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Hard Quadratic equations in real and complex number systems and their solutions MCQs for JEE

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Part of Complex Numbers and Quadratic Equations in JEE Main Mathematics.

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Q1MathsUnit 2: Complex Numbers and Quadratic Equations

What are the solution(s) to the system of equations

\boldsymbol{y}=\boldsymbol{x}^{2}-\mathbf{9}

and

\boldsymbol{y}-\boldsymbol{3}=

x ?

Q2MathsUnit 2: Complex Numbers and Quadratic Equations

A family is going to a theme park having

t

members in the family. Each ticket costs

\$ 80,

and the number of tickets needs to be bought can be calculated from the expression

t^{2}-

4 t-90=6

when

t>0 .

What is the total cost of the theme park tickets that the family paid?

Q3MathsUnit 2: Complex Numbers and Quadratic Equations

Determine the nature of roots of the equation

x^{2}+2 x \sqrt{3}+3=0

Q4MathsUnit 2: Complex Numbers and Quadratic Equations

Determine all ordered pairs that satisfy

(x-y)^{2}+x^{2}=25,

where

x

and

y

are integers and

x \geq 0 .

Find the number of different values of

y

that occur

Q5MathsUnit 2: Complex Numbers and Quadratic Equations

Determine whether the equation

5 x^{2}=

5 x

is quadratic or not.

Q6MathsUnit 2: Complex Numbers and Quadratic Equations

The produce of a square field when sold at the rate of Rs. 1.50 per 100 sq. metres fetches Rs.

1350 .

What will be the cost of putting a fence all round the field at the rate of 50 paise per metre?

Q7MathsUnit 2: Complex Numbers and Quadratic Equations

Solve

: 3^{4 x+1}-2 \times 3^{2 x+2}-81=0

Q8MathsUnit 2: Complex Numbers and Quadratic Equations

a^{2}-4 a-1=0, a \neq 0,

then the value of

a^{2}+3 a+\frac{1}{a^{2}}-\frac{3}{a}

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