1
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
If n is the degree of the polynomial,

$${\left[ {{2 \over {\sqrt {5{x^3} + 1} - \sqrt {5{x^3} - 1} }}} \right]^8} + $$ $${\left[ {{2 \over {\sqrt {5{x^3} + 1} + \sqrt {5{x^3} - 1} }}} \right]^8}$$

and m is the coefficient of xn in it, then the ordered pair (n, m) is equal to :
A
(24, (10)8)
B
(8, 5(10)4)
C
(12, (20)4)
D
(12, 8(10)4)
2
JEE Main 2017 (Online) 9th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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
3
JEE Main 2017 (Online) 8th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If (27)999 is divided by 7, then the remainder is :
A
1
B
2
C
3
D
6
4
JEE Main 2017 (Offline)
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
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
$${2^{21}} - {2^{11}}$$
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