1
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of $${\left( {{2^{1/3}} + {1 \over {2{{\left( 3 \right)}^{1/3}}}}} \right)^{10}}$$ is :
A
1 : 2(6)1/3
B
1 : 4(6)1/3
C
2(36)1/3 : 1
D
4(36)1/3 : 1
2
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
Out of Syllabus
Let (x + 10)50 + (x $$-$$ 10)50 = a0 + a1x + a2x2 + . . . . + a50x50, for all x $$\in$$ R; then $${{{a_2}} \over {{a_0}}}$$ is equal to
A
12.25
B
12.75
C
12.00
D
12.50
3
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
4
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
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