Phrases Quadratic Equations Previous Year Question Paper and Solution with PDF

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Phrases Quadratic Equations PYQ

Qus : 1Phrases 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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Qus : 2Phrases 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 Previous Year PYQPhrases NIMCET 2023 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

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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Qus : 5Phrases 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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Qus : 6Phrases 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 Previous Year PYQPhrases NIMCET 2022 PYQ

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Qus : 7Phrases PYQ

The quadratic equation whose roots are

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Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

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Qus : 8Phrases 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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Qus : 9Phrases 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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Qus : 10Phrases 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

Qus : 11Phrases 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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Qus : 12Phrases 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 Previous Year PYQPhrases NIMCET 2021 PYQ

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Qus : 13Phrases 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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Qus : 14Phrases 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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