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2020 15 questions

Q42020 · 6 Sept 2020 · Shift 2
The common difference of the A.P. $b_{1}, b_{2}, \dots, b_{m}$ is 2 more than the common difference of A.P. $a_{1}, a_{2}, \dots, a_{n}$ . If $a_{40} = - 159$ , $a_{100} = - 399$ and $b_{100} = a_{70}$ , then $b_{1}$ is equal to :
1. A.127
2. B.81
3. C. $- 127$
4. D. $- 81$
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Answer: D
Q52020 · 3 Sept 2020 · Shift 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 :
1. A. $\frac{1}{4}$
2. B. $\frac{1}{5}$
3. C. $\frac{1}{7}$
4. D. $\frac{1}{6}$
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Answer: D
Q182020 · 3 Sept 2020 · Shift 2
If the sum of the series $20 + 19 \frac{3}{5} + 19 \frac{1}{5} + 18 \frac{4}{5} + \dots$ upto nth term is 488 and the $n^{th}$ term is negative, then :
1. A. $n = 41$
2. B. $n = 60$
3. C. $n^{th} term is - 4$
4. D. $n^{th} term is - 4 \frac{2}{5}$
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Answer: C
Q232020 · 3 Sept 2020 · Shift 2· Numerical answer
If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that $4^{th}$ A.M. is equal to $2^{nd}$ G.M., then m is equal to _______.
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Answer: 39
Q112020 · 2 Sept 2020 · Shift 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 :
1. A. $[- 3, \infty)$
2. B. $(- \infty, 9]$
3. C. $(- \infty, - 9] \cup [- 3, \infty)$
4. D. $(- \infty, - 3] \cup [9, \infty)$
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Answer: D
Q152020 · 2 Sept 2020 · Shift 1
If $∣ x ∣ < 1$ , $∣ y ∣ < 1$ and $x \neq = y$ , then the sum to infinity of the following series $(x + y) + (x^{2} + x y + y^{2}) + (x^{3} + x^{2} y + x y^{2} + y^{3}) + \dots$
1. A. $\frac{x + y - x y}{( 1 + x ) ( 1 + y )}$
2. B. $\frac{x + y - x y}{( 1 - x ) ( 1 - y )}$
3. C. $\frac{x + y + x y}{( 1 + x ) ( 1 + y )}$
4. D. $\frac{x + y + x y}{( 1 - x ) ( 1 - y )}$
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Answer: B
Q82020 · 2 Sept 2020 · Shift 2
If the sum of first 11 terms of an A.P., $a_{1}, a_{2}, a_{3}, \dots$ is 0 $(a \neq = 0)$ , then the sum of the A.P., $a_{1}, a_{3}, a_{5}, \dots, a_{23}$ is $k a_{1}$ , where $k$ is equal to :
1. A. $\frac{121}{10}$
2. B. $- \frac{121}{10}$
3. C. $\frac{72}{5}$
4. D. $- \frac{72}{5}$
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Answer: D
Q202020 · 2 Sept 2020 · Shift 2
Let $S$ be the sum of the first 9 terms of the series : ${x + k a} + {x^{2} + (k + 2) a} + {x^{3} + (k + 4) a} + {x^{4} + (k + 6) a} + \dots$ where $a \neq = 0$ and $x \neq = 1$ . If $S = \frac{x ^{10} - x + 45 a ( x - 1 )}{x - 1}$ , then $k$ is equal to :
1. A.-3
2. B.1
3. C.-5
4. D.3
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Answer: A
Q152020 · 9 Jan 2020 · Shift 2
Let $a_{n}$ be the $n^{th}$ term of a G.P. of positive terms. $n = 1 \sum 100 a_{2 n + 1} = 200 and n = 1 \sum 100 a_{2 n} = 100,$ then $\sum_{n = 1}^{200} a_{n}$ is equal to :
1. A.150
2. B.175
3. C.225
4. D.300
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Answer: A
Q212020 · 9 Jan 2020 · Shift 2· Numerical answer
The number of terms common to the two A.P.'s 3, 7, 11, ....., 407 and 2, 9, 16, ....., 709 is ______.
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Answer: 14
Q22020 · 8 Jan 2020 · Shift 1
Let $f : R \to R$ be such that for all $x \in R$ $(2^{1 + x} + 2^{1 - x})$ , $f (x)$ and $(3^{x} + 3^{- x})$ are in A.P., then the minimum value of $f (x)$ is
1. A.2
2. B.0
3. C.3
4. D.4
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Answer: C
Q52020 · 8 Jan 2020 · Shift 2
If the $1 0^{th}$ term of an A.P. is $\frac{1}{20}$ and its $2 0^{th}$ term is $\frac{1}{10}$ , then the sum of its first 200 terms is
1. A.100
2. B. $100 \frac{1}{2}$
3. C. $50 \frac{1}{4}$
4. D.50
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Answer: B
Q162020 · 7 Jan 2020 · Shift 1
Five numbers are in A.P. whose sum is 25 and product is 2520. If one of these five numbers is $- \frac{1}{2}$ , then the greatest number amongst them is:
1. A. $\frac{21}{2}$
2. B.27
3. C.7
4. D.16
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Answer: D
Q42020 · 7 Jan 2020 · Shift 2
Let $a_{1}, a_{2}, a_{3}, \dots$ be a G.P. such that $a_{1} < 0$ , $a_{1} + a_{2} = 4$ and $a_{3} + a_{4} = 16$ . If $\sum_{i = 1}^{9} a_{i} = 4 λ$ , then $λ$ is equal to:
1. A.171
2. B.-171
3. C.-513
4. D. $\frac{511}{3}$
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Answer: B
Q182020 · 7 Jan 2020 · Shift 2
If the sum of the first 40 terms of the series, 3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 + ..... is (102)m, then m is equal to :
1. A.20
2. B.5
3. C.10
4. D.25
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Answer: A