MHT-CET Triumph Maths MCQs (Based On XI & XII Syllabus MH . - Free Download PDF

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MHT-CETTRIUMPHMULTIPLE CHOICETEMATHEMATICSNTWritten in accordance with the latest MHT-CET Paper Pattern which includes topics based on Std. XII Sc.and relevant chapters of Std. XI Sc. (Maharashtra State Board)Salient FeaturesN Includes all chapters of Std. XII and relevant chapters of Std. XI as per latestMHT-CET Syllabus.O Exhaustive subtopic wise coverage of MCQs. Important formulae provided in each chapter.C Various competitive exam questions updated till the latest year. Includes MCQs from JEE (Main) 2016, 2017 and 2018. Includes MCQs upto MHT-CET 2018.E Evaluation test provided at the end of each chapter.PL Two Model Question Papers with answer key at the end of the book.SAMScan the adjacent QR code or visit www.targetpublications.org/tp12750to download Hints for relevant questions and Evaluation Test in PDFformat.Printed at: Repro India Ltd., 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.P.O. No. 134996TEID: 12750 JUP

PREFACENT“Triumph Mathematics” is a complete and thorough guide to prepare students for MHT-CET examination. Thisbook is based on the MHT-CET syllabus which includes topics based on Std. XII Sc. and relevant chapters of Std.XI Sc. (Maharashtra State Board)Formulae that form a key part for solving MCQs have been provided in each chapter. Shortcuts for easy and lesstedious solving are also included.MCQs in each chapter are divided into three sections:TEClassical Thinking: consisting of straight forward questions including knowledge based questions.Critical Thinking: consisting of questions that require some understanding of the concept.Competitive Thinking: consisting of questions from various competitive examinations like MHT- CET, JEE (Main),Assam CEE, KEAM, Karnataka CET, TS EAMCET, AP EAMCET, Gujrat CET etc.NAn Evaluation Test has been provided at the end of each chapter and two Model Question Papers(as per MHT-CET pattern) to assess the level of preparation of the student on a competitive level.OHints have been provided in downloadable format to relevant MCQs which are broken down to thesimplest form possible.CThe journey to create a complete book is strewn with triumphs, failures and near misses. If you thinkwe’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] faithfullyEBest of luck to all the aspirants!SAMEdition: FirstDisclaimerThis reference book is transformative work based on textual contents published by Bureau of Textbook. We the publishers are making this reference book which constitutes as fairuse 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 samein examinations.This work is purely inspired upon the course work as prescribed by the Maharashtra State Board of Secondary and Higher Secondary Education, Pune. Every care has been takenin 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 anyperson 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.

MHT-CET PAPER PATTERN NT 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 and HigherSecondary Education with approximately 20% weightage given to Std. XI and 80% weightage will be givento Std. XII curriculum.Difficulty level of questions will be at par with JEE (Main) for Mathematics, Physics, Chemistry and at parwith NEET for Biology.There will be no negative marking.Questions will be mainly application based.Details of the papers are as given below:TE Approximate No. of Multiple ChoiceQuestions (MCQs) based onSubjectStd. XI10Physics1040Chemistry1040Biology (Botany)Paper IIIBiology .ii.EQuestions will be set onthe entire syllabus of Physics, Chemistry, Mathematics and Biology subjects of Std. XII, andchapters / units from Std. XI curriculum as mentioned below:PL MathematicsOPaper IIStd. XIICPaper IMark(s) PerNPaperSubject1PhysicsMSr. No.ChemistrySA234MathematicsChapters / Units of Std. XIMeasurements, Scalars and Vectors, Force, Friction in solids and liquids,Refraction of Light, Ray optics, Magnetic effect of electric current,Magnetism.Some basic concepts of chemistry, States of matter: Gases and liquids,Redox reactions, Surface chemistry, Nature of chemical bond, Hydrogen,s-Block elements (Alkali and alkaline earth metals), Basic principles andtechniques in organic chemistry, Alkanes.Trigonometric functions, Trigonometric functions of Compound Angles,Factorization Formulae, Straight Line, Circle and Conics, Sets, Relationsand Functions, Probability, Sequences and series.BiologySection I – BotanySection II – ZoologyDiversity in organisms, Biochemistry of cell, Plant Water Relations andMineral Nutrition, Plant Growth and Development.Organization of Cell, Animal tissues, Human Nutrition, HumanRespiration.

