Binomial Theorem

MCQ's collected from all Engineering Entrance Examinations (Click here)


Important Formulas:


   


 


  ,   


 


  , , ,


  is












16.  


17.  


18. If    is a rational number and   then   In the above series the general term is


19. If    is a rational number and   then


20. If    is a rational number and   then


21. If    is a rational number and   then


22. If    is a rational number and   then  


23. If    is a rational number and   then


24.  If    is a rational number and   then


25. If    is a rational number and   then


26. If    is a rational number and   then


27. If    is a rational number and   then


28. If    is a rational number and   then


29. Let and where, for   is the integral part of then. If  is not an integer , then   is the numerically greatest term in the binomial expansion of


30.Let and where, for   is the integral part of then. If  is  an integer , then are numerically greatest term in the binomial expansion of


31.The coefficient of in the expansion of is where for all


32.The  term independent of in the expansion of is where


33.The number of non zero terms in the expansion of is   if is odd


34.The number of non zero terms in the expansion of is   if is even.


35.The number of non zero terms in the expansion of is   if is even.


36.The number of non zero terms in the expansion of is   if is odd


37. Multinomial Theorem: If and then .............1

where the summation is taken over all non negative integers    such that   and the number of terms in the expansion of 1 is


38.If  and   is polynomial , then sum of the coefficients in is


39.If  and   is polynomial , then sum of the coefficients of odd power of     in is   [sum of the coefficients of even terms]


40.If  and   is polynomial , then sum of the coefficients of odd power of     in is   [sum of the coefficients of odd terms]


41.If the coefficients of three consecutive terms in the expansion of   are in A.P., then


42. The middle term in the expansion of is


for_BINOMIAL-THEOREM