MY CART (5)

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
Menu
                   

the highest prime less than 50, that divides the binomial coefficient 100C50 ? a) 37, b) 31, c)47 d)43

3 years ago

Share

Answers : (1)

                                        

100C50 = 100!/(50!)2


 


We can express the factorials as exponents of prime numbers. But that is not suppossedly required. We start with the highest ones.


 


Exponent of 47 in 100! = [100/47] = 2


Exponent of 47 in (50!)^2  =  [50/47]*2 = 1*2 = 2


So the exponent of 47 in (50!)^2 and 100! is same, hence they cancel out.


 


(For mcq purposes you can make an intelligent guess from right his point. You require a number that divides 100 thrice but 50 once. 33 is the required number).


Exponent of 43 in 100! = [100/43] = 2


Exponent of 43 in (50!)^2  =  [50/43]*2 = 1*2 = 2


 


Exponent of 37 in 100! = [100/37] = 2


Exponent of 37 in (50!)^2  =  [50/37]*2 = 1*2 = 2


 


Exponent of 33 in 100! = [100/33] = 3


Exponent of 33 in (50!)^2  =  [50/33]*2 = 1*2 = 2


 


Here, one 33 remains uncancelled in the numerator. So the answer is actually 33. But as i dont see an option, i would go for 31 because the other numbers dont satisfy the condition whereas 31 does. But it isnt the HIGHEST prime number doing that.

3 years ago

Post Your Answer

Solve : 5(5^x+5^-x)=26
 
 
Dear Student. Assume 5 x = y and then try to solve the quadratic equation in terms of y. Then replace back the orginial value of y and find the value of x. Thanks.
  img
Vijay Mukati one month ago
 
5(5 x + 5 -x ) = 26 let 5 x = y so 5 - x = 1/y 5(y + 1/y) = 26 5( (y2 + 1)/y ) = 26 (y2 + 1)/y = 26/5 so 5 x = 5 x = 1
 
Abishek arun one month ago
Dear Sir Please get this questions solved .. Thank a lot
 
 
The range for this function will be [-1, 1]. Because the value fo function is -1 for x less than or equal to -1 and is equal to 1 for x greater than or equal to x. and is equal to x for x in...
  img
Vijay Mukati 15 days ago
mathematics(Ratio and proportion)sample question and answer
 
 
Kindly refer to any Maths book for it. Thanks.
  img
Vijay Mukati one month ago
solve the triangle in which c=3.4 cm , angleA=25,and angleB=85
 
 
From Sine rule (SinA)/a=(SinB)/b=(SinC)/c (Sin25 0 )/a=(Sin85 0 )/b=(Sin70 0 )/3.4 a=1.5295 b=3.6054 c=3.4
 
2016 years ago
integrate [sin(x+a)]/[sin(x+b)] a and b are constants
 
 
use over here substitution let x+a=t and further solve plz aprve
 
grenade 2 months ago
 
the then u could use by parts
 
grenade 2 months ago
Supply missing number 45 , 41, _ , 50 , 25 , 29 ? correct answer is 17 but i require solution
 
 
Every term is equal to the sum of square of digits of previous term. For example, 41 = 4 2 + 5 2 missing term = 4 2 + 1 2 = 17 and then you can verify for rest of the series like 1 2 + 7 2...
 
Hasan Naqvi 2 months ago
 
Dear Aakash, Your point redemption request has been approved. Please check your mail inbox and revert to us at the earliest so that we can issue gift voucher to you. Thanks Forum Team
 
Forum Team 14 days ago
View all Questions »
More Questions On Algebra

Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details