Years IIT-JEE CHAPTERWISE SOLVED PAPERS MATHEMATICS
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2 Years IIT-JEE CHAPTERWISE SOLVED PAPERS MATHEMATICS
3 Information contained in this work has been obtained by Career Point from sources believed to be reliable. However, neither Career Point nor its authors guarantee the accuracy or completeness of any information published herein, and neither Career Point nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that Career Point and its authors are supplying information but are not attempting to render any professional services. If such services are required, the assistance of an appropriate professional should be sought. CAREER POINT CP Tower, Road No.-, IPIA, Kota (Raj.) publication@cpil.in Copyright 06, by Career Point Ltd. No part of this publication may be reproduced or distributed in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise or stored in a database or retrieval system without the prior written permission of the Publishers. The program listings (if any) may be entered, stored and eecuted in a computer system, but they may not be reproduced for publication. This edition can be eported from India only by the publisher. Published by Career Point Ltd. CP Tower, Road No.-, IPIA, Kota (Raj.) publication@cpil.in
4 Preface Whenever a student decides to prepare for any eamination, her/his first and foremost curiosity about the type of questions that he/she has to face. This becomes more important in the contet of competitive eaminations where there is neck-to-neck race. We feel great pleasure to present before you this book. We have made an attempt to provide chapter wise questions asked in IIT-JEE / JEE Advanced from 978 to 06 along with solutions. Solutions to the questions are not just sketch rather have been written in such a manner that the students will be able to under the application of concept and can answer some other related questions too. We firmly believe that the book in this form will definitely help a genuine, hardworking student. We have tried our best to keep errors out of this book. Comment and criticism from readers will be highly appreciated and incorporated in the subsequent edition. We wish to utilize the opportunity to place on record our special thanks to all team members of Content Development for their efforts to make this wonderful book. Career Point Ltd.
5 Chapter CONTENTS Page No.. Logarithm and their Properties. Theory of Equations 5 0. Sequences & Series 9 0. Comple Numbers Permutation & Combination Binomial Theorem Probability Determinants Matrices Functions Limits Cont...
6 Chapter Page No.. Continuity & Differentiability Differentiation Tangent & Normal Monotonicity Maima & Minima Indefinite Integration Definite Integration Area under the curve Differential Equation 9 6. Point & Straight Lines Circle Parabola Cont...
7 ,, Chapter Page No.. Ellipse 9 5. Hyperbola Vectors D Geometry Trigonometric ratio & Identities Trigonometric Equations Inverse Trigonometric Functions Properties of Triangles Height & Distance Mathematical Induction Miscellaneous Model Test Papers Practice Test [Paper ] 579 Practice Test [Paper ] 585 Practice Test [Paper ] 59 Practice Test [Paper ] 599
8 Chapter Logarithm and their Properties ONLY ONE CORRECT ANSWER. The least value of the epression 0 (0.0), for >, is : [980] (A) 0 (B) (C) 0.0 (D) None of these. If 0. ( ) < 0.09 ( ), then lies in the interval : [985, M] (A) (, ) (B) (, ) (C) (, ) (D) None of these 5 ( ) +. The equation (A) at least one real solution (B) eactly three real solutions (C) eactly one irrational solution (D) comple roots = has : [987, M]. The number 7 is : [990, M] (A) an integer (B) a rational number (C) an irrational number (D) a prime number ONE OR MORE THAN ONE CORRECT ANSWERS. If =, then = [0] (A) (B) (C) (D) ANALYTICAL & DESCRIPTIVE QUESTIONS. Solve for the following equation : ( + ) (6 + + ) = ( + 7) ( + + 9) [987, M]. The value of is [0] 5. The number of solutions of ( ) = ( ) is : [00] (A) (B) (C) (D) 0 6. Let ( 0, y 0 ) be the solution of the following equations () ln = (y) ln ln = ln y Then 0 is [0] (A) (B) 6 (C) (D) 6
9 TOPIC- WISE JEE Advanced Questions with Solutions ANSWERS Only One Correct Answer. (D). (A). (B). (C) 5. (B) 6. (C) One or More than One Correct Answers. (A,B,C) Analytical & Descriptive Question. =.
10 LOGARITHM AND THEIR PROPERTIES SOLUTIONS Only One Correct Answer. Here, 0 (0) ( ) = = = 0 + () 0 using, A.M. G.M., we get or 0 (0.0) least value is. 0 / (). 0. ( ) < 0.09 ( ) Here, > 0 and (0.) ( ) < ( ) (0.) > and 0. ( ) < 0. ( ) > and (0.) ( ) < 0 > and > > and > (, ) 5 ( ) +. = ( ) 5 + = ( ) 5 + = ( ) + ( ) 5( ) = 0 Put, = y y + y 5y = 0 (y ) (y + ) (y + ) = 0 y =,, =,, =, /,. Let = 7 = 7. Which is only possible for irrational number. 5. ( ) = ( ) = / ( ) ( ) = ( ) ( ) = ( ) ( ) = = = = 0 ( 5) ( 5) = 0 ( ) ( 5) = 0 =, or = 5 Hence, = 5 [ = makes ( ) undefined]. Therefore, (B) is the answer. 6. () ln = (y) ln ln (ln + ln ) = ln (ln + ln y) ln. ln ln ln y = (ln ) (ln )...() ln = ln y ln. ln = lny. ln ln ln y = ln ln Solving () & () ln = ln = One or More than One Correct Answers. = Take both sides = ( ) = ( ) ( ) =...()
11 = = = Analytical & Descriptive Question. ( + ) (6 + + ) = ( + 7) ( + + 9) ( + ) ( + ).( + 7) = ( + 7) ( + ) + ( + ) ( + 7) = ( + 7) ( + ) Put ( + ) ( + 7) = y TOPIC- WISE JEE Advanced Questions with Solutions. Let =... = + = = 6 = +7 6 = 6 + / = 6 +./ 9 = 6 = 8 y + = 0 y y y + = 0 (y ) (y ) = 0 y = or y = ( + ) ( + 7) = or ( + ) ( + 7) = + 7 = + or ( + 7) = ( + ) = or + 7 = = = 0 ( + ) ( + ) = 0 =,. =,, But, eists only when, > > 0, + > 0 and + 7 > 0 > = is the only solution.
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