CONTENTChapter NameStd. XI12Trigonometric Functions23Trigonometric Functions of Compound Angles34Factorization Formulae46Straight Line57Circle and Conics61Sets, Relations and Functions74Sequence and Series811ProbabilityPage No.NTSr. No.TextbookChapterNo.NTE11129385784113142Std. XII1Mathematical Logic102Matrices113Trigonometric Functions202124Pair of Straight Lines233135Vectors248146Three Dimensional Geometry264157Line275168Plane289179Linear plications of Derivatives3824Integration410225Definite Integrals455236Applications of Definite Integral481247Differential Equations493258Probability Distribution521269Binomial Distribution532Model Question Paper - I539Model Question Paper - II5431920SAM21CEPL18O9Note: Questions of standard XI are indicated by ‘*’ in each Model Question Paper.167184

TextbookChapter No.Chapter 02: Trigonometric Functions02SubtopicsNTTrigonometric FunctionsTrigonometry in Graphical MotionTrigonometric Functions2.2Fundamental IdentitiesIncomputergraphics,Trigonometry is used ingraphicalmotionandrotation,3Drotationmatrices are used to rotateobjects and these matricesare made up of severaltrigonometric functions.NTE2.1Chapter at a glanceTrigonometric Functions with the help of standard unit circle:Let m XOP be the angle in standard position and P(x, y) be the point on the terminal ray such thatl(OP) r 0. Then,Yxyi.sin ii.cos rrP(x, y)yriii. tan , (if x 0)iv.cosec , (if y 0)xy XX rxMOvi.cot , (if y 0)v.sec , (if x 0)xy2.Interrelation between trigonometric functions:1, (if sin 0)ii.i.cosec sin sin iii. tan , (if cos 0)iv.cos PLECO1.ii.iii.Signs of trigonometric functions in different quadrants:SA3.QuadrantIIIIIIIVY Trigonometric functions do not depend upon the position of point P on terminal ray butdepends upon the measure of angle ( ).Co-terminal angles have same trigonometric functions.P (x, y) (cos , sin )MNote: i.1, (if cos 0)cos cos cot , (if sin 0)sin sec YSigns of the T-functionsAll T-functions are positivesin and cosec are positive.All others are negative.tan and cot are positive.All others are negative.cos and sec are positive.All others are negative.sin is ve(II)X tan is ve(III)All are ve(I)Ocos is ve(IV)XY 1

MHT-CET Triumph Maths (MCQs)Mnemonics:The above table can be memorized with the help ofAllsintan(I)(II)(III)0 (0c) π 6 Trigonometricfunctionsc π 4 60 c π 3 sin 0121232cos 132112tan 0131cot 31sec 1cosec 90 c π 2 313C23E2c180 ( c)270 3π 2 22–100–101 0 00 0 2 –1 1231 –1 ii.1 tan2 sec2 sec2 tan2 1sec2 1 tan2 iii.1 cot2 cosec2 cosec2 1 cot2 cosec2 cot2 1Domain and range of trigonometric functions:i.The domain, range and period of the six trigonometric functions are given below:M6.sin2 cos2 11 sin2 cos2 1 cos2 sin2 DomainRRRange[–1, 1][–1, 1]Period2 2 tan x x R: x (2n 1) , n I 2 R cot x{x R : x n , n I}R R– (–1, 1)2 R– (–1, 1)2 SAT-functionssin xcos xsec xcosec x2 x R: x (2n 1) , n I 2 {x R : x n , n I}360 (2 c)0Fundamental Identities:For any angle of measure ,i.c1O2PL5.45 30 NTAngles CoffeeN4. ToTE AddSugarTrigonometric functions of particular angles:cos(IV)

Chapter 02: Trigonometric Functionsiii.Standard inequalities of trigonometric functions:a. 1 sin 1b. 1 cos 1c.sec 1 or sec 1d.cosec 1 or cosec 1Periodicity of trigonometric (circular) functions:A function is periodic if its value repeats after every fixed interval. The fixed interval is called period.f(x) f(x n), for all x and x n in domain of f, and n 0a.sin ( 2n ) sin , cos ( 2n ) cos , where n IHence sin and cos are periodic functions and the period is 2 .tan ( n ) tan , cot ( n ) cot , where n ITEb.NTii.Hence tan and cot are periodic functions and the period is .Trigonometric functions of negative angle:i.sin ( ) sin ii.cos ( ) cos iii.tan( ) tan iv.cot ( ) cot v.sec ( ) sec vi.cosec ( ) cosec N7.OShortcuts1 sec tan xIf x sec tan , then2.If x cosec cot , then3.sin 1 sin 2 . sin n nC1.E1 cosec cot x sin 1 sin 2 . sin n 1cos 1 cos 2 . cos n n cos 1 cos 2 . cos n 15.i.ii.6.i.ii.7.sin4 cos4 1 2sin2 cos2 PL4.sin cosec 2 sin 1sin cosec 2 sin 1SAMcos sec 2 cos 1cos sec 2 cos 18.sin6 cos6 1 3sin2 cos2 9.sin2 cos4 cos2 sin4 1 sin2 cos2 10.sin2 cosec2 2, cos2 sec2 2 and sec2 cosec2 411.If sec tan m, m 1, then lies in the first quadrant.If sec tan m, 0 m 1, then lies in the fourth quadrant.If sec tan m, m 1, then lies in the second quadrant.If sec tan m, 1 m 0, then lies in the third quadrant.3

