குரூப் 4 கணிதம் Online Test

Explanation
The given expression can be simplified as follows:
(2⁰ + 4⁻¹) x 2² = (1 + 1/4) x 4 = (4/4 + 1/4) x 4 = 5/4 x 4 = 5
Therefore, the correct answer is 5.

Explanation
In the given question, it is stated that there are 30 positive numbers in the first x terms of a series. Therefore, the total count of numbers in the series would be x + 30. Since we are asked to find the count of negative numbers, we subtract the total count of numbers from the count of positive numbers. Therefore, the count of negative numbers would be (x + 30) - x, which simplifies to 30. Hence, the correct answer is x - 31.

Explanation
The given equation is x√3 - 2 = 2√3 + 4. To solve for x, we need to isolate x on one side of the equation.

First, we can move the 2√3 term to the left side by adding it to both sides of the equation: x√3 - 2√3 = 2√3 + 4 + 2√3. Simplifying this gives x√3 - 2√3 = 4 + 2√3.

Next, we can combine like terms on the left side of the equation: (x - 2)√3 = 4 + 2√3.

To isolate x, we divide both sides of the equation by √3: (x - 2) = (4 + 2√3)/√3.

Simplifying the right side gives (x - 2) = 4/√3 + 2√3/√3.

Since √3/√3 = 1, the right side simplifies further to (x - 2) = 4/√3 + 2.

To rationalize the denominator, we multiply the numerator and denominator of 4/√3 by √3: (x - 2) = (4/√3)(√3/√3) + 2(√3/√3).

This gives (x - 2) = 4√3/3 + 2√3/√3.

Simplifying further gives (x - 2) = (4√3 + 2√3)/√3.

To rationalize the denominator again, we multiply the numerator and denominator by √3: (x - 2) = [(4√3 + 2√3)/√3](√3/√3).

This gives (x - 2) = (6√3)/3.

Simplifying gives (x - 2) = 2√3.

Finally, to solve for x, we add 2 to both sides of the equation: x = 2 + 2√3.

Therefore, the value of x is 2 + 2√3, which matches option ஆ)

Explanation
The given question asks us to find the value of 6.052 ÷ 17.8. To solve this, we divide 6.052 by 17.8. The result is 0.34. Therefore, the correct answer is அ) 34.

Explanation
The given sequence is 2, 3, 4, 5, 6. Each number in the sequence is obtained by adding 1 to the previous number. So, the next number in the sequence would be 6 + 1 = 7. However, none of the given options have 7 as a choice. Therefore, the correct answer is not available.

Explanation
The given question asks for the value of x in the expression 260 / 2 x 6. To find the value of x, we need to perform the operations in the expression from left to right. First, we divide 260 by 2, which gives us 130. Then, we multiply 130 by 6, which equals 780. Therefore, the value of x is 30.

Explanation
The given question is asking for the number of squares obtained in a specified pattern. The correct answer, 2n, suggests that the number of squares obtained is directly proportional to the value of n. This means that for every increment of n, the number of squares will double. Therefore, if n is increased by 1, the number of squares will be multiplied by 2.

Explanation
If A completes the job in 10 days and B completes the same job in 15 days, it means that A is more efficient than B. So, if they both work together and complete the job in 1500 units of currency, we can assume that A contributed 10/25 (or 2/5) of the work and B contributed 15/25 (or 3/5) of the work. Therefore, A's share of the payment would be 2/5 of 1500, which is 600 units of currency.

Explanation
The total profit or loss made by selling two calculators for Rs. 594 each, with a profit of 10% and a discount of 10%, is 1.

Explanation
One student's score decreases from 40 to 39, causing the average score of the class to change from 40 to 39. This means that the student who scored 39 must have had a higher score originally, and the only option higher than 39 is 70. Therefore, the correct answer is 70.

Explanation
In 2014, the ratio of the ages of the son and the father was 1:4, and in 2022, the ratio became 3:8. This means that over the 8-year period, the son's age increased by a factor of 3 (from 1 to 3) and the father's age increased by a factor of 2 (from 4 to 8). We can calculate the son's age in 2014 by dividing the age in 2022 (3) by the increase factor (3) and multiplying by the age in 2014 (1), which gives us 1. We can then calculate the father's age in 2014 by dividing the age in 2022 (8) by the increase factor (2) and multiplying by the age in 2014 (4), which gives us 16. Therefore, the sum of their ages in 2014 is 1 + 16 = 17, and the son and father's ages in 2010 would be 17 - 8 = 9 and 17 - 1 = 16, respectively. The difference between their ages in 2010 is 16 - 9 = 7.

Explanation
The area of the rectangle can be calculated by multiplying the length and width. In this case, the length is 9 meters and the width is 6.4 meters. Therefore, the area of the rectangle is 9 x 6.4 = 57.6 square meters. Since the question asks for the number of square tiles needed to cover the floor, we need to divide the area of the rectangle by the area of each tile. If each tile has an area of 40 square meters, then the number of tiles needed is 57.6 / 40 = 1.44. Since we cannot have a fraction of a tile, we round up to the nearest whole number. Therefore, the correct answer is 2.

Explanation
The question states that the third number from the first number among the three given numbers is half, and the third number from the first number among the three given numbers is 3 times the third number. If the sum of these three numbers is 27, the smallest number among them would be 9.

Explanation
The question provides information about different expenses such as clothing, food, education, and rent. It also gives the total expenses and the amount spent on other expenses. To find the percentage of expenses on clothing, we need to divide the amount spent on clothing by the total expenses and multiply by 100. In this case, the amount spent on clothing is 75 and the total expenses are 300. So, (75/300) * 100 = 25%. However, the question asks for the percentage of expenses on clothing as a proportion of the total expenses minus other expenses. So, we need to subtract the amount spent on other expenses (110) from the total expenses (300) and then calculate the percentage of clothing expenses. (75/(300-110)) * 100 = 12.5%. Therefore, the correct answer is இ) 12.5%.

Explanation
If the amount doubles in 20 years, then the annual growth rate can be calculated by taking the 20th root of 2 (since the amount doubles every year). The 20th root of 2 is approximately 1.035, which is equivalent to a 3.5% growth rate. However, the question asks for the growth rate for two years, so we need to calculate the square of the growth rate. 3.5% squared is approximately 0.1225, which is equivalent to a 12.25% growth rate for two years. Therefore, the correct answer is 5%.

Explanation
If the sum of 5 numbers is 20 and removing one number reduces the sum by 5, then the number that was removed must be 5. Therefore, the remaining sum of the 4 numbers is 15.

Explanation
When three coins are flipped at the same time, the possible outcomes are 2^3 = 8. Out of these 8 outcomes, there are 2 outcomes where all three coins show heads (HHH) and 2 outcomes where all three coins show tails (TTT). Therefore, the probability of getting either all heads or all tails is 2/8 = 1/4.

Explanation
The price of the dress has increased from Rs. 2100 to Rs. 2520. To find the percentage increase, we can use the formula: (New Value - Old Value) / Old Value * 100. Plugging in the values, we get (2520 - 2100) / 2100 * 100 = 420 / 2100 * 100 = 0.2 * 100 = 20%. Therefore, the correct answer is 20%.