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

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IMPORTANT

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

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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 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}

.

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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:

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 36

If

f (x)

is a quadratic polynomial, such that

f (5) = 75

and

f (- 5) = 45

,

f (p) = f (q) = 0

, then find

p \times q

, given that the value of the constant term in the polynomial is

10

:

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 37

If

|a| + a + b = 75

and

a + |b| - b = 150

, then what is the value of

|a| + |b|

?

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 38

If

[x]

represents the greatest integer less than or equal to

x

, then the value of

[315^{\frac{1}{3}}] + [316^{\frac{1}{3}}] + [317^{\frac{1}{3}}] + . . . . + [515^{\frac{1}{3}}]

is: