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 on Std. XII Sci. and relevant chapters of Std. XI Sci. (Maharashtra State Board)

Balbharati Registration No.: 2018MH0022 P.O. No. 1696TEID: 1919

© 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, mechanical

including photocopying; recording or by any information storage and retrieval system without permission in writing from the Publisher.

Printed at: Print to Print, Mumbai

Includes 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.

Salient Features

MHT-CET TRIUMPH

Scan the adjacent QR code to download Hints for relevant questions, Solution to Evaluation Test and MHT-CET paper 2020 in PDF format.

Scan the adjacent QR code to download Model Paper II and Solution.

Scan the adjacent QR code to download Model Paper I and Solution.

Mathematics

Sample

Con

tent

“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. For 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. As 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. Promptness 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.” Our 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 self-assessment. 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. The journey to create a complete book is strewn with triumphs, failures and near misses. If you think we’ve nearly missed something or want to applaud us for our triumphs, we’d love to hear from you. Please write to us on: [email protected] A book affects eternity; one can never tell where its influence stops.

Best of luck to all the aspirants! From, Publisher Edition: First

PREFACE

Sample

Con

tent

FEATURES

Shortcuts to help students save time while dealing with questions. This is our attempt to highlight content that would come handy while solving questions.

Shortcuts

1. f ( ) df ( )

x xx

= log |f(x)| + c 2. f ( ) d

f ( )

x xx

= 2 f ( ) cx

3. ∫[f(x)]n f (x) dx =

n +1f( )n +1x + c, n 1

Shortcuts

1. Elementary Transformations: Symbol Meaning

Ri Rj Interchange of ith and jth rows Ci Cj Interchange of ith and jth columns Ri kRi Multiplying the ith row by non-

zero scalar k Ci kCi Multiplying the ith column by

non-zero scalar k Ri Ri + kRj Adding k times the elements of

jth row to the corresponding elements of ith row

Ci Ci + kCj Adding k times the elements of jth column to the corresponding elements of ith column

Chapter at a glance

Chapter at a glance includes short and precise summary along with Tables and Key formulae in the chapter. This is our attempt to make tools of formulae accessible at a glance for the students while solving problems.

Chapter at a glance

Classical Thinking section encompasses straight forward questions includingknowledge based questions. This is our attempt to revise chapter inits basic form and warm up the studentsto deal with complex MCQs.

Classical Thinking

5.1 Area under the curve 1. Area bounded by the curve y = x3, X-axis and

ordinates x = 1 and x = 4 is (A) 64 sq. units (B) 27 sq. units

(C) 1274

sq. units (D) 2554

sq. units

Classical Thinking Sample

Con

tent

FEATURES

Critical Thinking section encompasses challenging questions which test understanding, rational thinking and application skills of the students. This is our attempt to take the students from beginner to proficient level in smooth steps.

Critical Thinking 3.1 Trigonometric equations and the

solutions 1. The values of in between 0 and 360 and

satisfying the equation 1tan 03

is equal to

(A) = 150 and 300 (B) = 120 and 300 (C) = 60 and 240 (D) = 150 and 330

Critical Thinking

Subtopic wise segregation

Every section is segregated sub-topic wise. This is our attempt to cater to individualistic pace and preferences of studying a chapter and enabling easy assimilation of questions based on the specific concept.

Subtopics 1.1 Derivative of Composite functions 1.2 Derivative of Inverse functions 1.3 Logarithmic Differentiation 1.4 Derivative of Implicit functions 1.5 Derivative of Parametric functions 1.6 Higher Order derivatives

Competitive Thinking section encompasses questions from various competitive examinations like MHT CET, JEE, etc. This is our attempt to give the students practice of competitive questions and advance them to acquire knack essential to solve such questions.

Competitive Thinking

2.6 Maxima and Minima 94. If f(x) = x3 – 3x has minimum value at x = a, then a =

[MHT CET 2019] (A) –1 (B) –3

(C) 1 (D) 3


Sample

Con

tent

FEATURES

Evaluation test

Evaluation Test covers questions from chapter for self-evaluation purpose. This is our attempt to provide the students with a practice test and help them assess their range of preparation of the chapter.

