1.### If the radius of a circle is diminished by 10%, then its area is diminished by:

Answer:
19%

Explanation:

When the radius of a circle is diminished by 10%, the area of the circle is diminished by a greater percentage. This is because the area of a circle is directly proportional to the square of its radius. Therefore, if the radius is reduced by 10%, the area will be reduced by a larger percentage. To calculate the exact percentage, we can use the formula for the area of a circle: A = πr^2. If the radius is diminished by 10%, the new radius will be 90% of the original radius. Plugging this into the formula, we get A' = π(0.9r)^2 = 0.81πr^2. This means that the new area is 81% of the original area. Therefore, the area is diminished by 19%.

2.### At what time after 4.00 p.m. is the minute's hand clock exactly aligned with the hour hand?

Answer:
4:21:49.5

Explanation:

At 4:21:49.5, the minute's hand and the hour hand are exactly aligned. The minute's hand moves 12 times faster than the hour hand, so in 12 hours (from 4.00 p.m. to 4.00 a.m.), the minute's hand will make one complete revolution around the clock while the hour hand will move to the next hour mark. Therefore, after 4.00 p.m., the minute's hand and the hour hand will be aligned at 4:21:49.5.

3.### If (2x-y)=4 then (6x-3y) =?

Answer:
12

Explanation:

The given equation (2x-y)=4 can be rewritten as 2x-y=4. We need to find the value of (6x-3y). By multiplying both sides of the equation 2x-y=4 by 3, we get 6x-3y=12. Therefore, the value of (6x-3y) is 12.

4.### What is the missing number in this series?
8 2 14 6 11 ? 14 6 18 12

Answer:
8

5.### A person has 4 coins each of different denominations. What is the number of different sums of money
the person can form(using one or more coins at a time)?

Answer:
15

Explanation:

The number of different sums of money the person can form using one or more coins at a time can be found using the concept of combinations. Since there are 4 coins of different denominations, the total number of different sums can be calculated by finding all possible combinations of choosing 1, 2, 3, or 4 coins.The formula to calculate the total number of combinations is:Total combinations = 2^N - 1Where N is the number of coins.For N = 4,Total combinations = 2^4 - 1= 16 - 1 = 15Therefore, the number of different sums of money the person can form is 15.So, the correct answer is 15.

6.### A cow is tethered in the middle of the field with a 14-foot-long rope. If the cow grazes 100 sq. ft. per day, then approximately what time will be taken by the cow to graze the whole field? (Approx)

Answer:
6.15 days

Explanation:

To determine approximately how much time it will take for the cow to graze the whole field, you need to calculate the total area of the field and then divide it by the rate at which the cow grazes.

The cow is tethered with a 14-foot rope. Since the rope is attached to the cow at the center of the field, it can move in a circular area with a radius of 14 feet. The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.

Area of the circular grazing area = π * (14 feet)^2 ≈ 615.75 square feet (rounded to two decimal places)

The cow grazes 100 square feet per day. To calculate the time it takes to graze the whole circular area, divide the total area of the field by the grazing rate:

Time (in days) = Total Area / Grazing Rate Time = 615.75 square feet / 100 square feet per day ≈ 6.16 days

So, it will take approximately 6 days for the cow to graze the whole field if it grazes 100 square feet per day.

The cow is tethered with a 14-foot rope. Since the rope is attached to the cow at the center of the field, it can move in a circular area with a radius of 14 feet. The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.

Area of the circular grazing area = π * (14 feet)^2 ≈ 615.75 square feet (rounded to two decimal places)

The cow grazes 100 square feet per day. To calculate the time it takes to graze the whole circular area, divide the total area of the field by the grazing rate:

Time (in days) = Total Area / Grazing Rate Time = 615.75 square feet / 100 square feet per day ≈ 6.16 days

So, it will take approximately 6 days for the cow to graze the whole field if it grazes 100 square feet per day.

7.### The two colors seen at the extreme ends of the pH chart are:

Answer:
Red and blue

Explanation:

The correct answer is red and blue because the pH chart is a visual representation of the acidity or alkalinity of a substance. The colors on the chart range from red (indicating acidity) to blue (indicating alkalinity), with green being neutral. Therefore, the extreme ends of the pH chart would be represented by red and blue.

8.### If the value of x lies between 0 and 1, which of the following is the largest?

Answer:
1/x

Explanation:

The given question asks for the largest value among x, x^2, -x, and 1/x when x lies between 0 and 1. When x is between 0 and 1, the value of 1/x will be the largest because as x approaches 0, 1/x approaches infinity. On the other hand, x and x^2 will be smaller values, and -x will be negative but smaller than 1/x. Therefore, 1/x is the largest value among the given options.

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