NIMCET Quadratic Equations Previous Year Question Paper and Solution with PDF

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NIMCET Previous Year Questions (PYQs)

NIMCET Quadratic Equations PYQ

Qus : 1

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

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Solution

Qus : 2

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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Solution

Number of Roots

Given:

$ e^x \sin x = 1 $ has two real roots → say $ x_1 $ and $ x_2 $

Apply Rolle’s Theorem:

Since $ f(x) = e^x \sin x $ is continuous and differentiable, and $ f(x_1) = f(x_2) $, ⇒ There exists $ c \in (x_1, x_2) $ such that $ f'(c) = 0 $

Compute:

\[ f'(x) = e^x(\sin x + \cos x) = 0 \Rightarrow \tan x = -1 \] At this point, \[ e^x \cos x = -1 \]

\[ \boxed{\text{At least one root}} \]

Qus : 3

Not Available

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Solution

Qus : 4

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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Solution

Qus : 5

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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Solution

Qus : 6

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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Solution

Qus : 7

The quadratic equation whose roots are

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Solution

Qus : 8

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

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Solution

Qus : 9

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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Solution

Qus : 10

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

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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 : 11

Let

and

be the roots f the equation

and

are the roots of the equation

, then the value of r,

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Solution

Qus : 12

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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Solution

Qus : 13

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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Solution

Qus : 14

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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Solution

Qus : 15

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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Solution

Qus : 16

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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Solution

Qus : 17

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

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Solution

Qus : 18

$a, b, c$ 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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Solution

Qus : 19

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

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Solution

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Rahul , Droper
Commented Apr 22 , 2022

why not this pyq section is showing all the questions . it just show 5 to 10 question in each section . help me out sir

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NIMCET Previous Year Questions (PYQs)

NIMCET Quadratic Equations PYQ

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Number of Roots

Solution

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Solution

Solution

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