1. If f(x) is a polynomial of degree 2, such that

f(0) = 3, f (0) = 7, f (0) = 8, then 2

1

f ( )dx x =

(A) 116

(B) 136

(C) 176

(D) 196

Evaluation Test

Miscellaneous section incorporates MCQs whose solutions require knowledge of concepts covered in different sub-topics of the same chapter or from different chapters. This is our attempt to develop cognitive thinking in the students which is essential to solve questions involving fusion of multiple key concepts.

Miscellaneous Miscellaneous 39. The distance from the origin to the orthocentre of the

triangle formed by the lines x + y – 1 = 0 and 6x2 – 13xy + 5y2 = 0 is

[AP EAMCET 2019]

(A) 11 22

(B) 13

(C) 11 (D) 11 224

Sample

Con

tent

There will be three papers of Multiple Choice Questions (MCQs) in ‘Mathematics’, ‘Physics and

Chemistry’ 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 and

Higher Secondary Education with approximately 20% weightage given to Std. XI and 80% weightage

will be given to Std. XII curriculum.

Difficulty level of questions will be at par with JEE (Main) for Mathematics, Physics, Chemistry and at

par with NEET for Biology.

There will be no negative marking.

Questions will be mainly application based.

Details of the papers are as given below:

Paper Subject Approximate No. of Multiple

Choice Questions (MCQs) based on Mark(s) Per Question

Total Marks Std. XI Std. XII

Paper I Mathematics 10 40 2 100

Paper II Physics 10 40

1 100 Chemistry 10 40

Paper III Biology 20 80 1 100 Questions will be set on

i. the entire syllabus of Std. XII of 2020-21 of Physics, Chemistry, Mathematics and Biology

subjects excluding portion which is deleted by Maharashtra State Bureau of Textbook Production

and Curriculum Research, Pune, and ii. chapters / units from Std. XI curriculum as mentioned below:

Sr. No. Subject Chapters / Units of Std. XI

1 Physics Motion in a plane, Laws of motion, Gravitation, Thermal properties of matter, Sound, Optics, Electrostatics, Semiconductors

2 Chemistry

Some Basic Concepts of Chemistry, Structure of Atom, Chemical Bonding, Redox Reactions, Elements of Group 1 and Group 2, States of Matter: Gaseous and Liquid States, Basic Principles and techniques of Chemistry, Adsorption and Colloids, Hydrocarbons

3 Mathematics Trigonometry - II, Straight Line, Circle, Measures of Dispersion, Probability, Complex Numbers, Permutations and Combinations, Functions, Limits, Continuity

4 Biology Biomolecules, Respiration and Energy Transfer, Human Nutrition, Excretion and osmoregulation

MHT-CET PAPER PATTERN

Sample

Con

tent

Sr. No.

Textbook Chapter No. Chapter Name Page No.

Std. XI1 3 Trigonometry - II 1 2 5 Straight Line 25 3 6 Circle 48 4 8 Measures of Dispersion 63 5 9 Probability 70 6 1 Complex Numbers 93 7 3 Permutations and Combinations 117 8 6 Functions 132 9 7 Limits 148 10 8 Continuity 166

Std. XII11 1 Mathematical Logic 18312 2 Matrices 200 13 3 Trigonometric Functions 21414 4 Pair of Straight Lines 242 15 5 Vectors 25516 6 Line and Plane 288 17 7 Linear Programming 32018 1 Differentiation 33819 2 Applications of Derivatives 366 20 3 Indefinite Integration 39321 4 Definite Integration 434 22 5 Application of Definite Integration 457 23 6 Differential Equations 468 24 7 Probability Distribution 49425 8 Binomial Distribution 505 26 MHT-CET 2020 Question Paper 513

Note: Questions of Standard XI are indicated by ‘*’ in each Model Question Paper.

This 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 making this reference book which constitutes as fair use of textual contents which are transformed by adding and elaborating, with a view to simplify the same to 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 be responsible 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 on the 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 for the benefit of students.

