MEDIUM

CAT

IMPORTANT

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$Q_{1} (x)$ and $Q_{2} (x)$ are quadratic functions such that $Q_{1} (10) = Q_{2} (8) = 0$ . If the corresponding equations $Q_{1} (x) = 0$ and $Q_{2} (x) = 0$ have a common root and $Q_{1} (4) \times Q_{2} (5) = 36$ , what is the value of the common root?

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Important Questions on Quadratic and Other Equations

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 28

Q_{1} (x)

and

Q 2 (x)

are quadratic functions such that

Q_{1} (10) = Q 2 (8) = 0

. If it is known that the coefficient of

x^{2}

for

Q_{1} (x) = 0

\frac{1}{15}

and that of

Q_{2} (x) = 0

1

, then which of the following option is a possible value of the sum of the roots of

Q_{2} (x) = 0

MEDIUM

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 29

Which of the following could be a possible value of $' x'$ for which, each of the fractions is in its simplest form, where $[x]$ stands for greatest integer less than or equal to $' x'$ ?

$\frac{[x] + 7}{10}$ , $\frac{[x] + 18}{11}$ , $\frac{[x] + 31}{12}$ , $\frac{[x] + 46}{13}$ ,...., $\frac{[x] + 1489}{39}$ and $\frac{[x] + 1567}{40}$ .

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 30

If $x - y = 8$ and $P = 7 x^{2} - 12 y^{2}$ , where $x$ , $y > 0$ . What is the maximum possible value of $P$ ?

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 31

If the equation

5 x + 9 y + 17 z = a

4 x + 8 y + 12 z = b

, and

2 x + 3 y + 8 z = c

have at least one solution for

x

y

, and

z

and

a

b

, and

c \neq 0

, then which of the following is true?

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 32

If the roots of the equation

x^{3} - a x^{2} + b x - 1080 = 0

are in the ratio

2 : 4 : 5

, find the value of the coefficient of

x^{2}

MEDIUM

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 33

If the roots of the equation

p x^{3} - 20 x^{2} + 4 x - 5 = 0

, where

p \neq 0

, are

l

m

and

n

, then what is the value of

\frac{1}{l m} + \frac{1}{m n} + \frac{1}{\ln}

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 34

The cost of

10

pears,

8

grapes and

6

mangoes is

₹ 44

. The cost of

5

pears,

4

grapes and

3

mangoes is

₹

22

. Find the cost of

4

mangoes and

3

grapes, if the cost of each items, in rupees, is a natural number and the cost of no two items is the same.

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 35

The number positive integral solutions to the system of equation

a_{1} + a_{2} + a_{3} + a_{4} + a_{5} = 47

and

a_{1} + a_{2} = 37

is:

Q1x and Q2x are quadratic functions such that Q110=Q28=0. If the corresponding equations Q1x=0 and Q2x=0 have a common root and Q14×Q25=36, what is the value of the common root?

Important Questions on Quadratic and Other Equations

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$Q_{1} (x)$ and $Q_{2} (x)$ are quadratic functions such that $Q_{1} (10) = Q_{2} (8) = 0$ . If the corresponding equations $Q_{1} (x) = 0$ and $Q_{2} (x) = 0$ have a common root and $Q_{1} (4) \times Q_{2} (5) = 36$ , what is the value of the common root?