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Q:

In measuring the sides of a rectangle, one side is taken 5% in excess and the other 4% in deficit. Find the error percent in the area, calculate from the those measurements.

A) .7%	B) 0.8%
C) 0.9%	D) 0.3%

Answer & Explanation Answer: B) 0.8%

Explanation:

let x and y be the sides of the rectangle then

correct area = $\frac{105}{100} x \times \frac{96}{100} y$

Error% = $\frac{504}{500} x y - x y = \frac{4}{500} x y$ %

$\frac{4}{500} x y \times \frac{1}{x y} \times 100 = \frac{4}{5} = 0.8$

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Q:

The length of a rectangle is twice its breadth if its length is decreased by 5cm and breadth is increased by 5cm, the area of the rectangle is increased by 75 sq cm. Find the length of the rectangle.

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

Answer & Explanation Answer: B) 40

Explanation:

let length = 2x and breadth = x then
(2x-5) (x+5) = (2x * x)+75
5x-25 = 75 => x=20
length of the rectangle = 40 cm

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Q:

A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?

A) 126	B) 120
C) 146	D) 156

Answer & Explanation Answer: A) 126

Explanation:

There are 8 students and the maximum capacity of the cars together is 9.

We may divide the 8 students as follows

Case I: 5 students in the first car and 3 in the second
Case II: 4 students in the first car and 4 in the second

Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.

Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.

Therefore, the total number of ways in which 8 students can travel is:
$8 C_{3} + 8 C_{4}$ =56 + 70= 126

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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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