1
JEE Main 2020 (Online) 3rd September Morning Slot
+4
-1
If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is :
A
$${1 \over 4}$$
B
$${1 \over 5}$$
C
$${1 \over 7}$$
D
$${1 \over 6}$$
2
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
If the sum of first 11 terms of an A.P.,
a1, a2, a3, .... is 0 (a $$\ne$$ 0), then the sum of the A.P.,
a1 , a3 , a5 ,....., a23 is ka1 , where k is equal to :
A
$${{121} \over {10}}$$
B
-$${{121} \over {10}}$$
C
$${{72} \over 5}$$
D
-$${{72} \over 5}$$
3
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
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
4
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
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
$${{x + y + xy} \over {\left( {1 - x} \right)\left( {1 - y} \right)}}$$
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