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Q:

In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?

A) 4! x 4!	B) 5! x 5!
C) 4! x 5!	D) 3! x 4!

Answer & Explanation Answer: C) 4! x 5!

Explanation:

The word EDUCATION is a 9 letter word, with none of the letters repeating.

The vowels occupy 3rd,5th,7th and 8th position in the word and the remaining 5 positions are occupied by consonants

As the relative position of the vowels and consonants in any arrangement should remain the same as in the word EDUCATION, the vowels can occupy only the afore mentioned 4 places and the consonants can occupy1st,2nd,4th,6th and 9th positions.

The 4 vowels can be arranged in the 3rd,5th,7th and 8th position in 4! Ways.

Similarly, the 5 consonants can be arranged in1st,2nd,4th,6th and 9th position in5! Ways.

Hence, the total number of ways = 4! × 5!

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Q:

One side of a rectangular field is 15m and one of its diagonal is 17m. Find the area of field?

A) 110	B) 120
C) 130	D) 140

Answer & Explanation Answer: B) 120

Explanation:

Other side = [(17 x 17) - (15 x 15)] = (289 - 225) = 8m
Area = 15 x 8 =120 sq. m

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Q:

If the radius of a circle is decreased by 50%, find the percentage decrease in its area.

A) 55%	B) 65%
C) 75%	D) 85%

Answer & Explanation Answer: C) 75%

Explanation:

Let original radius = R.

New radius = $\frac{50}{100} R$ = $\frac{50}{100} R$

Original area = $\frac{R}{2}$ and new area = ${πR}^{2}$

$\frac{3 {πR}^{2}}{4} * \frac{1}{{πR}^{2}} * 100$

Decrease in area = $π {(\frac{R}{2})}^{2} = \frac{{πR}^{2}}{4}$ = 75%

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Q:

A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?

A) 1260	B) 1400
C) 1250	D) 1600

Answer & Explanation Answer: A) 1260

Explanation:

A team of 6 members has to be selected from the 10 players. This can be done in $10 C_{6}$ or 210 ways.

Now, the captain can be selected from these 6 players in 6 ways.
Therefore, total ways the selection can be made is 210×6= 1260

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Q:

Find the ratio of the areas of the incircle and circumcircle of a square.

A) 1:1	B) 1:2
C) 1:3	D) 1:4

Answer & Explanation Answer: B) 1:2

Explanation:

Let the side of the square be x. Then, its diagonal = $\sqrt{2 x^{2}} = \sqrt{2 x}$

Radius of incircle = $\frac{x}{2}$

Radius of circum circle= $\sqrt{2} \times \frac{x}{2} = \frac{x}{\sqrt{2}}$

Required ratio = $\frac{{πx}^{2}}{4} : \frac{{πx}^{2}}{2} = \frac{1}{4} : \frac{1}{2} = 1 : 2$

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Q:

When six fairs coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads ?

A) 15	B) 42
C) 16	D) 40

Answer & Explanation Answer: B) 42

Explanation:

The question requires you to find number of the outcomes in which at most 3 coins turn up as heads.

i.e., 0 coins turn heads or 1 coin turns head or 2 coins turn heads or 3 coins turn heads.

The number of outcomes in which 0 coins turn heads is $6 C_{0}$ =1

The number of outcomes in which 1 coin turns head is = $6 C_{1}$ =6

The number of outcomes in which 2 coins turn heads is $6 C_{2}$ =15

The number of outcomes in which 3 coins turn heads is $6 C_{3}$ =20

Therefore, total number of outcomes =1+6+15+20= 42 outcomes

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Q:

A sector of 120, cut out from a circle, has an area of $\frac{66}{7} c m^{2}$ . Find the radius of the circle ?

A) 1	B) 2
C) 3	D) 4

Answer & Explanation Answer: C) 3

Explanation:

Let the radius of the circle be r cm. Then,

$\frac{120}{360} {πr}^{2} = \frac{66}{7}$

$r^{2} = \frac{66}{7} * \frac{7}{22} * 3$

r=3.

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Q:

Two concentric circles form a ring. The inner and outer circumferences of ring are $\frac{518}{7}$ m and $\frac{352}{7}$ m respectively. Find the width of the ring.

A) 4	B) 5
C) 6	D) 7

Answer & Explanation Answer: A) 4

Explanation:

Let the inner and outer radii be r and R metres.

Then $2 πR = \frac{352}{7} = > R = \frac{352}{7} * \frac{7}{22} * \frac{1}{2} = 8 m$

$2 πR = \frac{528}{7} = > R = \frac{528}{7} * \frac{7}{22} * \frac{1}{2} = 12 m$

=> Width of the ring = (R - r) = (12 - 8) m = 4 m.

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Filed Under: Area
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