1
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
Let $$\alpha$$ > 0, $$\beta$$ > 0 be such that
$$\alpha$$3 + $$\beta$$2 = 4. If the maximum value of the term independent of x in
the binomial expansion of $${\left( {\alpha {x^{{1 \over 9}}} + \beta {x^{ - {1 \over 6}}}} \right)^{10}}$$ is 10k,
then k is equal to :
A
176
B
336
C
352
D
84
2
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
3
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
$$\alpha - \beta = -132$$
4
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
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