1
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
$${{2016!} \over {16!}}$$
2
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
3
JEE Main 2015 (Offline)
+4
-1
Out of Syllabus
The sum of coefficients of integral power of $$x$$ in the binomial expansion $${\left( {1 - 2\sqrt x } \right)^{50}}$$ is :
A
$${1 \over 2}\left( {{3^{50}} - 1} \right)$$
B
$${1 \over 2}\left( {{2^{50}} + 1} \right)$$
C
$${1 \over 2}\left( {{3^{50}} + 1} \right)$$
D
$${1 \over 2}\left( {{3^{50}}} \right)$$
4
JEE Main 2014 (Offline)
+4
-1
Out of Syllabus
If the coefficints of $${x^3}$$ and $${x^4}$$ in the expansion of $$\left( {1 + ax + b{x^2}} \right){\left( {1 - 2x} \right)^{18}}$$ in powers of $$x$$ are both zero, then $$\left( {a,\,b} \right)$$ is equal to:
A
$$\left( {14,{{272} \over 3}} \right)$$
B
$$\left( {16,{{272} \over 3}} \right)$$
C
$$\left( {16,{{251} \over 3}} \right)$$
D
$$\left( {14,{{251} \over 3}} \right)$$
EXAM MAP
Medical
NEET