मराठी

Which of the following is larger? 9950 + 10050 or 10150 - Mathematics

Advertisements
Advertisements

प्रश्न

Which of the following is larger? 9950 + 10050  or 10150

बेरीज
Advertisements

उत्तर

We have (101)50 = (100 + 1)50

= `100^50 + 50(100)^49 + (50*49)/(2*1) (100)^48 + (50*49*48)/(3*2*1) (100)^47 +` ......(1)

Similarly 9950 = (100 – 1)50

= `100^50 - 50 * 100^59 + (50*49)/(2*1) (100)^48 - (50*49*48)/(3*2*1) (100)^47 +`  ....(2)

Subtracting (2) from (1), we get

10150 – 9950 = `2  50*(100)^49 + (50*49*48)/(3*2*1) 100^47 +`  ....

⇒ 10150 – 9950 = `100^50 + 2  (50*49*48)/(3*2*1)  10^47 +`  ....

⇒ 10150 – 9950 > 10050

Hence 10150 > 9950 + 10050

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Binomial Theorem - Solved Examples [पृष्ठ १३७]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
पाठ 8 Binomial Theorem
Solved Examples | Q 13 | पृष्ठ १३७

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Expand the expression: (1– 2x)5


Expand the expression: `(2/x - x/2)^5`


Expand the expression: (2x – 3)6


Expand the expression: `(x/3 + 1/x)^5`


Using Binomial Theorem, evaluate the following:

(96)3


Using Binomial Theorem, evaluate of the following:
(102)5


Using binomial theorem, evaluate f the following:

(101)4


Using binomial theorem, evaluate the following:

(99)5


Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000.


Find (a + b)4 – (a – b)4. Hence, evaluate `(sqrt3 + sqrt2)^4 - (sqrt3 - sqrt2)^4`


Find (x + 1)6 + (x – 1)6. Hence or otherwise evaluate `(sqrt2 + 1)^6 + (sqrt2 -1)^6`


Prove that `sum_(r-0)^n 3^r  ""^nC_r = 4^n`


Find the coefficient of x5 in the product (1 + 2x)6 (1 – x)7 using binomial theorem.


If a and b are distinct integers, prove that a – b is a factor of an – bn, whenever n is a positive integer.

[Hint: write an = (a – b + b)n and expand]


Find an approximation of (0.99)5 using the first three terms of its expansion.


Using binomial theorem determine which number is larger (1.2)4000 or 800?

 

Find the value of (1.01)10 + (1 − 0.01)10 correct to 7 places of decimal.

 

Show that  \[2^{4n + 4} - 15n - 16\]  , where n ∈  \[\mathbb{N}\]  is divisible by 225.

 
  
  

Find the rth term in the expansion of `(x + 1/x)^(2r)`


Expand the following (1 – x + x2)4 


Evaluate: `(x^2 - sqrt(1 - x^2))^4 + (x^2 + sqrt(1 - x^2))^4`


Determine whether the expansion of `(x^2 - 2/x)^18` will contain a term containing x10?


Find the term independent of x in the expansion of `(sqrt(x)/sqrt(3) + sqrt(3)/(2x^2))^10`.


If a1, a2, a3 and a4 are the coefficient of any four consecutive terms in the expansion of (1 + x)n, prove that `(a_1)/(a_1 + a_2) + (a_3)/(a_3 + a_4) = (2a_2)/(a_2 + a_3)`


If the coefficients of x7 and x8 in `2 + x^n/3` are equal, then n is ______.


The coefficient of xp and xq (p and q are positive integers) in the expansion of (1 + x)p + q are ______.


The number of terms in the expansion of (a + b + c)n, where n ∈ N is ______.


If z = `sqrt(3)/2 + i^5/2 + sqrt(3)/2 - i^5/2`, then ______.


Find the coefficient of x in the expansion of (1 – 3x + 7x2)(1 – x)16.


Find the sixth term of the expansion `(y^(1/2) + x^(1/3))^"n"`, if the binomial coefficient of the third term from the end is 45.


If the coefficient of second, third and fourth terms in the expansion of (1 + x)2n are in A.P. Show that 2n2 – 9n + 7 = 0.


In the expansion of (x + a)n if the sum of odd terms is denoted by O and the sum of even term by E. Then prove that O2 – E2 = (x2 – a2)n 


The total number of terms in the expansion of (x + a)100 + (x – a)100 after simplification is ______.


Given the integers r > 1, n > 2, and coefficients of (3r)th and (r + 2)nd terms in the binomial expansion of (1 + x)2n are equal, then ______.


The sum of the last eight coefficients in the expansion of (1 + x)16 is equal to ______.


If the coefficients of (2r + 4)th, (r – 2)th terms in the expansion of (1 + x)18 are equal, then r is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×