1
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
Out of Syllabus
Let Sn = 1 + q + q2 + . . . . . + qn and Tn = 1 + $$\left( {{{q + 1} \over 2}} \right) + {\left( {{{q + 1} \over 2}} \right)^2}$$ + . . . . . .+ $${\left( {{{q + 1} \over 2}} \right)^n}$$ where q is a real number and q $$\ne$$ 1. If   101C1 + 101C2 . S1 + .... + 101C101 . S100 = $$\alpha$$T100 then $$\alpha$$ is equal to
A
202
B
200
C
2100
D
299
2
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
Out of Syllabus
The value of r for which 20Cr 20C0 + 20Cr$$-$$1 20C1 + 20Cr$$-$$2 20C2 + . . . . .+ 20C0 20Cr  is maximum, is
A
20
B
15
C
10
D
11
3
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
The sum of the real values of x for which the middle term in the binomial expansion of $${\left( {{{{x^3}} \over 3} + {3 \over x}} \right)^8}$$ equals 5670 is :
A
0
B
8
C
6
D
4
4
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
The positive value of $$\lambda$$ for which the co-efficient of x2 in the expression x2 $${\left( {\sqrt x + {\lambda \over {{x^2}}}} \right)^{10}}$$ is 720, is -
A
4
B
$$2\sqrt 2$$
C
3
D
$$\sqrt 5$$
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