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Phrases Previous Year Questions (PYQs)

Phrases Quadratic Equations PYQ


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





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Phrases Previous Year PYQPhrases NIMCET 2023 PYQ

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Phrases PYQ
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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Phrases PYQ
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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Phrases Previous Year PYQPhrases NIMCET 2024 PYQ

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Phrases PYQ
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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Phrases Previous Year PYQPhrases NIMCET 2022 PYQ

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Phrases PYQ
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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Phrases PYQ
The quadratic equation whose roots are  is





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Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

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





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Phrases Previous Year PYQPhrases NIMCET 2021 PYQ

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Phrases PYQ
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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Phrases Previous Year PYQPhrases NIMCET 2017 PYQ

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





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Phrases Previous Year PYQPhrases 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

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





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Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

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Phrases PYQ
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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Phrases PYQ
If \alpha and \beta are the roots of the equation 2x^{2}+ 2px + p^{2} = 0, where p is a non-zero real number, and \alpha^{4} and \beta^{4} are the roots of x^{2} - rx + s = 0, then the roots of 2x^{2} - 4p^{2}x + 4p^{4} - 2r = 0 are:





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Phrases Previous Year PYQPhrases NIMCET 2014 PYQ

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Phrases PYQ
If x and y are positive real numbers satisfying the system of equations x^{2}+y\sqrt{xy}=336 and y^{2}+x\sqrt{xy}=112, then x + y is:





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Phrases Previous Year PYQPhrases NIMCET 2014 PYQ

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Phrases PYQ
The value of k for which the equation (k-2)x^{2}+8x+k+4=0 has both real, distinct and negative roots is





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Phrases Previous Year PYQPhrases NIMCET 2015 PYQ

Solution


Phrases PYQ
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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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

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





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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

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Phrases PYQ
a, b, c are positive integers such that a^{2}+2b^{2}-2bc=100 and 2ab-c^{2}=100. Then the value of \frac{a+b}{c} is





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Phrases Previous Year PYQPhrases NIMCET 2015 PYQ

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Phrases PYQ
If x^{2} + 2ax + 10 - 3a > 0 for all x ∈ R, then





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Phrases Previous Year PYQPhrases NIMCET 2014 PYQ

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