Disclaimer

CONTENTS

Sample

Con

tent

505

Subtopics 8.1 Bernoulli Trial, Binomial Distribution,

Mean & Variance of Binomial Distribution

1. Binomial distribution: Let a random variable X denote the number of

successes in n trials. Let p and q be the probabilities of success and failure. Then in the n independent trials, the probability that there will be r successes and nr failures is

P(X = r) = nrC pr qnr, r = 0, 1, 2, …., n

The probability distribution of the random variable X is given by

X 0 1 2 … R … n P(x) n n

0C q n 1 n 11C p q n 2 n 2

2C p q … n r n rrC p q … n n

nC p Hence, the probability distribution is called the

binomial distribution. A discrete r.v. X taking values 0, 1, 2, …, n is

said to follow binomial distribution with n and p as parameters if its p.m.f. is given by

P(X = x) = p(x)

=

n nC p q , 0,1,2,...,n0 p 1,q 1 p

0, otherwise

x xx x

X ~ B(n, p) denotes that X follows Binomial Distribution with parameters n and p.

Note: n

0P( )

xx

=

nn n

0C p qx x

xx

= (q + p)n = 1

2. Mean and Variance of Binomial distribution: For the binomial distribution, P(X = r) = n

rC prqnr, r = 0, 1, 2, …., n Mean () = E(X) = np Variance (2) = npq Standard deviation () = npq

1. The mean of binomial distribution is greater

than the variance. 2. Probability of occurrence of the event exactly

r times: P(X = r) = nCrqnr pr. 3. Probability of occurrence of the event at least

r times: P(X r) = nCrqnr pr + …. + nCn pn. 4. Probability of occurrence of the event at most

r times: P(0 X r) = qn + nC1qn1 p + ….+ nCrqnr pr. 5. If the probability of happening of an event in one

trial be p, then the probability of successive happening of that event in r trials is pr.

8.1 Bernoulli Trial, Binomial Distribution,


1. If there are n independent trials, p and q the

probability of success and failure respectively, then probability of exactly r successes is

(A) nCn+r pr qn–r (B) nCn pr–1 qr+1 (C) nCr pr qn–r (D) nCr pr+1 qr–1

2. Let X B (n = 10, p = 0.2). Then P (X = 1) is (A) 0.2684 (B) 0.3684 (C) 0.4684 (D) 0.5684

Shortcuts Chapter at a glance

The binomial distribution for throwing 3 dice is given by 3

rC pr q3 r.

When 3 dice are thrown …...

Classical Thinking

Binomial Distribution08Textbook

Chapter No.

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506

MHT-CET Triumph Maths (MCQs)

506

3. In a simultaneous toss of four coins, the probability of getting exactly three heads is

(A) 12

(B) 13

(C) 14

(D) 15

4. In tossing 10 coins, the probability of getting

exactly 5 heads is

(A) 9128

(B) 63256

(C) 12

(D) 193256

5. If a die is thrown 7 times, then the probability of

obtaining 5 exactly 4 times is

(A) 7C4

416

356

(B) 7C4

316

456

(C) 41

6

356

(D) 31

6

456

6. A die is thrown 5 times, then the probability that

an even number will come up exactly 3 times is

(A) 516

(B) 12

(C) 316

(D) 32

7. A die is thrown two times. If getting an odd

number is considered as a success, then the probability of two successes is

(A) 12

(B) 34

(C) 23

(D) 14

8. A coin is tossed 3 times. The probability of

obtaining at least two heads is

(A) 18

(B) 38

(C) 12

(D) 23

9. For a binomial distribution, (A) Mean < variance (B) Mean = variance (C) Mean > variance (D) Mean = 1 variance 10. A die is thrown 5 times. Getting an odd number

is considered as a success. Then the variance of distribution of success is

(A) 83

(B) 38

(C) 45

(D) 54



1. If the probability that a student is not a swimmer

is 15

, then the probability that out of 5 students

one is swimmer is

(A) 5C1

445

15

(B) 5C145

415

(C) 45

415

(D) 554

5

15

2. A man makes attempts to hit the target. The

probability of hitting the target is 3.5

Then the

probability that a man hits the target exactly 2 times in 5 attempts, is

(A) 144625

(B) 723125

(C) 216625

(D) 323125

3. The probability that a bulb produced by a

factory will fuse after 150 days of use is 0.05. The probability that out of 5 such bulbs none will fuse after 150 days of use is

