मराठी

Number of terms in the expansion of (a + b)n where n ∈ N is one less than the power n.

Advertisements
Advertisements

प्रश्न

Number of terms in the expansion of (a + b)n where n ∈ N is one less than the power n.

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर
Advertisements

उत्तर

This statement is False.

Explanation:

Since, the number of terms in the given expression (a + b)n is 1 more than n

i.e., n + 1

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Binomial Theorem - Exercise [पृष्ठ १४६]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11
पाठ 8 Binomial Theorem
Exercise | Q 40 | पृष्ठ १४६

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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


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


Find ab and n in the expansion of (a + b)n if the first three terms of the expansion are 729, 7290 and 30375, respectively.


Find a if the coefficients of x2 and x3 in the expansion of (3 + ax)9 are equal.


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


Find the value of `(a^2 + sqrt(a^2 - 1))^4 + (a^2 - sqrt(a^2 -1))^4`


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


Find the expansion of (3x2 – 2ax + 3a2)3 using binomial theorem.


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

 

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`


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


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 coefficient of x15 in the expansion of (x – x2)10.


Find the coefficient of x4 in the expansion of (1 + x + x2 + x3)11.


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 


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 4OE = (x + a)2n – (x – a)2n 


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 number of terms in the expansion of (x + y + z)n ______.


The coefficient of a–6b4 in the expansion of `(1/a - (2b)/3)^10` is ______.


Let the coefficients of x–1 and x–3 in the expansion of `(2x^(1/5) - 1/x^(1/5))^15`, x > 0, be m and n respectively. If r is a positive integer such that mn2 = 15Cr, 2r, then the value of r is equal to ______.


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


Let `(5 + 2sqrt(6))^n` = p + f where n∈N and p∈N and 0 < f < 1 then the value of f2 – f + pf – p is ______. 


The positive integer just greater than (1 + 0.0001)10000 is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×