1
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
The coefficient of x−5 in the binomial expansion of

$${\left( {{{x + 1} \over {{x^{{2 \over 3}}} - {x^{{1 \over 3}}} + 1}} - {{x - 1} \over {x - {x^{{1 \over 2}}}}}} \right)^{10}},$$ where x $$\ne$$ 0, 1, is :
A
1
B
4
C
$$-$$ 4
D
$$-$$ 1
2
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
If (27)999 is divided by 7, then the remainder is :
A
1
B
2
C
3
D
6
3
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
$${2^{21}} - {2^{11}}$$
4
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
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