MHT-CET Triumph Maths (MCQs)2.22.139and tan , then cos is42182715(B)(C)(D)62784(A)(A)(C)sec tan is equal tosec tan 14(B)4sin cos 1 cot 1 tan (A) 0(C) cos sin (A)(C)(A)(C)6.11(B)(D) , then tan x is2(B)13IInd quadrantIVth quadrant13.(D)M3(D)SA2(B)4(C)8(D)10.411and cos ( ) , where22 and are positive acute angles, then(A) 45 , 15 (B) 15 , 45 (C) 60 , 15 (D) 15 , 60 10115and lies in the Ist quadrant,then cos is1(A)65(C)6(B)(D) 165 621and lies in the second29quadrant, then the value of sec tan is2255(B)(C) (D) (A)5522(B)(D) , sec4x sec2x2tan4 x tan2 x2 tan2 x16.Which of the following is true?(A) tan2 sin2 tan2 sin2 (B) sec2 cosec2 sec2 cosec2 (C) cosec2 cot2 cosec2 cot2 (D) none of these17.If x sec tan , then x 16If sin 3 cos , then is equal to(B) 30 (A) 45 (C) 75 (D) 60 9.1is equal to(A) tan4x tan2 x(C) tan2 x tan4 x2(A)If tan For any real number x (2n 1)1tan 2 60 cosec 30 If x sin 45 cos 60 , then x sec 45 cot 2 30 15.not defined cos2 tan2 63411(A)(B) (C)228.(D)If sin sin27.111014.0PL(C)and lies in the fourth10quadrant, then sec 1 1(B)(A)1111(C)31and cos , then lies in22Ist quadrantIIIrd quadrantWhen x (A)1cos sin and tan 1, then lies in2first quadrant(B) second quadrantthird quadrant(D) fourth quadrantIf sin 5.12(D)1OIf sin 4.(B)(D)2E3.(C)If tan TE(A)12.NIf 5 sin 3, then2.20, then cos is equal to21201 (B) 41212120 (D) 2921If tan If sin C1.11.Trigonometric FunctionsFundamental IdentitiesNTClassical Thinking(A)(C)If sin ( ) 18.12cot x tan x (A) cot 2x(C) sec x cosec x1 x(B) 2 sec (D) 2 tan (B)(D)2 cot2 xcot2 2x

