Mathematics · JEE

Important Questions: Quadratic equations in real and complex number systems and their solutions for JEE

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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

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?

Q4MathsUnit 2: Complex Numbers and Quadratic Equations

A number exceeds by 40 when added by

20 \%

of itself. The number is

Q5MathsUnit 2: Complex Numbers and Quadratic Equations

3 x-\frac{1}{2 x}=6,

then the value of

9 x^{2}+

\frac{1}{4 x^{2}}

Q6MathsUnit 2: Complex Numbers and Quadratic Equations

x+2 y+3 z=0

and

x^{3}+4 y^{3}+

\mathbf{9} z^{3}=18 x y z ;

evaluate:

\frac{(x+2 y)^{2}}{x y}+\frac{(2 y+3 z)^{2}}{y z}+

\frac{(3 z+x)^{2}}{z x}

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Important questions test core concepts that appear frequently across JEE Main and Advanced papers — definitions, standard formulas, and classic problem types.

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Key areas include Quadratic equations in real and complex number systems and their solutions. Prioritise these before moving to edge cases.

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