(A) 1 – 519

20

(B) 519

20

(C) 53

4

(D) 90 51

4

4. A contest consists of predicting the results as

win, draw or defeat of 7 football matches. A person sent his entry by predicting at random. The probability that his entry will contain exactly 4 correct predictions is

(A) 7

83

(B) 7

163

(C) 7

2803

(D) 7

5603

5. A coin is tossed successively three times. The

probability of getting exactly one head or 2 heads is

(A) 14

(B) 12

(C) 34

(D) 32

Critical Thinking

Sample

Con

tent

507

Chapter 08: Binomial Distribution

6. A die is thrown ten times. If getting an even number is considered as a success, then the probability of four successes is

(A) 10C4

412

(B) 10C4

612

(C) 10C4

812

(D) 10C6

1012

7. The records of a hospital show that 10% of the

cases of a certain disease are fatal. If 6 patients are suffering from the disease, then the probability that only three will die is

(A) 1458 10–5 (B) 1458 10–6 (C) 41 10–6 (D) 8748 10–5 8. If X denotes the number of sixes in four

consecutive throws of a dice, then P(X = 4) is

(A) 11296

(B) 46

(C) 1 (D) 12951296

9. In a box of 10 electric bulbs, two are defective.

Two bulbs are selected at random one after the other from the box. The first bulb after selection being put back in the box before making the second selection. The probability that both the bulbs are without defect is

(A) 925

(B) 1625

(C) 45

(D) 825

10. A die is thrown three times. Getting a 3 or 6 on

the top face is considered success. Then the probability of at least two successes is

(A) 29

(B) 727

(C) 127

(D) 527

11. The probability that a man can hit a target is

34

. He tries 5 times. The probability that he will

hit the target at least three times is

(A) 291364

(B) 371464

(C) 471502

(D) 459512

12. If three dice are thrown together, then the

probability of getting 5 on at least one of them is

(A) 125216

(B) 215216

(C) 1216

(D) 91216

13. 8 coins are tossed simultaneously. The probability of getting at least 6 heads is

(A) 5764

(B) 229256

(C) 764

(D) 37256

14. An experiment succeeds twice as often as it

fails. The probability that in 4 trials there will be at least three successes is

(A) 427

(B) 827

(C) 1627

(D) 2427

15. The items produced by a firm are supposed to

contain 5% defective items. The probability that a sample of 8 items will contain less than 2 defective items is

(A) 2720

71920

(B) 533400

61920

(C) 15320

7120

(D) 3516

6120

16. If X follows a binomial distribution with

parameters n = 6 and p. If 9P(X = 4) = P(X = 2), then p =

(A) 13

(B) 12

(C) 14

(D) 1 17. If X follows a binomial distribution with

parameters n = 6 and p. If 4 P(X = 4) = P (X = 2), then p =

(A) 12

(B) 14

(C) 16

(D) 13

18. A fair coin is tossed a fixed number of times. If

the probability of getting 7 heads is equal to that of getting 9 heads, then the probability of getting 3 heads is

(A) 12

352

(B) 14

352

(C) 12

72

(D) 14

72

19. Let X be the number of successes in ‘n’

independent Bernoulli trials with probability of

success p = 34

. The least value of ‘n’ so that

P(X 1) 0.9375 is (A) 1 (B) 2 (C) 3 (D) 4

Sample

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tent

508


508

20. Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is

(A) 6 (B) 7 (C) 8 (D) 5 21. The probability of hitting a target is 1

3. Then

minimum number of times the target should be hit so that probability of at least one success is

greater than 56

is

(A) 3 (B) 4 (C) 5 (D) None of these 22. A die is thrown thrice. If getting a four is

considered a success, then the mean and variance of the distribution of the number of successes are

(A) 12

, 112

(B) 16

, 512

(C) 56

, 12

(D) 12

, 512

23. A die is tossed twice. Getting a number greater

than 4 is considered a success. Then the variance of the distribution of the number of successes is

