Choose the Correct options
0 of 20 questions completed
Questions:
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading…
You must sign in or sign up to start the quiz.
You must first complete the following:
0 of 20 questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 point(s), (0)
Earned Point(s): 0 of 0, (0)
0 Essay(s) Pending (Possible Point(s): 0)
Average score 

Your score 

Let m be the smallest positive integer such that the coefficient of \(x^2\) in the expansion of \({\left( {1 + x} \right)^2}{\left( {x + 1} \right)^3} + …. + {(1 + x)^{49}} + {(1 + mx)^{50}}\) is \({\left( {3x + 1} \right)^{51}}{C_3}\) for some +ve integer n. Then n is equal to
coefficient of in the expansion of
51n+1 must be perfect square
when n=5
m=16 when n=5
The coefficient of three consecutive terms of \({\left( {1 + x} \right)^{n + 5}}\) are in the ratio 5:10:14; then n=
Thus, and
For solving for r, we obtained r=4
Thus
The sum of coefficients of all odd degree terms in the expansion of \({\left( {x + \sqrt {{x^3} – 1} } \right)^5} + {\left( {x – \sqrt {{x^3} – 1} } \right)^5},(x > 1)\) is
Here a=x, b=
Sum of coefficient of odd degree terms = 2{110+5+5}=2
The coefficient of \({x^{10}}\) in the expansion of \({\left( {1 + x} \right)^2}{\left( {1 + {x^2}} \right)^3}{(1 + {x^3})^4}\) is
So, coefficient of
The coefficient of \({x^{2}}\) in the expansion of the product \(\left( {2 – {x^2}} \right)\left[\left( {1 + 2x + 3{x^2}} \right)^6 + \left( {1 – 4{x^2}} \right)^6\right]\) is
So, coefficient of coefficient in
– constant term in
The value of \(\left( {{}^{21}{C_1} – {}^{10}{C_1}} \right) + \left( {{}^{21}{C_2} – {}^{10}{C_2}} \right) + \left( {{}^{21}{C_3} – {}^{10}{C_3}} \right) + \left( {{}^{21}{C_4} – {}^{10}{C_4}} \right) + \cdots + \left( {{}^{21}{C_{10}} – {}^{10}{C_{10}}} \right) \) is
The coefficient of \({{x^{ – 5}}}\) in the expansion of \({\left( {{x^2} – \frac{5}{{{x^3}}}} \right)^{10}}\) is
205r= 5
5r=25
r=5
coefficient of is
If no. of terms in the expansion of \({(1 – \dfrac{2}{x} + \dfrac{4}{{{x^2}}})^n},x \ne 0\) is 28, then the sum of the coefficient of all the terms in this expansion is
The no. of terms in the expansion of is
n=6
Sum of coefficients
If \({\left( {1 + x} \right)^{2016}} + x{\left( {1 + x} \right)^{2015}} + {x^2}{(1 + x)^{2014}} + …. + {x^{2016}} = \sum\limits_{i = 10}^{2016} {{a_i}{x^i},} \) then \({{a_{17}}}\) is
let
coefficient of
If \({\left( {a + bx} \right)^{ – 3}} = \dfrac{1}{{27}} + \dfrac{1}{3}x + …,\) the ordered pair (a,b) equals to
We have,
(a,b)=(3,9)
If \({r^\text{th}}\) and \({(r + 1)^{th}}\) term in the expansion of \({\left( {p + q} \right)^n}\) are equal, then the value of \(\dfrac{{(n + 1)q}}{{r(p + q)}}\) is
If \({x^{2x}}\) occurs \({\left( {x + \frac{2}{{{x^2}}}} \right)^n}\), then n2r must be of the form.
n2r=3r
If two consecutive terms in the expansion of \({\left( {3 + 2x} \right)^{74}}\), whose coefficients are equal, are
have equal coefficients.
The coefficient of x in the expansion of \(\left( {1 + x} \right)\left( {1 + 2x} \right)\left( {1 + 3x} \right) \cdots \left( {1 + 100x} \right)\) is
The coefficient of x in the expansion of
is
=5050
The coefficient of \( x^{r}\) in the expansion of \({\left( {1 + x} \right)^{ – 2}}\) is
coefficient of is r+1.
The coefficient of \( x^{20} \) in the expansion of \({\left( {1 + 3x + 3{x^2} + {x^3}} \right)^{20}}\) is
Coefficient of is
The \({9^{{\text{th}}}}\) term of the expansion of \({\left( {3x – \frac{1}{{2x}}} \right)^8}\) is
Find the \({11^{{\text{th}}}}\) term in the expansion of \({\left( {4x – \frac{1}{{2{x^2}}}} \right)^{12}}\).
If the expansion in powers of x of the function \(\dfrac{1}{{\left( {1 – ax} \right)\left( {1 – bx} \right)}}\) is \({a_0} + {a_1}x + {a_2}{x^2} + \cdots ,\) then coefficient of \({x^n}\) is
coefficient of in the expansion is
If the \({2^{{\text{nd}}}}\) term in the expansion of \(\left( \sqrt[13]{a} + \dfrac{a}{{\sqrt {{a^{ – 1}}} }} \right)^n\) is \(14{a^{\frac{5}{2}}}\), then the value of \(\dfrac{{{}^n{C_3}}}{{{}^n{C_2}}}\) is