Phrases Progressions Previous Year Question Paper and Solution with PDF

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Previous Year Questions
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Phrases Previous Year Questions (PYQs)

Phrases Progressions PYQ

Qus : 1Phrases PYQ

The sum of infinite terms of a decreasing GP is equal to the greatest value of the function

in the interval [-2,3] and the difference between the first two terms is f'(0). Then the common ratio of GP is

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Phrases Previous Year PYQPhrases NIMCET 2019 PYQ

Solution

Qus : 2Phrases PYQ

If $a, b, c$ are in GP and $log a - log 2b$, $log 2b - log 3c$ and $log 3c - log a$ are in AP, then $a, b, c$are the lengths of the sides of a triangle which is

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Phrases Previous Year PYQPhrases NIMCET 2019 PYQ

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Qus : 3Phrases PYQ

Not Available

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Phrases Previous Year PYQPhrases NIMCET 2019 PYQ

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Qus : 4Phrases PYQ

If $a, a, a_2, ., a_{2n-1},b$ are in AP, $a, b_1, b_2,...b_{2n-1}, b $are in GP and $a, c_1, c_2,... c_{2n-1}, b $ are in HP, where a, b are positive, then the equation $a_n x^2-b_n+c_n$ has its roots

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Phrases Previous Year PYQPhrases NIMCET 2019 PYQ

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Qus : 5Phrases PYQ

If $x=1+\sqrt[{6}]{2}+\sqrt[{6}]{4}+\sqrt[{6}]{8}+\sqrt[{6}]{16}+\sqrt[{6}]{32}$ then ${\Bigg{(}1+\frac{1}{x}\Bigg{)}}^{24}$ =

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Phrases Previous Year PYQPhrases NIMCET 2024 PYQ

Solution

Qus : 6Phrases PYQ

The number of solutions of ${5}^{1+|\sin x|+|\sin x{|}^2+\ldots}=25$ for $x\in(-\mathrm{\pi},\mathrm{\pi})$ is

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Phrases Previous Year PYQPhrases NIMCET 2024 PYQ

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Qus : 7Phrases PYQ

Which term of the series $\frac{\sqrt[]{5}}{3},\, \frac{\sqrt[]{5}}{4},\frac{1}{\sqrt[]{5}},\, ...$ is $\frac{\sqrt{5}}{13}$ ?

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Phrases Previous Year PYQPhrases NIMCET 2022 PYQ

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Qus : 8Phrases PYQ

In a Harmonic Progression, $p^{th}$ term is $q$ and the $q^{th}$ term is $p$. Then $pq^{th}$ term is

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Phrases Previous Year PYQPhrases NIMCET 2022 PYQ

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Qus : 9Phrases PYQ

Sum to infinity of a geometric is twice the sum of the first two terms. Then what are the possible values of common ratio?

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Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

Solution

Qus : 10Phrases PYQ

Suppose that m and n are fixed numbers such that the mth term am is equal to n and nth term an is equal to m, (m≠n), the the value of (m+n)th term is

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Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

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Qus : 11Phrases PYQ

The harmonic mean of two numbers is 4. Their arithmetic mean A and the geometric mean G satisfy the relation 2A+G² = 27, then the two numbers are

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Phrases Previous Year PYQPhrases NIMCET 2017 PYQ

Solution

Qus : 12Phrases PYQ

Three positive number whose sum is 21 are in arithmetic progression. If 2, 2, 14 are added to them respectively then resulting numbers are in geometric progression. Then which of the following is not among the three numbers?

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Phrases Previous Year PYQPhrases NIMCET 2017 PYQ

Solution

Let the three terms in A.P. be a – d, a, a + d.

given that a – d + a + a + d = 21

a = 7

then the three term in A.P. are 7 – d, 7, 7 + d

According to given condition 9 – d, 9, 21 + d are in G.P.

(9)² = (9 – d) (21 + d)

81 = 189 + 9d – 21d – d²

81 = 189 – 12d – d²

d² + 12d – 108 = 0

d(d + 18) – 6 (d + 18) = 0

(d – 6) (d + 18) = 0

We get, d = 6, –18

Putting d = 6 in the term 7 – d, 7, 7 + d we get 1, 7, 13.

Qus : 13Phrases PYQ

If $H_1,H_2,\ldots,H_n$ are n harmonic means between a and b $(b\ne a)$;,then $\frac{{{H}}_n+a}{{{H}}_n-a}+\frac{{{H}}_n+b}{{{H}}_n-b}$

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Phrases Previous Year PYQPhrases NIMCET 2021 PYQ

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Qus : 14Phrases PYQ

are positive real numbers whose product is a fixed number c, then the minimum of

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Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

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Qus : 15Phrases PYQ

The four geometric means between 2 and 64 are

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Phrases Previous Year PYQPhrases NIMCET 2021 PYQ

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Qus : 16Phrases PYQ

An arithmetic progression has 3 as its first term. Also, the sum of the first 8 terms is twice the sum of the first 5 terms. Then what is the common difference?

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Qus : 17Phrases PYQ

The sum of infinite terms of decreasing GP is equal to the greatest value of the function $f(x) = x^3 + 3x – 9$ in the interval [–2, 3] and difference between the first two terms is f '(0). Then the common ratio of the GP is

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Phrases Previous Year PYQPhrases NIMCET 2023 PYQ