1
JEE Main 2021 (Online) 25th February Evening Shift
+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
$$2\sqrt a$$
2
JEE Main 2021 (Online) 25th February Morning Shift
+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
3
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
4
JEE Main 2020 (Online) 6th September Morning Slot
+4
-1
Let a , b, c , d and p be any non zero distinct real numbers such that
(a2 + b2 + c2)p2 – 2(ab + bc + cd)p + (b2 + c2 + d2) = 0. Then :
A
a, c, p are in G.P.
B
a, b, c, d are in G.P.
C
a, b, c, d are in A.P.
D
a, c, p are in A.P.
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