1
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
In the expansion of $${\left( {{x \over {\cos \theta }} + {1 \over {x\sin \theta }}} \right)^{16}}$$, if $${\ell _1}$$ is the least value of the term independent of x when $${\pi \over 8} \le \theta \le {\pi \over 4}$$ and $${\ell _2}$$ is the least value of the term independent of x when $${\pi \over {16}} \le \theta \le {\pi \over 8}$$, then the ratio $${\ell _2}$$ : $${\ell _1}$$ is equal to :
A
8 : 1
B
16 : 1
C
1 : 8
D
1 : 16
2
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
If $$\alpha$$ and $$\beta$$ be the coefficients of x4 and x2 respectively in the expansion of
$${\left( {x + \sqrt {{x^2} - 1} } \right)^6} + {\left( {x - \sqrt {{x^2} - 1} } \right)^6}$$, then
A
$$\alpha + \beta = 60$$
B
$$\alpha - \beta = 60$$
C
$$\alpha + \beta = -30$$
D
$$\alpha - \beta = -132$$
3
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
The coefficient of x7 in the expression
(1 + x)10 + x(1 + x)9 + x2(1 + x)8 + ......+ x10 is:
A
120
B
330
C
420
D
210
4
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
The greatest positive integer k, for which 49k + 1 is a factor of the sum
49125 + 49124 + ..... + 492 + 49 + 1, is:
A
32
B
60
C
63
D
65
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