Home
Class 12
MATHS
The constant term in the expansion of ...

The constant term in the expansion of
`(log(x^(logx))-log_(x^(2))100)^(12)` is (base of lof is 10) `"_____"`.

A

495

B

924

C

1050

D

5050

Text Solution

Verified by Experts

The correct Answer is:
A
`logx=t`
`(t^(2)-(1)/(t))^(12)`
`T_(r+1)=""^(12)C_(r)(t^(2))^(12-r)(-(1)/(t))^(r)=""^(12)C_(r)t^(24-3r)(-1)^(r)`
For constant term r=8 & coefficient `""^(12)C_(8)`
`(12xx11xx10xx9)/(24)=45xx11=495`
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 1

    VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION-2)|10 Videos

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|78 Videos

  • MOCK TEST 10

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

Similar Questions

Explore conceptually related problems

Constant term in the expansion of ( x- (1)/(x)) ^(10) is

9^(1+logx)-3^(1+logx)-210=0 where the base of log is 10

The coefficient of x^(n) in the expansion of log_(a)(1+x) is

The third term in the expansion of (x + x ^[log_10 x])^5 is 10^6 then x =

Solve the equation: (log(x+1))/(logx)=2

The sixth term in the expansion of ( sqrt(2^(log(10-3^x))) + (2^((x-2)log3))^(1/5))^m is equal to 21, if it is known that the binomial coefficient of the 2nd 3rd and 4th terms in the expansion represent, respectively, the first, third and fifth terms of an A.P. (the symbol log stands for logarithm to the base 10) The value of m is

The sixth term in the expansion of ( sqrt(2^(log(10-3^x))) + (2^((x-2)log3))^(1/5))^m is equal to 21, if it is known that the binomial coefficient of the 2nd 3rd and 4th terms in the expansion represent, respectively, the first, third and fifth terms of an A.P. (the symbol log stands for logarithm to the base 10) The value of m is

The sixth term in the expansion of ( sqrt(2^(log(10-3^x))) + (2^((x-2)log3))^(1/5))^m is equal to 21, if it is known that the binomial coefficient of the 2nd 3rd and 4th terms in the expansion represent, respectively, the first, third and fifth terms of an A.P. (the symbol log stands for logarithm to the base 10) The value of m is

If the third term in the expansion of (x + x log_10 x)^5 is 10^6 then x is

The domain of f(x)=log|logx| is