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2019 18 questions

Q192019 · 12 Apr 2019 · Shift 1
Let $S_{n}$ denote the sum of the first n terms of an A.P. If $S_{4} = 16$ and $S_{6} = - 48$ , then $S_{10}$ is equal to :
1. A.-320
2. B.-380
3. C.-460
4. D.-210
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Answer: A
Q252019 · 12 Apr 2019 · Shift 1
For $x \in R$ , let [x] denote the greatest integer $\leq x$ , then the sum of the series $[- \frac{1}{3}] + [- \frac{1}{3} - \frac{1}{100}] + [- \frac{1}{3} - \frac{2}{100}] + \dots + [- \frac{1}{3} - \frac{99}{100}]$ is :
1. A.-153
2. B.-135
3. C.-133
4. D.-131
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Answer: C
Q52019 · 12 Apr 2019 · Shift 2
If $α$ , $β$ and $γ$ are three consecutive terms of a non-constant G.P. such that the equations $α x^{2} + 2 β x + γ = 0$ and $x^{2} + x - 1 = 0$ have a common root, then $α (β + γ)$ is equal to :
1. A. $α γ$
2. B.0
3. C. $β γ$
4. D. $α β$
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Answer: C
Q172019 · 12 Apr 2019 · Shift 2
If $a_{1}, a_{2}, a_{3}, \dots$ are in A.P. such that $a_{1} + a_{7} + a_{16} = 40$ , then the sum of the first 15 terms of this A.P. is :
1. A.120
2. B.200
3. C.150
4. D.280
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Answer: B
Q202019 · 10 Apr 2019 · Shift 1
If $a_{1}, a_{2}, a_{3}, \dots, a_{n}$ are in A.P. and $a_{1} + a_{4} + a_{7} + \dots + a_{16} = 114$ , then $a_{1} + a_{6} + a_{11} + a_{16}$ is equal to :
1. A.38
2. B.98
3. C.76
4. D.64
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Answer: C
Q142019 · 10 Apr 2019 · Shift 2
Let $a$ , b and c be in G.P. with common ratio r, where $a \neq = 0$ and $0 < r \leq \frac{1}{2}$ . If 3a, 7b and 15c are the first three terms of an A.P., then the $4^{th}$ term of this A.P. is :
1. A. $a$
2. B. $\frac{7}{3} a$
3. C.5a
4. D. $\frac{2}{3} a$
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Answer: A
Q192019 · 10 Apr 2019 · Shift 2
Let $a_{1}, a_{2}, a_{3}, \dots$ be an A.P. with $a_{6} = 2$ . Then the common difference of this A.P., which maximises the product $a_{1} a_{4} a_{5}$ , is :
1. A. $\frac{3}{2}$
2. B. $\frac{6}{5}$
3. C. $\frac{8}{5}$
4. D. $\frac{2}{3}$
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Answer: C
Q252019 · 10 Apr 2019 · Shift 2
The angles A, B and C of a triangle ABC are in A.P. and $a : b = 1 : 3$ . If c = 4 cm, then the area (in sq. cm) of this triangle is :
1. A. $23$
2. B. $43$
3. C. $\frac{4}{3}$
4. D. $\frac{2}{3}$
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Answer: A
Q132019 · 9 Apr 2019 · Shift 1
Let the sum of the first n terms of a non-constant A.P., $a_{1}, a_{2}, a_{3}, \dots$ be $50 n + \frac{n ( n - 7 )}{2} A$ , where A is a constant. If d is the common difference of this A.P., then the ordered pair $(d, a_{50})$ is equal to
1. A.(A, 50+45A)
2. B.(50, 50+45A)
3. C.(A, 50+46A)
4. D.(50, 50+46A)
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Answer: C
Q32019 · 9 Apr 2019 · Shift 2
If the sum and product of the first three terms in an A.P. are 33 and 1155, respectively, then a value of its $1 1^{t h}$ term is :-
1. A.−25
2. B.−36
3. C.25
4. D.−35
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Answer: A
Q302019 · 9 Apr 2019 · Shift 2
The sum of the series 1 + 2 × 3 + 3 × 5 + 4 × 7 +.... upto 11th term is :-
1. A.945
2. B.916
3. C.915
4. D.946
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Answer: D
Q242019 · 8 Apr 2019 · Shift 2
If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is :
1. A.5 : 9 : 13
2. B.5 : 6 : 7
3. C.4 : 5 : 6
4. D.3 : 4 : 5
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Answer: C
Q112019 · 12 Jan 2019 · Shift 1
The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is :
1. A.36
2. B.28
3. C.32
4. D.24
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Answer: B
Q152019 · 12 Jan 2019 · Shift 2
If $^{n} C_{4}$ , $^{n} C_{5}$ and $^{n} C_{6}$ are in A.P., then n can be :
1. A.11
2. B.12
3. C.9
4. D.14
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Answer: D
Q242019 · 12 Jan 2019 · Shift 2
If the sum of the first 15 terms of the series $(\frac{3}{4})^{3} + (1 \frac{1}{2})^{3} + (2 \frac{1}{4})^{3} + 3^{3} + (3 \frac{3}{4})^{3} + \dots$ is equal to $225 k$ , then k is equal to :
1. A.9
2. B.108
3. C.27
4. D.54
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Answer: C
Q42019 · 11 Jan 2019 · Shift 2
If $1 9^{th}$ term of a non-zero A.P. is zero, then its $(4 9^{th} term) : (2 9^{th} term)$ is :
1. A.2 : 1
2. B.4 : 1
3. C.1 : 3
4. D.3 : 1
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Answer: D
Q72019 · 9 Jan 2019 · Shift 1
If a, b, c be three distinct real numbers in G.P. and a + b + c = xb , then x cannot be
1. A.2
2. B.-3
3. C.4
4. D.-2
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Answer: A
Q222019 · 9 Jan 2019 · Shift 1
Let $a_{1}, a_{2}, \dots, a_{30}$ be an A.P., $S = i = 1 \sum 30 a_{i} and T = i = 1 \sum 15 a_{(2 i - 1)} .$ If $a_{5} = 27$ and $S - 2 T = 75$ , then $a_{10}$ is equal to :
1. A.47
2. B.42
3. C.52
4. D.57
Show answer
Answer: C