(A) 29

(B) 49

(C) 13

(D) 89

24. A card is drawn at random 4 times, with

replacement, from a pack of 52 playing cards. If getting a red card is considered as success, then the mean and variance of the distribution are respectively

(A) 1, 2 (B) 2, 1

(C) 1, 34

(D) 34

, 1 25. If X has binomial distribution with mean np

and variance npq, then P(X = k)P(X = k 1)

is

(A) n k p.k 1 q

(B) n k +1 p.k q

(C) n +1 q.k p

(D) n 1 q.k +1 p

26. Two cards are drawn successively with

replacement from a well shuffled deck of 52 cards, then the mean of the number of aces is

(A) 113

(B) 313

(C) 213

(D) 413

27. If X ~ B(16, p) and E(X) = 12.8, then the standard deviation of X is

(A) 256 (B) 16 (C) 2.56 (D) 1.6 28. If the mean and variance of a binomial variate

X are 2 and 1 respectively, then the probability that X takes a value greater than or equal to 1 is

(A) 23

(B) 45

(C) 78

(D) 1516

29. The mean and variance of a binomial

distribution are 4 and 3 respectively, then the probability of getting exactly six successes in this distribution is

(A) 16C6

1014

634

(B) 16C6

614

1034

(C) 12C6

1014

634

(D) 12C6

614

634



1. If r.v. X ~ B 1n 5, p

3

, then P (2 X 4) =

[MH CET 2016]

(A) 80243

(B) 40243

(C) 40343

(D) 80343

2. A coin is tossed 10 times. The probability of

getting exactly six heads is [Kerala (Engg.) 2002]

(A) 512513

(B) 105512

(C) 100153

(D) 10C6 3. In a box containing 100 eggs, 10 eggs are rotten.

The probability that out of a sample of 5 eggs none are rotten, if the sampling is with replacement, is [UPSEAT 2000]

(A) 51

10

(B) 51

5

(C) 59

5

(D) 59

10


Sample

Con

tent

509


4. Probability that a person will develop immunity after vaccination is 0.8. If 8 people are given the vaccine then probability that all develop immunity is [MHT CET 2017]

(A) (0.2)8 (B) (0.8)8 (C) 1 (D) 8C6 (0.2)6 (0.8)2

5. The probability function of a binomial

distribution is

P(x) = 6x

px q6 – x, x = 0, 1, 2, … , 6.

If 2P(2) = 3P(3), then p = [Gujrat CET 2017]

(A) 13

(B) 14

(C) 12

(D) 15

6. A fair coin is tossed n times. If the probability that

head occurs 6 times is equal to the probability that head occurs 8 times, then n is equal to

[AMU 2000] (A) 15 (B) 14 (C) 12 (D) 7 7. One hundred identical coins each with

probability p of showing up heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is

[MP PET 2001] (A) 1

2 (B) 49

101

(C) 50101

(D) 51101

8. A coin is tossed 2n times. The chance that the

number of times one gets head is not equal to the number of times one gets tail is [DCE 2002]

(A) 2

(2n!)(n!)

2n12

(B) 1 – 2

(2n!)(n!)

(C) 1 – 2 n

(2n!) 1.(n!) 4 (D) None of these

9. If a die is thrown twice, the probability of

occurrence of 4 at least once is [UPSEAT 2003] (A) 11

36 (B) 7

12

(C) 3536

(D) None of these 10. A bag contains 2 white and 4 black balls. A ball

is drawn 5 times with replacement. The probability that at least 4 of the balls drawn are white is [AMU 2001]

(A) 8141

(B) 10243

(C) 11243

(D) 841

11. An unbiased die with faces marked 1, 2, 3, 4, 5

and 6 is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is

[Roorkee 2000]

(A) 1681

(B) 181

(C) 8081

(D) 6581

12. The probability that an event A occurs in a

single trial of an experiment is 0.6. In the first three independent trials of the experiment, the probability that A occurs at least once is

[GUJ CET 2019] (A) 0.930 (B) 0.936 (C) 0.925 (D) 0.927 13. A die is thrown four times. The probability of

getting perfect square in at least one throw is [MHT CET 2018]

