1
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
Out of Syllabus
Let S be the sum of the first 9 terms of the series :
{x + k$$a$$} + {x2 + (k + 2)$$a$$} + {x3 + (k + 4)$$a$$}
+ {x4 + (k + 6)$$a$$} + .... where a $$\ne$$ 0 and x $$\ne$$ 1.

If S = $${{{x^{10}} - x + 45a\left( {x - 1} \right)} \over {x - 1}}$$, then k is equal to :
A
-3
B
1
C
-5
D
3
2
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
Out of Syllabus
If |x| < 1, |y| < 1 and x $$\ne$$ y, then the sum to infinity of the following series

(x + y) + (x2+xy+y2) + (x3+x2y + xy2+y3) + ....
A
$${{x + y - xy} \over {\left( {1 + x} \right)\left( {1 + y} \right)}}$$
B
$${{x + y - xy} \over {\left( {1 - x} \right)\left( {1 - y} \right)}}$$
C
$${{x + y + xy} \over {\left( {1 + x} \right)\left( {1 + y} \right)}}$$
D
$${{x + y + xy} \over {\left( {1 - x} \right)\left( {1 - y} \right)}}$$
3
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in :
A
[-3, $$\infty$$)
B
(-$$\propto$$, 9]
C
(-$$\propto$$, -9] $$\cup$$ [-3, $$\infty$$)
D
(-$$\propto$$, -3] $$\cup$$ [9, $$\infty$$)
4
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
Let an be the nth term of a G.P. of positive terms.

$$\sum\limits_{n = 1}^{100} {{a_{2n + 1}} = 200}$$ and $$\sum\limits_{n = 1}^{100} {{a_{2n}} = 100}$$,

then $$\sum\limits_{n = 1}^{200} {{a_n}}$$ is equal to :
A
150
B
175
C
225
D
300
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