## Vineet Loomba is teaching live on Unacademy Plus

SOLVED EXAMPLES BINOMIAL THEOREM JEE MAIN RANK BOOSTER COURSE PREPARED BY: ER. VINEET LOOMBA ITIAN IIT-JEE MENTOR

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME ** B.Tech. From IIT Roorkee -$ IIT-JEE Mentor Since 2010. -^ Doubts/Feedback in Comment Section * Comment other topics you want to revise. * Follow me @ https://unacademy.com/user/vineetloomba to get unacademy updates or search me on Google * Share among your peers as SHARING is CARING!!

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Other Detailed Courses Made so far on Unacademv: V Strategy for JEE Main and Advanced V Sets, Relations and Functions V Trigonometry V Applications of Derivatives Limits, Continuity. Differentiability V Indefinite Integration V Definite Integration V Complex Number V Logarithmic Functions V Sequences Series V Most Important Questions in IIT-JEE Permutations Combinations Binomial Theorem V Straight Lines V Applications of Integrals V Circles (Detailed Course) V Probability MathematicS V Parabola (Detailed Course) v Inverse Trigonometry V Mathematical Reasoning V Ellipse (Detailed Course) V Hyperbola Upcoming Courses next month: Coordinate Geometry > Differential Equations Differential Equations MATHEMATI ER. VINEET LOOMBA (IIT RooRKee)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example # Find the number of rational terms in the expansion of (9174 + 81'6)100. SUCCESS IN JEE MAIN 2019 ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) 1000 The general term in the expansion of (91/4 +81/6 IS 1000-r 1000-r r r1100C 94 The above term will be rational if exponent of 3 and 2 are integers It means2 The possible set of values of r is 0, 2, 4, 6 =1000c, 32 22 1000-r and must be integers 2 .., 1000) Hence, number of rational terms is 501 SUCCESS IN EE MAIN 2019 ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Find the middle term(s) in the expansion of Y214 1 14 2 Solution: 2 14+2 th term. Here, n is even, therefore middle term is It means Ta is middle term 7 429 2 x-1 =- Ta4C, X14. Ans. 2 SUCCESS IN JEE MAIN 2019 ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) th&M.1)th Solution Here, n is odd therefore, middle terms are l- - 2 It means T. & T are middle terms 4 189 aAns T6 = 9C5 (3a)9-51-6. a19. Ans 16 SUCCESS IN EE MAIN 2019 ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example # Find the numerically greatest term in the expansion of (3 - 5x)" when x-5. Solution. Let rth and (r1)th be two consecutive terms in the expansion of (3-5x)15 T., 2T 3.(15)! (15-r)!r! 5. 5 (16-r)23r 16-r23r4rs 16 rs 4 SUCCESS IN JEE MAIN 2019 ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example # Find the last two digits of the number (17)1 Solution. (17)'0(289)5 = (290-1)5 - A multiple of 1000 1449 Hence, last two digits are 49 SUCCESS IN JEE MAIN 2019 ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example # If x is so small such that its square and higher powers may be neglected (1- -3x)1'2 +(1-x)513 then find the value of (4 +x) 1/2 Solution 513 (4+x) 1/2 4 2 x 19 812 x Ans. 24 SUCCESS IN EE MAIN 2019 ER. VINEET LOOMBA (IIT RooRKEe)