1
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1

Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5 . Let the sum of its first five terms be $$\frac{98}{25}$$. Then the sum of the first 21 terms of an AP, whose first term is $$10\mathrm{a r}, \mathrm{n}^{\text {th }}$$ term is $$\mathrm{a}_{\mathrm{n}}$$ and the common difference is $$10 \mathrm{ar}^{2}$$, is equal to :

A
$$21 \,\mathrm{a}_{11}$$
B
$$22 \,\mathrm{a}_{11}$$
C
$$15 \,\mathrm{a}_{16}$$
D
$$14 \,\mathrm{a}_{16}$$
2
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1

Suppose $$a_{1}, a_{2}, \ldots, a_{n}$$, .. be an arithmetic progression of natural numbers. If the ratio of the sum of first five terms to the sum of first nine terms of the progression is $$5: 17$$ and , $$110 < {a_{15}} < 120$$, then the sum of the first ten terms of the progression is equal to

A
290
B
380
C
460
D
510
3
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

Consider two G.Ps. 2, 22, 23, ..... and 4, 42, 43, .... of 60 and n terms respectively. If the geometric mean of all the 60 + n terms is $${(2)^{{{225} \over 8}}}$$, then $$\sum\limits_{k = 1}^n {k(n - k)}$$ is equal to :

A
560
B
1540
C
1330
D
2600
4
JEE Main 2022 (Online) 25th July Evening Shift
+4
-1
Out of Syllabus

The sum $$\sum\limits_{n = 1}^{21} {{3 \over {(4n - 1)(4n + 3)}}}$$ is equal to

A
$$\frac{7}{87}$$
B
$$\frac{7}{29}$$
C
$$\frac{14}{87}$$
D
$$\frac{21}{29}$$
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