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NIMCET Previous Year Questions (PYQs)

NIMCET Progressions PYQ


NIMCET PYQ 2019
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

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NIMCET PYQ 2019
If a,b,c are in GP and logalog2b, log2blog3c and log3cloga are in AP, then a,b,care the lengths of the sides of a triangle which is





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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

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NIMCET PYQ 2019
If a,a,a2,.,a2n1,b are in AP, a,b1,b2,...b2n1,bare in GP and a,c1,c2,...c2n1,b are in HP, where a, b are positive, then the equation anx2bn+cn has its roots





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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

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NIMCET PYQ 2024
If x=1+62+64+68+616+632 then (1+1x)24 =





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2024
The number of solutions of 51+|sinx|+|sinx|2+=25 for x(π,π) is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
Which term of the series 53,54,15,... is 513 ?





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2022
In a Harmonic Progression, pth term is q and the qth term is p. Then pqth term is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
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

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NIMCET PYQ 2018
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

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NIMCET PYQ 2018
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

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NIMCET PYQ 2017
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

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NIMCET PYQ 2017
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.

NIMCET PYQ 2021
If H1,H2,,Hn are n harmonic means between a and b (ba);,then Hn+aHna+Hn+bHnb





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

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NIMCET PYQ 2018
If  are positive real numbers whose product is a fixed number c, then the minimum of  is





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

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NIMCET PYQ 2021
The four geometric means between 2 and 64 are 





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

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NIMCET PYQ 2020
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

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NIMCET PYQ 2023
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

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NIMCET PYQ 2023
If a, b, c, d are in HP and arithmetic mean of ab, bc, cd is 9 then which of the following number is the value ofad?





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