1
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
If the sum of the first 15 terms of the series $${\left( {{3 \over 4}} \right)^3} + {\left( {1{1 \over 2}} \right)^3} + {\left( {2{1 \over 4}} \right)^3} + {3^3} + {\left( {3{3 \over 4}} \right)^3} + ....$$ is equal to 225 k, then k is equal to :
A
9
B
108
C
27
D
54
2
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
If sin4$$\alpha$$ + 4 cos4$$\beta$$ + 2 = 4$$\sqrt 2$$ sin $$\alpha$$ cos $$\beta$$; $$\alpha$$, $$\beta$$ $$\in$$ [0, $$\pi$$],
then cos($$\alpha$$ + $$\beta$$) $$-$$ cos($$\alpha$$ $$-$$ $$\beta$$) is equal to :
A
$$- \sqrt 2$$
B
0
C
$$-$$ 1
D
$$\sqrt 2$$
3
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
If   nC4, nC5 and nC6 are in A.P., then n can be :
A
11
B
12
C
9
D
14
4
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
Let  Sk = $${{1 + 2 + 3 + .... + k} \over k}.$$ If   $$S_1^2 + S_2^2 + .....\, + S_{10}^2 = {5 \over {12}}$$A,  then A is equal to :
A
283
B
156
C
301
D
303
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