprobability 0.9, the minimum number of timea unbiased coin needs to be tossed is[WB JEE 2018](A) 3(B) 4(C) 5(D) 6A box contains 15 green and 10 yellow balls.If 10 balls are randomly drawn, one-by-one,with replacement, then the variance of thenumber of green balls drawn is[JEE (Main) 2017](A)625(B)125(C)6(D)4The probability that an event A occurs in asingle trial of an experiment is 0.3. Sixindependent trials of the experiment areperformed. What is the variance of probabilitydistribution of occurrence of event A?[Gujrat CET 2018](A) 1.8(B) 0.18(C) 12.6(D) 1.26mpl20.4If X B (n, p) with n 10, p 0.4, then E(X2) [MHT CET 2018](A) 4(B) 2.4(C) 3.6(D) 18.4Sa21.22.23.51025.(D)11614The mean and variance of a binomialdistribution are 8 and 4 respectively. What is(X 1)?[KEAM 48154096(B)(D)29.(A) 1 2 (C) 1 2 2192563725613409625204810(B) 1 2 (D) 1 2 69If X is a binomial variate with mean 6 andvariance 2, then the value of P(5 X 7) is[AP EAMCET 2018](A)(C)30.1212124Let X B (n, p), ifE(X) 5, Var(X) 2.5, then P (X 1) [MH CET 2016]11The mean and variance of a binomialdistribution are 6 and 4. The parameter n is[MP PET 2000](A) 18(B) 12(C) 10(D) 9A r.v. X B (n, p). If values of mean andvariance of X are 18 and 12 respectively thentotal number of possible values of X are[MHT CET 2017](A) 54(B) 55(C) 12(D) 18(B)The mean and variance of a random variable Xhaving a binomial distribution are 6 and 3respectively. The probability of variable X lessthan 2 is[GUJ CET 2019](A)28.128126The mean and variance of a binomialdistribution are 4 and 2 respectively. Then theprobability of 2 successes is[AIEEE 2004; EAMCET 2016]C19.(B)e18.(A)172(B)ontent[JEE (Main) 2020]132184762656152646561(B)(D)4672656154626651In a binomial distribution the probability of1and standard deviation isgetting a success is43, then its mean is[EAMCET 2002](A) 6(B) 8(C) 12(D) 10
Chapter 08: Binomial DistributionAnswer KeyClassical (C)10. (D)1. (B)11. (D)21. (C)2. (A)12. (D)22. (D)3. (B)13. (D)23. (B)4. (C)14. (C)24. (B)Competitive Thinking1. (B)11. (A)21. (D)2. (B)12. (B)22. (A)3. (D)13. (B)23. (B)4. (B)14. (A)24. (A)ontentCritical Thinking5. (C)15. (A)25. (B)6. (D)16. (C)26. (C)7. (A)17. (D)27. (D)8. (A)18. (A)28. (D)9. (B)19. (B)29. (B)10. (B)20. (B)5. (A)15. (D)25. (B)6. (B)16. (C)26. (A)7. (D)17. (D)27. (B)8. (C)18. (B)28. (B)9. (A)19. (B)29. (B)10. (C)20. (D)30. (C)Evaluation TestFor a binomial variate X if n 5 andP(X 1) 8P(X 3), then p (C)2.4513(D)1523(C)11612716, then P(X 4) equals811(B)811(D)8mA die is thrown 100 times. If getting an oddnumber is considered a success, the variance ofthe number of successes is(A) 50(B) 25(C) 10(D) 100SaIn eight throws of a die 1 or 3 is considered asuccess. Then the standard deviation of thesuccess is(A)(C)5.(C)7.16943(B)(D)31, then p lies in the interval32 1 3 (A) , (B) 2 4 (C)(D) 11 ,1 12 8.The sum of the mean and variance of a binomialdistribution is 15 and the sum of their squares is117. The mean of the distribution is(A) 6(B) 9(C) 3(D) 129.In a trial the probability of success is twice theprobability of failure. In six trials the probabilityof at least four successes will be(A) 3 11 , 4 12 1 2 As a business strategy, 20% of the new internetservice subscribers selected randomly receive aspecial promotion. If a group of 5 suchsubscribers signs for the service, then theprobability that at least two of them get thespecial promotion is(A)8323Consider 5 independent Bernoulli’s trials eachwith probability of success p. If the probabilityof at least one failure is greater than or equal to 0, A coin is tossed 3 times by 2 persons. Theprobability that both get equal number of heads,is(A)pl(A)4.6.If in a binomial distribution n 4,P(X 0) 1
MHT-CET Triumph Maths (MCQs)11.The mean and variance of a binomialdistribution (p q)n are 20 and 16 respectively.Then, the pair (n, p) is(A) 1 50, 5 (B)2 50, 5 (C)1 100, 5 (D)2 100, 5 For an initial screening of an admission test, acandidate is given fifty problems to solve. If theprobability that the candidate solve any problemis4, then the probability that he is unable to5solve less than two problems is:164 1 25 5 48(A)201 1 5 5 49(C)(B)316 4 25 5 (D)54 4 5 5 4849Let a random varibale X have a binomialdistribution with mean 8 and variance 4.If P(X 2) (A)(C)k, then k is equal to21617137(B)(D)1121C12.ontent10.A rifleman is firing at a distant target and hasonly 10% chance of hitting it. The least numberof rounds, he must fire in order to have morethan 50% chance of hitting it at least once is(A) 5(B) 7(C) 9(D) 1114.In a binomial distribution B n,p . If the4e13. 1 pl probability of at least one success is greater than9, then n is greater than1011(B)log10 4 log10 3log10 4 log10 3or equal tom(A)(C)(D)4log10 4 log10 3Let X denote the number of times heads occurin n tosses of a fair coin. If P (X 4), P (X 5)and P (X 6) are in A.P., the valu
Includes MHT-CET 2020 Question Paper (14th October) along with Answer key. Various competitive examination questions updated till the latest year. Evaluation test provided at the end of each chapter. T
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Electromagnetic Interference: MIL- STD-461F Ballistic Shock: MIL-STD-810G Life Fire: MIL- STD-810G Explosive Environment: MIL -STD 810G Altitude to 60,000ft: MIL -STD 29595 Explosive Decompression: MIL- STD-810G Salt fog: MIL -STD 810G Sand and Dust requirements: MIL-STD-810G Extreme operating . environments . Commercial NATO