(A) 1681

(B) 6581

(C) 2381

(D) 5881

14. Probability of guessing correctly at least 7 out of

10 answers in a “True” or “False” test is [MH CET 2016]

(A) 1164

(B) 1132

(C) 1116

(D) 2732

15. If in a certain experiment the probability of

success in each trial is 34

times the proabability

of failure, then the probability of at least one success in 5 trials is [MHT CET 2019]

(A) 1 – 53

7

(B) 53

7

(C) 54

7

(D) 1 – 54

7

16. If getting a head on a coin when it is tossed is

considered as success, then the probability of having more number of failures when ten fair coins are tossed simultaneously, is

[TS EAMCET 2019]

(A) 8

1052

(B) 7

732

(C) 9

1932

(D) 10

6382

Sample

Con

tent

510


510

17. In a workshop, there are five machines and the probability of any one of them to be out of

service on a day is 14

. If the probability that at

most two machines will be out of service on the

same day is 33

4

k, then k is equal to

[JEE (Main) 2020]

(A) 172

(B) 4

(C) 174

(D) 178

18. In order to get a head at least once

probability 0.9, the minimum number of time a unbiased coin needs to be tossed is

[WB JEE 2018] (A) 3 (B) 4 (C) 5 (D) 6 19. A box contains 15 green and 10 yellow balls.

If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is

[JEE (Main) 2017]

(A) 625

(B) 125

(C) 6 (D) 4 20. The probability that an event A occurs in a

single trial of an experiment is 0.3. Six independent trials of the experiment are performed. What is the variance of probability distribution of occurrence of event A?

[Gujrat CET 2018] (A) 1.8 (B) 0.18 (C) 12.6 (D) 1.26 21. If 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) 18.4 22. The mean and variance of a binomial

distribution are 6 and 4. The parameter n is [MP PET 2000] (A) 18 (B) 12 (C) 10 (D) 9 23. A r.v. X ~ B (n, p). If values of mean and

variance of X are 18 and 12 respectively then total number of possible values of X are

[MHT CET 2017] (A) 54 (B) 55 (C) 12 (D) 18

24. The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then P(X = 1) is [AIEEE 2003]

(A) 132

(B) 116

(C) 18

(D) 14


distribution are 8 and 4 respectively. What is (X = 1)? [KEAM 2018]

(A) 8

12

(B) 12

12

(C) 6

12

(D) 4

12


distribution are 4 and 2 respectively. Then the probability of 2 successes is

[AIEEE 2004; EAMCET 2016]

(A) 28256

(B) 219256

(C) 128256

(D) 37256

27. The mean and variance of a random variable X

having a binomial distribution are 6 and 3 respectively. The probability of variable X less than 2 is [GUJ CET 2019]

(A) 132048

(B) 134096

(C) 154096

(D) 252048

28. Let X ~ B (n, p), if E(X) = 5, Var(X) = 2.5, then P (X 1) =

[MH CET 2016]

(A) 111

2

(B) 101

2

(C) 61

2

(D) 91

2

29. If X is a binomial variate with mean 6 and

variance 2, then the value of P(5 X 7) is [AP EAMCET 2018]

(A) 47626561

(B) 46726561

(C) 52646561

(D) 54626651

30. In a binomial distribution the probability of

getting a success is 14

and standard deviation is

3, then its mean is [EAMCET 2002] (A) 6 (B) 8 (C) 12 (D) 10

Sample

Con

tent

511


Classical Thinking 1. (C) 2. (A) 3. (C) 4. (B) 5. (A) 6. (A) 7. (D) 8. (C) 9. (C) 10. (D) Critical Thinking 1. (B) 2. (A) 3. (B) 4. (C) 5. (C) 6. (D) 7. (A) 8. (A) 9. (B) 10. (B) 11. (D) 12. (D) 13. (D) 14. (C) 15. (A) 16. (C) 17. (D) 18. (A) 19. (B) 20. (B) 21. (C) 22. (D) 23. (B) 24. (B) 25. (B) 26. (C) 27. (D) 28. (D) 29. (B) Competitive Thinking 1. (B) 2. (B) 3. (D) 4. (B) 5. (A) 6. (B) 7. (D) 8. (C) 9. (A) 10. (C) 11. (A) 12. (B) 13. (B) 14. (A) 15. (D) 16. (C) 17. (D) 18. (B) 19. (B) 20. (D) 21. (D) 22. (A) 23. (B) 24. (A) 25. (B) 26. (A) 27. (B) 28. (B) 29. (B) 30. (C) 1. For a binomial variate X if n = 5 and

