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NIMCET Previous Year Questions (PYQs)

NIMCET Quadratic Equations PYQ


NIMCET PYQ 2023
If the equation |x^2 – 6x + 8| = a has four real solution then find the value of a?





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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

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NIMCET PYQ 2023
Between any two real roots of the equation e^x sin x = 1, the equation e^x cos x = –1 has





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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

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NIMCET PYQ 2024
Let C denote the set of all tuples (x,y) which satisfy x^2 -2^y=0 where x and y are natural numbers. What is the cardinality of C?





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
If \alpha , \beta are the roots of x^2-x-1=0 and A_n=\alpha^n+\beta^n, the Arithmetic mean of A_{n-1} and A_n is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2022
If the roots of the quadratic equation x^2+px+q=0 are tan 30° and tan 15° respectively, then the value of 2 + p - q is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2018
The quadratic equation whose roots are  is





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

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NIMCET PYQ 2021
For what value of p, the polynomial  x^4-3x^3+2px^2-6 is exactly divisible by (x-1)





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

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NIMCET PYQ 2017
α, β are the roots of the an equation x^2- 2x cosθ + 1 = 0, then the equation having roots αn and βn is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

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NIMCET PYQ 2017
The equation (x-a)3+(x-b)3+(x-c)3 = 0 has





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution


Let f(x) = (x – a)3 + (x – b)3 + (x – c)3.
Then f'(x) = 3{(x – a)2 + (x – b)2 + (x –c)2}
clearly , f'(x) > 0 for all x.
so, f'(x) = 0 has no real roots.
Hence, f(x) = 0 has two imaginary and one real root

NIMCET PYQ 2018
Let  and  be the roots f the equation  and  are the roots of the equation , then the value of r,





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

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NIMCET PYQ 2021
If α≠β and \alpha^2=5\alpha-3,\beta^2=5\beta-3, then the equation whose roots are \frac{\alpha}{\beta} and \frac{\beta}{\alpha} is 





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

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NIMCET PYQ 2020
Roots of equation are ax^2-2bx+c=0 are n and m , then the value of \frac{b}{an^2+c}+\frac{b}{am^2+c} is





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

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NIMCET PYQ 2020
If a + b + c = 0, then the value of 





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

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