Advertisements
Advertisements
प्रश्न
The two successive terms in the expansion of (1 + x)24 whose coefficients are in the ratio 1:4 are ______.
विकल्प
3rd and 4th
4th and 5th
5th and 6th
6th and 7th
Advertisements
उत्तर
The two successive terms in the expansion of (1 + x)24 whose coefficients are in the ratio 1:4 are 5th and 6th.
Explanation:
Let rth and (r + 1)th be two successive terms in the expansion (1 + x)24
∴ `"T"_(r + 1) = ""^24"C"_r * x^r`
`"T"_(r + 2) = "T"_(r + 1 + 1) = ""^24"C"_(r + 1) x^(r + 1)`
We have `(""^24"C"_r)/(""^24"C"_(r + 1)) = 1/4`
⇒ `((24!)/(r!(24 - r)!))/((24!)/((r + 1)!(24 - r - 1)!)) = 1/4`
⇒ `(24!)/(r!(24 - r)!) xx ((r - 1)!(24 - r - 1)!)/(24!) = 1/4`
⇒ `((r + 1) * r!(24 - r - 1)!)/(r!(24 - r)(24 - r - 1)!) = 1/4`
⇒ `(r + 1)/(24 - r) = 1/4`
⇒ 4r + 4 = 24 – r
⇒ 5r = 20
⇒ r = 4
∴ T4+1 = T5 and T4+2 = T6
APPEARS IN
संबंधित प्रश्न
Expand the expression: (2x – 3)6
Expand the expression: `(x/3 + 1/x)^5`
Using Binomial Theorem, evaluate of the following:
(102)5
Using binomial theorem, evaluate the following:
(99)5
Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000.
Find (x + 1)6 + (x – 1)6. Hence or otherwise evaluate `(sqrt2 + 1)^6 + (sqrt2 -1)^6`
Show that 9n+1 – 8n – 9 is divisible by 64, whenever n is a positive integer.
Find a if the coefficients of x2 and x3 in the expansion of (3 + ax)9 are equal.
If n is a positive integer, prove that \[3^{3n} - 26n - 1\] is divisible by 676.
Using binomial theorem determine which number is larger (1.2)4000 or 800?
Find the rth term in the expansion of `(x + 1/x)^(2r)`
Find the 4th term from the end in the expansion of `(x^3/2 - 2/x^2)^9`
Determine whether the expansion of `(x^2 - 2/x)^18` will contain a term containing x10?
Show that `2^(4n + 4) - 15n - 16`, where n ∈ N is divisible by 225.
Which of the following is larger? 9950 + 10050 or 10150
If the coefficients of x7 and x8 in `2 + x^n/3` are equal, then n is ______.
If (1 – x + x2)n = a0 + a1 x + a2 x2 + ... + a2n x2n , then a0 + a2 + a4 + ... + a2n equals ______.
The number of terms in the expansion of (a + b + c)n, where n ∈ N is ______.
Find the coefficient of x15 in the expansion of (x – x2)10.
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 number of terms in the expansion of (x + y + z)n ______.
If the coefficients of (2r + 4)th, (r – 2)th terms in the expansion of (1 + x)18 are equal, then r is ______.
The positive integer just greater than (1 + 0.0001)10000 is ______.
