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2021 13 questions

Q132021 · 1 Sept 2021 · Shift 2
Let $a_{1}, a_{2}, \dots, a_{21}$ be an AP such that $\sum_{n = 1}^{20} \frac{1}{a _{n} a _{n + 1}} = \frac{4}{9}$ . If the sum of this AP is 189, then $a_{6} a_{16}$ is equal to :
1. A.57
2. B.72
3. C.48
4. D.36
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Answer: B
Q242021 · 26 Aug 2021 · Shift 2· Numerical answer
Let $a_{1}, a_{2}, \dots, a_{10}$ be an AP with common difference $- 3$ and $b_{1}, b_{2}, \dots, b_{10}$ be a GP with common ratio 2. Let $c_{k} = a_{k} + b_{k}$ , $k = 1, 2, \dots, 10$ . If $c_{2} = 12$ and $c_{3} = 13$ , then $\sum_{k = 1}^{10} c_{k}$ is equal to ________.
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Answer: 2021
Q52021 · 27 Jul 2021 · Shift 2
If $tan (\frac{π}{9}), x, tan (\frac{7 π}{18})$ are in arithmetic progression and $tan (\frac{π}{9}), y, tan (\frac{5 π}{18})$ are also in arithmetic progression, then $∣ x - 2 y ∣$ is equal to :
1. A.4
2. B.3
3. C.0
4. D.1
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Answer: C
Q22021 · 25 Jul 2021 · Shift 1
Let $S_{n}$ be the sum of the first n terms of an arithmetic progression. If $S_{3 n} = 3 S_{2 n}$ , then the value of $\frac{S _{4 n}}{S _{2 n}}$ is :
1. A.6
2. B.4
3. C.2
4. D.8
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Answer: A
Q12021 · 22 Jul 2021 · Shift 2
Let $S_{n}$ denote the sum of first n-terms of an arithmetic progression. If $S_{10} = 530$ , $S_{5} = 140$ , then $S_{20} - S_{6}$ is equal to:
1. A. $1862$
2. B. $1842$
3. C. $1852$
4. D. $1872$
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Answer: A
Q262021 · 20 Jul 2021 · Shift 1· Numerical answer
Let a, b, c, d in arithmetic progression with common difference $λ$ . If $x + a - c x - 1 x - b + d x + b x + c x + d x + a x + b x + c = 2,$ then value of $λ^{2}$ is equal to ________.
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Answer: 1
Q142021 · 18 Mar 2021 · Shift 2
Let $S_{1}$ be the sum of first 2n terms of an arithmetic progression. Let $S_{2}$ be the sum of first 4n terms of the same arithmetic progression. If $(S_{2} - S_{1})$ is 1000, then the sum of the first 6n terms of the arithmetic progression is equal to :
1. A.7000
2. B.1000
3. C.3000
4. D.5000
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Answer: C
Q242021 · 16 Mar 2021 · Shift 1· Numerical answer
Consider an arithmetic series and a geometric series having four initial terms from the set {11, 8, 21, 16, 26, 32, 4}. If the last terms of these series are the maximum possible four digit numbers, then the number of common terms in these two series is equal to ___________.
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Answer: 3
Q142021 · 26 Feb 2021 · Shift 1
In an increasing geometric series, the sum of the second and the sixth term is $\frac{25}{2}$ and the product of the third and fifth term is 25. Then, the sum of $4^{th}, 6^{th}$ and $8^{th}$ terms is equal to :
1. A.30
2. B.32
3. C.26
4. D.35
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Answer: D
Q152021 · 26 Feb 2021 · Shift 1
The sum of the infinite series $1 + \frac{2}{3} + \frac{7}{3 ^{2}} + \frac{12}{3 ^{3}} + \frac{17}{3 ^{4}} + \frac{22}{3 ^{5}} + \dots\dots$ is equal to :
1. A. $\frac{9}{4}$
2. B. $\frac{13}{4}$
3. C. $\frac{15}{4}$
4. D. $\frac{11}{4}$
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Answer: B
Q192021 · 26 Feb 2021 · Shift 2
The sum of the series $\sum_{n = 1}^{\infty} \frac{n ^{2} + 6 n + 10}{( 2 n + 1 )!}$ is equal to :
1. A. $\frac{41}{8} e + \frac{19}{8} e^{- 1} - 10$
2. B. $\frac{41}{8} e - \frac{19}{8} e^{- 1} - 10$
3. C. $\frac{41}{8} e + \frac{19}{8} e^{- 1} + 10$
4. D. $- \frac{41}{8} e + \frac{19}{8} e^{- 1} - 10$
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Answer: B
Q252021 · 26 Feb 2021 · Shift 2· Numerical answer
If the arithmetic mean and geometric mean of the $p^{th}$ and $q^{th}$ terms of the sequence $- 16, 8, - 4, 2, \dots\dots$ satisfy the equation $4 x^{2} - 9 x + 5 = 0$ , then $p + q$ is equal to _________.
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Answer: 10
Q22021 · 25 Feb 2021 · Shift 2
A function f(x) is given by $f (x) = \frac{5 ^{x}}{5 ^{x} + 5}$ , then the sum of the series $f (\frac{1}{20}) + f (\frac{2}{20}) + f (\frac{3}{20}) + \dots + f (\frac{39}{20})$ is equal to :
1. A. $\frac{39}{2}$
2. B. $\frac{19}{2}$
3. C. $\frac{49}{2}$
4. D. $\frac{29}{2}$
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Answer: A