1
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
2
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
3
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.
4
JEE Main 2020 (Online) 5th September Evening Slot
+4
-1
If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eighth terms is 243, then the sum of the first 50 terms of this G.P. is :
A
$${2 \over {13}}\left( {{3^{50}} - 1} \right)$$
B
$${1 \over {13}}\left( {{3^{50}} - 1} \right)$$
C
$${1 \over {26}}\left( {{3^{49}} - 1} \right)$$
D
$${1 \over {26}}\left( {{3^{50}} - 1} \right)$$
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