NIMCET Progressions Previous Year Question Paper and Solution with PDF

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Previous Year Questions
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NIMCET Previous Year Questions (PYQs)

NIMCET Progressions PYQ

Qus : 1NIMCET 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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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution

Qus : 2NIMCET 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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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution

Qus : 3NIMCET PYQ

Not Available

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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution

Qus : 4NIMCET 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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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution

Qus : 5NIMCET 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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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution

Qus : 6NIMCET 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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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution

Qus : 7NIMCET 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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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution

Qus : 8NIMCET 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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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution

Qus : 9NIMCET PYQ

If one AM (Arithmetic mean) 'a' and two GM's (Geometric means) p and q be inserted between any two positive numbers, the value of p^3+q^3 is

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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution

Qus : 10NIMCET 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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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 11NIMCET 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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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 12NIMCET 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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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

Qus : 13NIMCET 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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NIMCET Previous Year PYQNIMCET 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 : 14NIMCET 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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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution

Qus : 15NIMCET PYQ

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

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 16NIMCET PYQ

The four geometric means between 2 and 64 are

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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution

Qus : 17NIMCET 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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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution

Qus : 18NIMCET 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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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