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Topic Question Set

Q 41 :

Consider an A.P.: $a_{1}, a_{2}, \dots, a_{n}$ ; $a_{1} > 0$ . If $a_{2} - a_{1} = \frac{- 3}{4}, a_{n} = \frac{1}{4} a_{1}$ and $\sum_{i = 1}^{n} a_{i} = \frac{525}{2},$ then $\sum_{i = 1}^{17} a_{i}$ is equal to: [2026]

952
136
476
238

1

2

3

4

(4)

Q 42 :

If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4, then the sum of its first twelve terms is [2026]

−20
−26
−24
−22

1

2

3

4

(4)

Q 43 :

Let the arithmetic mean of $\frac{1}{a} a n d \frac{1}{b} b e \frac{5}{16}, a > 2 .$ If $α$ is such that $a, 4, α, b$ are in A.P., then the equation $α x^{2} - a x + 2 (α - 2 b) = 0$ has: [2026]

both roots in the interval (-2,0)
one root in (0,2) and another in (-4,-2)
one root in (1,4) and another in (-2,0)
complex roots of magnitude less than 2

1

2

3

4

(3)

Q 44 :

Let $a_{1}, a_{2}, a_{3}, a_{4}$ be an A.P. of four terms such that each term of the A.P. and its common difference $l$ are integers. If $a_{1} + a_{2} + a_{3} + a_{4} = 48$ and $a_{1} a_{2} a_{3} a_{4} + l^{4} = 361,$ then the largest term of the A.P. is equal to [2026]

23
21
24
27

1

2

3

4

(4)

Q 45 :

The common difference of the A.P. $a_{1}, a_{2}, \dots, a_{m} i s 13$ more than the common difference of the A.P. $b_{1}, b_{2}, \dots, b_{n}$ . If $b_{31} = - 277, b_{43} = - 385 a n d a_{78} = 327$ , then $a_{1}$ is equal to [2026]

21
16
24
19

1

2

3

4

(4)

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