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[Page 2] Vikas Gupta Director Vibrant Academy India(P) Ltd. KOTA (Rajasthan) [AN ISO 9001-2008 CERTIFIED ORGANIZATION] Advanced Problems in Advanced Problems in Advanced Problems in MATHEMATICS MATHEMATICS MATHEMATICS for for for JEE JEE JEE (MAIN & ADVANCED) (MAIN & ADVANCED) (MAIN & ADVANCED) Pankaj Joshi Director Vibrant Academy India(P) Ltd. KOTA (Rajasthan) by : [Page 3] 1. Function 2. Limit 3. Continuity, Differentiability and Differentiation 4. Application of Derivatives 5. Indefinite and Definite Integration 6. Area Under Curves 7. Differential Equations CALCULUS 3 – 29 30 – 44 45 – 74 75 – 97 98 – 127 128 – 134 135 – 144 CONTENTS 8. Quadratic Equations 9. Sequence and Series 10. Determinants 11. Complex Numbers 12. Matrices 13. Permutation and Combinations 14. Binomial Theorem 15. Probability 16. Logarithms ALGEBRA 147 – 176 177 – 197 198 – 206 207 – 216 217 – 224 225 – 233 234 – 242 243 – 251 252 – 264 [Page 4] 17. Straight Lines 18. Circle 19. Parabola 20. Ellipse 21. Hyperbola CO-ORDINATE GEOMETRY 267 – 280 281 – 295 296 – 302 303 – 307 308 – 312 22. Compound Angles 23. Trigonometric Equations 24. Solution of Triangles 25. Inverse Trigonometric Functions TRIGONOMETRY 315 – 334 335 – 343 344 – 359 360 – 370 26. Vector & 3Dimensional Geometry VECTOR & 3DIMENSIONAL GEOMETRY 373 – 389 [Page 7] 1. Range of the function f x x ( ) log ( log ( sin )) = - + 2 2 2 2 16 1 is : (a) [ , ] 0 1 (b) ( , ] -• 1 (c) [ , ] - 1 1 (d) ( , ) -• • 2. The value of a and b for which| | , | | e a x b - - = 2 has four distinct solutions, are : (a) a Œ - • ( , ), 3 b = 0 (b) a Œ • ( , ), 2 b = 0 (c) a Œ • ( , ), 3 b R Œ (d) a Œ • ( , ), 2 b a = 3. The range of the function : f x x x ( ) tan sin = + - - 1 1 1 2 (a) ( , ) - p p 2 2 (b) [ , ] { } - - p p 2 2 0 (c) [ , ] - p p 2 2 (d) ( , ) - 3 4 3 4 p p 4. Find the number of real ordered pair(s) ( , ) x y for which : 16 16 1 2 2 x y x y + + + = (a) 0 (b) 1 (c) 2 (d) 3 5. The complete range of values of ‘ ’ a such that 1 2 2 Ê Ë Á ˆ ¯ ˜ = - | | x x a is satisfied for maximum number of values of x is : (a) ( , ) -• - 1