Years IIT-JEE CHAPTERWISE SOLVED PAPERS MATHEMATICS
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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.
Chapter CONTENTS Page No.. Logarithm and their Properties. Theory of Equations 5 0. Sequences & Series 9 0. Comple Numbers 70 50 5 5 Permutation & Combination 7 80 75 76 6. Binomial Theorem 8 9 8 85 7. Probability 9 0 05 8. Determinants 5 0 9 0 9. Matrices 5 5 6 0. Functions 5 70 58 59. Limits 7 80 7 75 Cont...
Chapter Page No.. Continuity & Differentiability 8 0 88 89 Differentiation 05 08 09. Tangent & Normal 5 7 8 5. Monotonicity 5 8 9 6. Maima & Minima 5 5 0 7. Indefinite Integration 5 6 55 56 8. Definite Integration 6 0 7 75 9. Area under the curve 05 8 0 0. Differential Equation 9 6. Point & Straight Lines 7 68 5 5. Circle 69 98 76 77. Parabola 99 8 0 05 Cont...
,, Chapter Page No.. Ellipse 9 5. Hyperbola 6 7 6. Vectors 8 55 57 7. D Geometry 8 98 89 90 8. Trigonometric ratio & Identities 99 506 50 50 9. Trigonometric Equations 507 50 5 5 0. Inverse Trigonometric Functions 5 58 5 5. Properties of Triangles 59 550 5 55. Height & Distance 55 560 55 55. Mathematical Induction 56 57 56. Miscellaneous 57 578 575 576 5. Model Test Papers 579 608 Practice Test [Paper ] 579 Practice Test [Paper ] 585 Practice Test [Paper ] 59 Practice Test [Paper ] 599
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 6 +... 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
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. =.
LOGARITHM AND THEIR PROPERTIES SOLUTIONS Only One Correct Answer. Here, 0 (0) ( ) = 0 + 0 = 0 + 0 = 0 + () 0 using, A.M. G.M., we get 0 + 0 0. 0 + 0 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. ( ) = ( ) = / ( ) ( ) = ( ) ( ) = ( ) ( ) = + 9 6 = 7 + 0 = 0 5 + 0 = 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 = ( ) = ( ) ( ) =...()
= = = Analytical & Descriptive Question. ( + ) (6 + + ) = ( + 7) ( + + 9) ( + ) ( + ).( + 7) = ( + 7) ( + ) + ( + ) ( + 7) = ( + 7) ( + ) Put ( + ) ( + 7) = y TOPIC- WISE JEE Advanced Questions with Solutions. Let =... = + = 0 + +.. = 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 = + + 9 + 9 + = 0 + 8 + + = 0 ( + ) ( + ) = 0 =,. =,, But, eists only when, 6 + + > 0. + + 9 > 0, + > 0 and + 7 > 0 > = is the only solution.