Math & Problem Solving Quiz

Substituting x = 1/9: Column A = √(1/9) − (1/9)² = 1/3 − 1/81 = 27/81 − 1/81 = 26/81 ≈ 0.321. Since 26/81 > 0, Column A is greater than Column B. The statement that both columns are equal is false.

Original area = 25,000. After 5% length increase and 10% breadth increase, new area = 25000 × 1.05 × 1.10 = 25000 × 1.155 = 28,875. The statement claims 28,775, which is incorrect. 25,000 × 1.155 = 28,875, not 28,775.

By comparing the two expressions, we see they are identical except for the terms -(c/x) in (i) and -(c/a) in (ii). For the expressions to be equal, the denominators must be the same, meaning x must equal a.

This is a duplicate of the previous question. VBODMAS stands for Vinculum, Brackets, Of, Division, Multiplication, Addition, and Subtraction. It defines the hierarchy of operations in arithmetic to avoid ambiguity in calculations.

VBODMAS is the standard acronym for the order of operations: Vinculum, Brackets, Of, Division, Multiplication, Addition, and Subtraction. This ensures mathematical expressions are solved consistently. The other options rearrange these letters incorrectly, violating standard mathematical rules.

53^4 = 53 × 53 × 53 × 53 = 7890481. This is calculated by multiplying 53 by itself four times. Option D matches this result exactly. The other options are close but incorrect calculations.

A number's remainder when divided by 9 is the same as the remainder of the sum of its digits divided by 9. The sum of 7+6+5+4+3+2+9+8+7+6+5+4+3+2+1+8 is 80. 80 divided by 9 is 8 with a remainder of 8.

267494 × 9999 = 267494 × (10000 - 1) = 2674940000 - 267494 = 2674672506. This uses the shortcut that multiplying by 9999 is the same as multiplying by 10000 and subtracting the original number. Option A matches this result.

Using Fermat's Little Theorem: for prime p=101, a^100 ≡ 1 (mod 101) when a is not divisible by 101. Therefore, 205^205 ≡ 205^(2×100 + 5) ≡ (205^100)^2 × 205^5 ≡ 1^2 × 205^5. Simplify: 205 ≡ 3 (mod 101), so 3^5 = 243 ≡ 41 (mod 101). The remainder is 41.

Let sides be 12x and 12y where x,y are coprime. Perimeter 2(12x + 12y) = 384, so x + y = 16. Coprime pairs (x,y) for 16 are (1,15), (3,13), (5,11), (7,9). There are 4 distinct pairs, representing 4 distinct rectangles.

Ram buys 15 oranges (3 sets of 5 at 5rs = 15rs) and 5 apples (3rs each = 15rs), totaling 30rs. If Kalu sold them for 30rs at a 16.67% (1/6) profit, Kalu's cost price (CP) is calculated as CP * (7/6) = 30. CP = 180/7 ≈ 25.71. 25 is the closest integer.

The area of a triangle is given by the formula (1/2) * base * height. If the base is halved to a/2 while the height b remains constant, the new area becomes (1/2) * (a/2) * b, which is half of the original area.

Given a = b = c = 10. Then x = log(a × b × c) = log(10 × 10 × 10) = log(1000). Using logarithm property: log(abc) = log(a) + log(b) + log(c) = log(10) + log(10) + log(10). Assuming base 10: log(10) = 1, so x = 1 + 1 + 1 = 3. The answer is 3, not log 100 or 3 ln 10.

Let current age be x. If you live 15 more years, you'll be 38, so x = 38 - 15 = 23. Daughter is 10 now and was born 3 years after marriage, so marriage was 10 + 3 = 13 years ago. Current year is 2024, so marriage year = 2024 - 13 = 2011. Option D is a joke option. The math works out correctly to 2011.

The relative speed is 130 - 120 = 10 km/hr. To cover the 1 km gap, it takes 1/10 of an hour, which is 6 minutes. Both have enough fuel: Rahul needs 0.3L to travel 12km in 6 mins, and Jai needs ~0.32L to travel 13km.

For ratio 1:2:3 with total 6 parts and Sohan's maximum of 9 bananas, each part must equal 3 bananas. So Shiv eats 3 (1×3), Ankit eats 6 (2×3), and Sohan eats 9 (3×3), giving total 18. This satisfies both the required ratio and each person's eating capacity.

Work rates are independent. Boys: 6 boys × 6 days = 36 boy-days produce 6 songs, so 1 song per 6 boy-days. Girls: 4 girls × 4 days = 16 girl-days produce 4 songs, so 1 song per 4 girl-days. For 12 boys and 12 girls working 12 days: Boys = 12 × 12 = 144 boy-days → 144/6 = 24 songs. Girls = 12 × 12 = 144 girl-days → 144/4 = 36 songs. Total = 24 + 36 = 60 songs.

This is a trick question testing logic. The shell is tied to the boat, so when water rises, the boat rises with it. The shell remains 3 metres above water level regardless of how much the water rises. Therefore the water will never touch the shell - the answer is "None of the Above" (no finite time).

To solve this question, the user needs to understand the concept of permutations. Permutations refer to the different ways a set of objects can be arranged in a particular order.

In this case, there are ten people, and the photographer wants to take pictures of all possible groupings. To find the number of pictures the photographer will take, we need to calculate the number of permutations of ten people taken at a time.

Now, and the user has to know how to calculate permutations.

Now let's go through each option and explain why it is right or wrong:

A. 100: This option is incorrect because it represents a simple multiplication of 10 (the number of people) by 10 (the number of positions the photographer can place them). However, this calculation does not account for the different arrangements and orderings that can be produced by shuffling the group.

B. 10 to the power 10: This option is incorrect because it represents the total number of possible arrangements when there are 10 choices for each of the 10 positions. However, this would be true if the photographer was arranging the group in a fixed order repeatedly, rather than shuffling them for each picture.

C. 362880: This option is incorrect because it represents the factorial of 10 (i.e., 10!), which is the total number of possible arrangements of 10 distinct objects in a fixed order. However, the question asks for the number of pictures taken when the group is shuffled, not arranged in a fixed order.

D. 3628800: This option is correct because it represents the total number of different pictures the photographer will take when shuffling the group of ten people. It is calculated by multiplying the number of choices for the first position (10) by the number of choices for the second position (9) by the number of choices for the third position (8), and so on, until there is one choice left for the last position (1). This can be written as 10 x 9 x 8 x ... x 1 = 10!.

Therefore, the correct answer is option D: 3628800.

On a sphere, longitude lines converge toward the poles. When you fly 500 km north from Delhi, you're at a different longitude. The east and west legs are along different latitude lines (different circumferences), but because of Earth's curvature and convergence, you end up slightly east of your starting point.