1
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
The sum of the infinite series
$$1 + {2 \over 3} + {7 \over {{3^2}}} + {{12} \over {{3^3}}} + {{17} \over {{3^4}}} + {{22} \over {{3^5}}} + ......$$ is equal to :
A
$${9 \over 4}$$
B
$${13 \over 4}$$
C
$${15 \over 4}$$
D
$${11 \over 4}$$
2
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
In an increasing geometric series, the sum of the second and the sixth term is $${{25} \over 2}$$ and the product of the third and fifth term is 25. Then, the sum of 4th, 6th and 8th terms is equal to :
A
30
B
32
C
26
D
35
3
JEE Main 2021 (Online) 25th February Morning Slot
+4
-1
If $$0 < \theta ,\phi < {\pi \over 2},x = \sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\theta } ,y = \sum\limits_{n = 0}^\infty {{{\sin }^{2n}}\phi }$$ and $$z = \sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\theta .{{\sin }^{2n}}\phi }$$ then :
A
xy $$-$$ z = (x + y)z
B
xyz = 4
C
xy + z = (x + y)z
D
xy + yz + zx = z
4
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
The common difference of the A.P.
b1, b2, … , bm is 2 more than the common
difference of A.P. a1, a2, …, an. If
a40 = –159, a100 = –399 and b100 = a70, then b1 is equal to :
A
127
B
81
C
–127
D
-81
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