1
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
$${1 \over 2}\left( {{3^{50}}} \right)$$
2
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
$$\left( {14,{{251} \over 3}} \right)$$
3
JEE Main 2013 (Offline)
+4
-1
The term independent of $$x$$ in expansion of
$${\left( {{{x + 1} \over {{x^{2/3}} - {x^{1/3}} + 1}} - {{x - 1} \over {x - {x^{1/2}}}}} \right)^{10}}$$ is
A
4
B
120
C
210
D
310
4
AIEEE 2012
+4
-1
If $$n$$ is a positive integer, then $${\left( {\sqrt 3 + 1} \right)^{2n}} - {\left( {\sqrt 3 - 1} \right)^{2n}}$$ is :
A
an irrational number
B
an odd positive integer
C
an even positive integer
D
a rational number other than positive integers
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