P(X = 1) = 8P(X = 3), then p =

(A) 45

(B) 15

(C) 13

(D) 23

2. If in a binomial distribution n = 4,

P(X = 0) = 1681

, then P(X = 4) equals

(A) 116

(B) 181

(C) 127

(D) 18

3. A die is thrown 100 times. If getting an odd

number is considered a success, the variance of the number of successes is

(A) 50 (B) 25 (C) 10 (D) 100 4. In eight throws of a die 1 or 3 is considered a

success. Then the standard deviation of the success is

(A) 169

(B) 83

(C) 43

(D) 23

5. Consider 5 independent Bernoulli’s trials each

with probability of success p. If the probability of at least one failure is greater than or equal to 3132

, then p lies in the interval

(A) 1 3,2 4

(B) 3 11,4 12

(C) 10,2

(D) 11,112

6. A coin is tossed 3 times by 2 persons. The

probability that both get equal number of heads, is

(A) 38

(B) 19

(C) 516

(D) 316

7. As a business strategy, 20% of the new internet

service subscribers selected randomly receive a special promotion. If a group of 5 such subscribers signs for the service, then the probability that at least two of them get the special promotion is

(A) 8193125

(B) 8213125

(C) 8233125

(D) 8173125

8. The sum of the mean and variance of a binomial

distribution is 15 and the sum of their squares is 117. The mean of the distribution is

(A) 6 (B) 9 (C) 3 (D) 12 9. In a trial the probability of success is twice the

probability of failure. In six trials the probability of at least four successes will be

(A) 400729

(B) 496729

(C) 500729

(D) 600729

Answer Key

Evaluation Test

Sample

Con

tent

512


512

10. The mean and variance of a binomial distribution (p + q)n are 20 and 16 respectively. Then, the pair (n, p) is

(A) 150,5

(B) 250,5

(C) 1100,5

(D) 2100,5

11. For an initial screening of an admission test, a

candidate is given fifty problems to solve. If the probability that the candidate solve any problem

is 45

, then the probability that he is unable to

solve less than two problems is:

(A) 48164 1

25 5

(B) 48316 4

25 5

(C) 49201 1

5 5

(D) 4954 4

5 5

12. Let a random varibale X have a binomial

distribution with mean 8 and variance 4.

If P(X 2) = 16

k2

, then k is equal to

(A) 17 (B) 1 (C) 137 (D) 121 13. A rifleman is firing at a distant target and has

only 10% chance of hitting it. The least number of rounds, he must fire in order to have more than 50% chance of hitting it at least once is

(A) 5 (B) 7 (C) 9 (D) 11 14. In a binomial distribution B 1n,p

4

. If the

probability of at least one success is greater than

or equal to 910

, then n is greater than

(A) 10 10

1log 4 log 3

(B) 10 10

1log 4 log 3

(C) 10 10

9log 4 log 3

(D) 10 10

4log 4 log 3

15. Let X denote the number of times heads occur

in n tosses of a fair coin. If P (X = 4), P (X = 5) and P (X = 6) are in A.P., the value of n is

(A) 7, 14 (B) 10, 14 (C) 12, 7 (D) 14, 12

1. (B) 2. (B) 3. (B) 4. (C) 5. (C) 6. (C) 7. (B) 8. (B) 9. (B) 10. (C) 11. (D) 12. (C) 13. (B) 14. (A) 15. (A)

Answers to Evaluation TestSample

Con

tent

https://www.targetpublications.org/mht-cet-maths-book-for-2021-engineering-and-pharmacy-entrance-exam-maharashtra-board.html

sample pdf of std 11 and 12 based mht cet triumph maths

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