Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 31

MEDIUM

CAT

IMPORTANT

Earn 100

The circumference of a circle and the perimeters of a pentagon and an octagon are the same. Their areas are denoted by $C, P$ and $O$ respectively. Which of the following is true for their areas?

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Important Questions on X+2 Maths

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 32

At what value of

x, {(\frac{1}{x})}^{x}

will attain the maximum value?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 33

The altitude of a right circular cone of the minimum volume circumscribed about a sphere of the radius r is:

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 34

The minimum value of

(x - a) (x - b)

is:

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 35

If

x, y

and

z

are arbitrary positive real numbers satisfying the equation

4 x^{2} y + 16 y^{2} z + 8 z^{2} x = 9

, then find the maximum possible value of the product

x y z

.

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 36

The minimum value of the quantity

\frac{(a^{2} + 3 a + 1) (b^{2} + 3 b + 1) (c^{2} + 3 c + 1)}{a b c}

, where

a, b

and

c

are positive real numbers, is:

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 37

A right circular cylindrical container closed on both the sides contains a fixed volume of motor oil. Suppose its base has the diameter

d

and its height is

h

. The overall surface area of the container is minimum when:

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 38

A rectangular box of volume

48 cu . ft

is to be constructed, so that its length is twice its width. The material to be used for the top and the four sides is three times costlier per

{ft}^{2}

than that used for the bottom. Then, the height (in ft) of the box that minimizes the cost is equal to:

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 39

A truck is to be driven for

300 km

on a highway at a constant speed of

x km / h

. The speed rules of the highway require

30 \leq x \leq 60

. The fuel costs

₹ 10

per litre and is consumed at the rate of

2 + \frac{x^{2}}{600}

liters per hour. The wages of the driver are

₹ 200

per hour. The most economical speed to drive the truck, in km/h, is: