1
JEE Main 2021 (Online) 26th February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
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
MCQ (Single Correct Answer)
+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 Evening Shift
MCQ (Single Correct Answer)
+4
-1
The minimum value of $$f(x) = {a^{{a^x}}} + {a^{1 - {a^x}}}$$, where a, $$x \in R$$ and a > 0, is equal to :
A
$$a + {1 \over a}$$
B
2a
C
a + 1
D
$$2\sqrt a $$
4
JEE Main 2021 (Online) 25th February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
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
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