## Vineet Loomba is teaching live on Unacademy Plus

EE MAIN AND ADVANCED RANK BoOSTER COURSE PREVIOUS YEAR QUESTIONS PERMUTATIONS COMBINATIONS JEE MAIN 2019 PREPARED BY: ER. VINEET LOOMBA IITIAN IIT-IEE MENTOR

SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B. Tech. From IIT Roorkee IIT-JEE Mentor Since 2010. .,. Verified Star Educator @ Unacademy Youtuber. Founder @ vineetloomba.com unacademy Many of my students are pursuing courses in IITs, NITs etc. Search "vineet loomba unacademy on GOOGLE

EE MAIN AND ADVANCED RANK BoOSTER COURSE PREVIOUS YEAR QUESTIONS PERMUTATIONS COMBINATIONS JEE MAIN 2019 PREPARED BY: ER. VINEET LOOMBA IITIAN IIT-IEE MENTOR

SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Other Detailed Courses Made so far on Unacademy: Strategy for JEE Main and Advanced Sets, Relations and Functions Trigonometry Applications of Derivatives Permutations Combinations Binomial Theorem Straight Lines Applications of Integrals Circles (Detailed Course) Probability Limits, Continuity, Differentiability Indefinite Integration ..#finite Into(Jtation Complex Number Logarithmic Functions Sequences Series Most Important Questions in IIT-JEE Mathematics Parabola (Detailed Course) Inverse Trigonometry Mathematical Reasoning Ellipse (Detailed Course) Hyperbola Differential Equations Upcoming Courses next month: Statistics Matrices Determinants MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT ROORKEE)

SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repitition of digits allowed) is equal to (2) 375 (4) 372 (JEE Main 2019) (1) 374 (3) 250 Solution: Number of numbers with 'I' digit 4 4 Number of numbers with '2' digits 4 x 5 20 Number of numbers with '3' digits 4 x 5 x 5 100 Number of numbers with '4' digits 2 x 5 x 5 x 5 250 Total number of numbers-4 + 20 + 100 + 250= 374 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT ROORKEE)

SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is: (2) 32 (4) 18 (IEE Main 2019) o, b) (3) 36 Solution: Area of AOAB V2 ab labi-100 > lal Ibl-100 (a, 0) 0 but 100 = 1 x 100, 2 50, 4 x 25, 5 x 20 or 10 x 10 For 1 x 100, a 1 or-1 and b 100 or 100 Total possible pairs are 8 and for 10 10 total possible pairs are 4. Required Answer = 4 8 + 4 = 36. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IT R OORKEE)

SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is (1) 200 (3) 500 (JEE Main 2019) (2) 350 (4) 300 Firstly select 2 girls by 5C2 ways. Solution: 3 boys can be selected in following 3 scenarios. (i) Selection of A and selection of any 2 other boys (except B) C2 ways (ii) Selection of B and selection of any 2 other boys (except A)52 ways (ii) Selection of 3 boys (except A and B) C3 ways Number of ways = 5C2 (5C2 + 5C2 + 5G)= 300 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT ROORKEE)

SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) The sum of all two digit positive numbers which when divided by7 yield 2 or 5 as remainder is (1) 1465 (3) 1365 Example: (JEE Main 2019) (2) 1356 (4) 1256 Solution: S2 12 + 19 + 26+.... +96 702 Required Sum 654 702- 1356 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT ROORKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Save Save for this Course (Free) MOST IMPORTANT QUESTIONS IN MATHEMATICS Recommend Lessons (Like) TEE MAIN AND ADVANCED PREPARED ER. VINEET LOOMS . Rate and Review the Course MADE EASY ITIAN IIT-IEE MENTOR 00:00 05:46 SURE SHOT SUCCESS IN JEE MAIN AND ADVANCED CIIT-IEE) Comments ib 91 likes 18 comments Share HINDI Crash Course Maths Sharing with friends (Hindi) Most Important Questions in IIT-JEE Mathematics (Chapter- Wise) Vineet Loomba 11k Followers Follow 5.0 (51 ratings) Edit review SUCCESS IN JEE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT ROORKEE)