JEE Main 2020 (Online) 2nd September Evening Slot | Sequences and Series Question 189 | Mathematics

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 :

$${{121} \over {10}}$$

-$${{121} \over {10}}$$

$${{72} \over 5}$$

-$${{72} \over 5}$$

JEE Main 2020 (Online) 2nd September Morning Slot

MCQ (Single Correct Answer)

-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 :

[-3, $$\infty $$)

(-$$ \propto $$, 9]

(-$$ \propto $$, -9] $$ \cup $$ [-3, $$\infty $$)

(-$$ \propto $$, -3] $$ \cup $$ [9, $$\infty $$)

JEE Main 2020 (Online) 2nd September Morning Slot

MCQ (Single Correct Answer)

-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) + ....

$${{x + y - xy} \over {\left( {1 + x} \right)\left( {1 + y} \right)}}$$

$${{x + y - xy} \over {\left( {1 - x} \right)\left( {1 - y} \right)}}$$

$${{x + y + xy} \over {\left( {1 + x} \right)\left( {1 + y} \right)}}$$

$${{x + y + xy} \over {\left( {1 - x} \right)\left( {1 - y} \right)}}$$

JEE Main 2020 (Online) 9th January Evening Slot

MCQ (Single Correct Answer)

-1

Let a_n be the n^th 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 :

150

175

225

300

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