MY CART (5)

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
                   

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

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
the 3 rd term and 7 th term of an A.P are 13 & 33 respy..find the nth term of the ap
 
 
Given, 3 rd term is 13.So, a+2d=13 7 th term is 33.So,a+6d=33 On solving, a=3,d=5 T n =a+(n-1)d T n =3+5n-5=5n-2 So, the nth term of this A.P is 5n-2.
 
CHANDRA KIRAN 3 months ago
 
Given, 3 rd term is 13.So, a+2d=13 7 th term is 33.So,a+6d=33 On solving, a=3,d=5 T n =a+(n-1)d T n =3+5n-5=5n-2 So, the nth term of this A.P is 5n-2.
 
CHANDRA KIRAN 3 months ago
 
a+2d=13 and a+6d=33. On solving, a=3,d=5. T n =a+(n-1)d=5n-2.
 
viswanath 3 months ago
How to find log base 3 of 243?
 
 
first of all conver 243 into something which will be the power of three and then simply use the log properties to solve for the answer plz aprve
 
grenade one month ago
 
the answer would have been 5 plz aprve
 
grenade one month ago
if 2x^2+6x+b is a quadratic equation, where b is less than zero. the the value of alpha/beta + beta/alphs is less than
 
 
Yes i miss that part Answer will be -2 At this step = [(9-2(b/2))/b/2] = (18-2b)/b = 18/b -2 Since b is less than 0 first term will be negative So maximum value of above will be -2.
  img
Harsh Patodia 3 months ago
 
i assume alpha and beta are roots of above equation sum of roots = -3 Product of roots= b/2 = = = (18-b)/b = 18/b -1 Since b is less than 0 first term will be negative So maximum value of...
  img
Harsh Patodia 3 months ago
 
I understand answer is less than 2
 
vinod 3 months ago
Q . IF THE DISTANCE OF ANY POINT ( x , y ) FROM THE ORIGIN IS DEFINED AS d( x,y) = max { | x | , | y | } , d( x,y) = a , non-zero constant, THEN THE LOCUS IS - A CIRCLE A SQUARE A STRAIGHT...
 
 
The answer, from the given options, should be A TRIANGLE. I got it by eliminating the rest of the options. P.S:- I have checked for the first three options. From them, i haven’t got the...
 
Yash Jain 6 months ago
 
it is a squre with line X=+a,-a Y=+a,-a
 
Abhishek Singh 6 months ago
1∫ -1 ( x + 3) dx
 
 
integration of x+3 from -1 to 1 is equal to (((x^2)/2)+3x) from -1 to 1 ((1/2)+(3))-((1/2)-3) =3+3 =6
 
Miryala Gopalakrishna 8 months ago
 
Ans:- 1 ∫ -1 (x+3)dx =[(x 2 /2)+3x] -1 1 =[(1 2 )/2 -(-1 2 )/2]+3(1-(-1)) =(1/2)-(1/2)+6 =6
 
Anusha 8 months ago
View all Questions »