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Q:

The diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas.

A) 4:25	B) 3:25
C) 3:15	D) 5:25

Answer & Explanation Answer: A) 4:25

Explanation:

Let the diagonals of the squares be 2x and 5x respectively.
Ratio of their areas = $\frac{1}{2} * {(2 x)}^{2} : \frac{1}{2} * {(5 x)}^{2} = 4 : 25$

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Filed Under: Area
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Q:

Find the area of a square, one of whose diagonals is 3.8 m long

A) 7.22	B) 6.22
C) 4.22	D) 3.22

Answer & Explanation Answer: A) 7.22

Explanation:

Area of the square = $\frac{1}{2} * {(d i a g o n a l)}^{2} = \frac{1}{2} * 3.8 * 3.8 = 7.22 m^{2}$

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Q:

How many 3 letters words can be formed using the letters of the words hexagon?

A) 120	B) 210
C) 160	D) 200

Answer & Explanation Answer: B) 210

Explanation:

Since the word hexagon contains 7 different letters,the number of permutations is $7 P_{3}$ = 7 x 6 x 5 =210

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Q:

The diagonal of a rectangle is $\sqrt{41}$ cm and its area is 20 sq. cm. The perimeter of the rectangle must be:

A) 18	B) 28
C) 38	D) 48

Answer & Explanation Answer: A) 18

Explanation:

$\sqrt{(l^{2} + b^{2})} = \sqrt{41}$ (or) $l^{2} + b^{2} = 41$

Also, $l b = 20$

${(l + b)}^{2} = l^{2 +} b^{2} + 2 l b$ = 41 + 40 = 81

(l + b) = 9.

Perimeter = 2(l + b) = 18 cm.

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Exam Prep: CAT , Bank Exams , AIEEE
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Q:

A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?

A) 30	B) 40
C) 50	D) 60

Answer & Explanation Answer: A) 30

Explanation:

Let the side of the square(ABCD) be x meters.

Then, AB + BC = 2x metres.

AC = $\sqrt{2 x}$ = (1.41x) m.

Saving on 2x metres = (0.59x) m.

Saving % = $\frac{0.59 x}{2 x} * 100$ = 30% (approx)

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Q:

The diagonal of the floor of a rectangular closet is 7 $\frac{1}{2}$ feet. The shorter side of the closet is 4 $\frac{1}{2}$ feet. What is the area of the closet in square feet?

A) 9	B) 18
C) 27	D) 36

Answer & Explanation Answer: C) 27

Explanation:

Other side = $\sqrt{d^{2} - s^{2}}$ = $\sqrt{(\frac{225}{4} - \frac{81}{4})}$ = $\sqrt{\frac{144}{4}}$ = 6 ft

Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.

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Filed Under: Area
Exam Prep: AIEEE , Bank Exams , CAT
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Q:

A polygon 7 sides.How many diagonals can be formed?

A) 14	B) 7
C) 15	D) 21

Answer & Explanation Answer: A) 14

Explanation:

$7 C_{2}$ - 7 = 14

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Filed Under: Permutations and Combinations

Q:

How many arrangements of the word TRIGONAL can be made if only two vowels and three consonants are used?

A) 6300	B) 3600
C) 6400	D) 7200

Answer & Explanation Answer: B) 3600

Explanation:

First we need to choose two vowels $3 C_{2}$ and then three consonants $5 C_{3}$ . Now that we have 5 letters required to make the word,arrange them in 5! ways.

So, $3 C_{2} * 5 C_{3} * 5! = 3600$

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