Chapter 02: Trigonometric Functions(B)22(A)(C)24.25. x y 1 a b (D)23236. x y 1 b a If cos x cos2 x 1, then the value ofsin2 x sin4 x is(A) 1(B) – 1 (C) 0(D) 2286If sin x sin x 1, then cos x 2 cos x cos4 x (A) 0(B) – 1 (C) 2(D) 1Which one of the following is incorrect?1(A) sin (B) cos 151(D) tan 20(C) sec 2Which of the following is possible?87(B) sin (A) cos 55sec 45(D)7.The smallest value of 5 cos 12 is(A) 5(B) 12 (C) 7(D)9.M2.3, then tan 3A 2(A)0(B)12(C)1(D)not definedIf tan (A B) 1, sec (A B) smallest positive value of B is25 (A)(B)2413 (C)(D)24If tan pp sin q cos , then the value ofisp sin q cos q(A)p2 q2p2 q 2(B)(C)0(D)p2 q 2p2 q2p qp qThe value of cos2 sec2 is always(A) less than 1(B) equal to 1(C) greater than 1, but less than 2(D) greater than or equal to 223, then the19 2411 24If sin (A B C) 1, tan (A B) 1and3sec (A C) 2, then(A) A 120 , B 60 , C 0 (B) A 60 , B 30 , C 0 (C) A 90 , B 60 , C 30 (D) A 120 , B 0 , C 60 Fundamental IdentitiesIf cos A 34, cos B and A 0,255 B 0, then the value of22 sin A 4 sin B (A) 4(B) 2(C) 4Trigonometric FunctionsSA1.If cos A 2.217Critical Thinking2.18.tan 45PL(C)26.232O23.23(B)2 b 3 a 3 1 x y 5.C22. a 3 b 3 1 x y 4.N21.0If sin x cosec x 2, then sinn x cosecn x isequal to(A) 2(B) 2n(C) 2n 1(D) 2n 2Which of the following relations is correct ?(A) sin 1 sin 1 (B) sin 1 sin 1 (C) sin 1 sin 1 (D)sin 1 sin 1 180Which of the following is correct ?(A) tan 1 tan 2(B) tan 1 tan 2(C) tan 1 tan 2(D) tan 1 1NT1(C) 1(D) 22If x a cos b sin and y a sin b cos ,then a2 b2 is equal to(B) x2 y2(A) x2 y22(C) (x y)(D) (x y)2If x a cos3 , y b sin3 , then(A)20.3.sin 2 20 cos 4 20 issin 4 20 cos 2 20 TEThe value ofE19.(D)010.If tan sec 3 and 0 , then isequal to 2 5 (B)(C)(D)(A)363611.If 3 , then22(A)(C)sec tan tan sec 1 sin is equal to1 sin (B)(D)sec tan sec2 tan2 5

MHT-CET Triumph Maths (MCQs)(C)17.1 cos 1 cos 1 cos 1 cos 2(B) sin 1(D) sin If sin 23.2pq, then sec tan p2 q 2(A)p qp q(C)p qp qIf sec tan (A)(C)If cos sin cos sin (A)2 sin (C) 2 sin 24.C1If sec tan , then lies in the2(A) first quadrant(B) second quadrant(C) third quadrant(D) fourth quadrant2 cos , then(B)(D)2 sin 2 cos 25.(B)pqp q2(D)pqp q2a2 1a2 12a2a 1a 1, then cos a 1a2 1(B)a2 12a(D)2a 12 a22a 2(B)(D)2a 4MSA19.If un sinn cosn , then 2 u6 3 u4 is equalto(A) 1(B) 12 sin2 cos2 (C) 1(D) 12 tan2 cos2 20.If sin x sin2 x 1, then the value ofcos12 x 3 cos10 x 3 cos8 x cos6 x 2 isequal to(A) 0(B) 1(C) – 1(D) 2The value ofis2 a2If 3 sin 4 cos 5, then the value of3 cos 4 sin is equal to(A) 0(B) 5(C) 5(D) 41, x R, x 0, then the value4xof sec tan is11(B)or 4x(A) – 2x or2x2x11(D) 2x or(C)4x2xIf sec x sin 6 cos6 1 3sin 2 cos 2 49 49 49 49 If sin x cos x a, then sin x cos x equals(C)622.OIf A lies in the second quadrant and3 tan A 4 0, then the value of2 cot A 5 cos A sin A is equal to 53 7(A)(B)1010723(D)(C)1010(A)18.2sin 1sin 2 sec 2 cos PL16.3 , then2(B)(D)NTIf (A)15.2 sec 2 cosec N(A)(C)14.If 10 sin4 15 cos4 6, then27 cosec6 8 sec6 (A) 125(B) 250(C) 50(D) 75 1 sin 1 sin is equal to 1 sin 1 sin of13.21.TEIf lies in the second quadrant, then the valueE12.(A)tan6(C)1 49(B)cot6(D)0 492sin 1 cos sin x, then1 cos sin 1 sin is equal to1(B) x(A)x(D) 1 x(C) 1 x26.If27.The value of the expressionsin 2 y 1 cos ysin y1 is1 cos ysin y1 cos y(A)(C)0sin y(B)(D)1cos y

Chapter 02: Trigonometric Functions(A)(C)30.(D)If A is an obtuse angle, thensin 3 A cos3 Asin A 2 tan A cot Asin A cos A1 tan 2 Ais equal to(A) 1(B) 1(C) 2(D) 2xaysin 1 0 andbxyx2 y 2sin cos 1 0, then 2 2 isababequal to(A) 2(B) 0(C) 2 (D) 1If37.The equation (a b)2 4ab sin2 is possibleonly when(A) 2a b(B) a b(C) a 2b(D) a b38.The maximum value of 12 sin 9 sin2 is(A) 3(B) 4(C) 5(D) 239.If y sin2 cos4 , then for all real values of (A) y [1, 2](B) y [13/16, 1](C) y [3/4, 13/16] (D) y [3/4, 1]Competitive Thinking2.1cos Trigonometric Functions1.5sin 3cos 5sin 2cos [Karnataka CET 1998]11(C)(D) 66If 5 tan 4, thenO29.(B)2sin 1 tan sin (1 tan ) 2If sin 1 sin 2 sin 3 3, thencos 1 cos 2 cos 3 (A) 3(B) 2(C) 1(D) 0NTsin 1 tan 2sin (1 tan )236.TEThevalueoftheexpression22sin tan (1 tan ) 2sin sec is(1 tan ) 2N28.(A)0(B)If x sin3 y cos3 sin cos andx sin y cos 0, then x2 y2 (A) – 1(B) 1(C) 1(D) 02.32.If a cos3 3a cos sin2 m anda sin3 3a cos2 sin n, then(m n)2/3 (m n)2/3 is equal to3.If sin cosec 2, the value ofsin10 cosec10 is[MP PET 2004](A) 10 (B) 210 (C) 29(D) 24.If tan A cot A 4,equal to(A) 110(C) 80sin 200 cos 200 isEC31.22a(C)2a 3(B)2a(D)2a3PL(A)2If tan2 tan2 tan2 tan2 tan2 tan2 2 tan2 tan2 tan2 1, then the value ofsin2 sin2 sin2 is(A) 0(B) – 1 (C) 1(D) 2M33.13If p 2sin cos , thenand q 1 cos sin 1 sin qpq 1(B) 1pq p 1(D) p q 1SA34.(A)(C)35.If x sec tan , y cosec cot , theny 1y 1(B) x (A) x y 1y 1(C)y 1 x1 x(D)y 1 x 1 x 25.If sin cosec 2, then sin2 cosec2 [MP PET 1992; MNR 1990;UPSEAT 2002](A) 1(B) 3(C) 2(D) 4(A)(C)6.7.negativezerothen tan4 A cot4 A is[Kerala (Engg.) 2002](B) 191(D) 194[K.U.K.C.E.E.T. 1995](B) positive(D) zero or positivecos 1 .cos 2 . cos 3 . cos 179 [Karnataka CET 1999; DCE 2005;MHT CET 2018]1(A) 0(B) 1(C) (D) –12 If x 0, , y 0, and sin x cos y 2, 2 2 then the value of x y is equal to[KEAM 2017] (A) 2π (B) π(C)(D)427

MHT-CET Triumph Maths (MCQs)If sin – cos 1, then the value of[KEAM 2018]sin3 – cos3 is equal to(A) 1(B) –1(C) 0(D) 2 4, then sin 3[IIT 1979; Pb. CET 1995; Orissa JEE 2002](A) – 4/5 but not 4/5(B) – 4/5 or 4/5(C) 4/5 but not – 4/54 4(D) Neither nor55If tan 10.2tand lies in the second1 t2quadrant, then cos is equal to[WB JEE 2011]21 tt2 1(A)(B)1 t21 t2 1 t21 t2(D)(C)1 t21 t2If sin 18.EIf cosec cot 2017, then quadrant in[TS EAMCET 2017]which lies is(A) I(B) IV (C) III (D) IIM13.3 , then cosec 2 2 cot is equal4to[Pb. CET 2000; AMU 2001;MP PET 2004](B) 1 cot (A) 1 cot (D) 1 cot (C) 1 cot IfPL12.If cosec cot SA14.is equal to 3(B)(A)515.85 319.21222pp 12(e x e x )2(D)(e x e x )(e x e x )If sin cos 1, then sin cos [Karnataka CET 1998](A) 0(B) 11(C) 2(D)2If 3 sin A 5 cos A 5, then the value of(3 cos A 5 sin A)2 is[MP PET 2010](A) 4(B) 5(C) 2(D) 920.If sec m and tan n, then1 1 (m n) m m n [Karnataka CET 2006](A) 2(B) 2m(C) 2n(D) mn21.If sin cos m and sec cosec n,then n(m 1) (m 1) [MP PET 1986](A) m(B) n(C) 2m(D) 2n22.If 2y cos x sin and 2x sec y cosec 3,then x2 4y2 [WB JEE 1988](A) 4(B) – 4(C) 2(D) 223.If

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 (Botany) 10 40 1 100 Biology (Zoology) 10 40 Questions will be set on i.