1
JEE Main 2017 (Offline)
+4
-1
Out of Syllabus
The value of $$\left( {{}^{21}{C_1} - {}^{10}{C_1}} \right) + \left( {{}^{21}{C_2} - {}^{10}{C_2}} \right) + \left( {{}^{21}{C_3} - {}^{10}{C_3}} \right)$$
$$\left( {{}^{21}{C_4} - {}^{10}{C_4}} \right)$$$$+ .... + \left( {{}^{21}{C_{10}} - {}^{10}{C_{10}}} \right)$$ is
A
$${2^{21}} - {2^{10}}$$
B
$${2^{20}} - {2^{9}}$$
C
$${2^{20}} - {2^{10}}$$
D
$${2^{21}} - {2^{11}}$$
2
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
If the coefficients of x−2 and x−4 in the expansion of $${\left( {{x^{{1 \over 3}}} + {1 \over {2{x^{{1 \over 3}}}}}} \right)^{18}},\left( {x > 0} \right),$$ are m and n respectively, then $${m \over n}$$ is equal to :
A
182
B
$${4 \over 5}$$
C
$${5 \over 4}$$
D
27
3
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1
For x $$\in$$ R, x $$\ne$$ -1,

if (1 + x)2016 + x(1 + x)2015 + x2(1 + x)2014 + . . . . + x2016 =

$$\sum\limits_{i = 0}^{2016} {{a_i}} \,{x^i},\,\,$$ then a17 is equal to :
A
$${{2017!} \over {17!\,\,\,2000!}}$$
B
$${{2016!} \over {17!\,\,\,1999!}}$$
C
$${{2017!} \over {2000!}}$$
D
$${{2016!} \over {16!}}$$
4
JEE Main 2016 (Offline)
+4
-1
Out of Syllabus
If the number of terms in the expansion of $${\left( {1 - {2 \over x} + {4 \over {{x^2}}}} \right)^n},\,x \ne 0,$$ is 28, then the sum of the coefficients of all the terms in this expansion, is :
A
243
B
729
C
64
D
2187
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