Learners' Club (Combined Aptitude Test)

The student scores 4 marks for every correct answer and loses 1 mark for every incorrect answer. Let's assume the student attempts x questions correctly. So, the number of incorrect answers would be 75 - x.
The total marks obtained can be calculated as 4x - (75 - x) = 125.
Simplifying the equation, we get 5x = 200.
Solving for x, we find x = 40. Therefore, the student attempts 40 questions correctly.

The correct answer is "Statement I is the cause and statement II is its effect." This means that the increasing standard of living among the middle class society is the cause, and the remarkable growth of the Indian Economy is the effect. This implies that as the standard of living improves for the middle class, it leads to the overall growth and development of the Indian economy.

The analogy here is that illiteracy is a lack of education, just as a flood is a result of excessive rain. Therefore, the correct answer is "Dam" because a dam is a structure built to control and prevent floods caused by excessive rainfall.

The alphabet opposite to A can be found by observing the pattern in the positions of the alphabets on the die. From the given figure, it can be observed that the alphabets B and E are always opposite to each other. Therefore, the alphabet opposite to A is E.

The given answer "Never" is correct because ice cubes melt when they come into contact with heat. In this scenario, the ice cube has already melted due to the heat of a nearby furnace. Therefore, it can be concluded that the ice cube will never be seen again in its solid form.

Q and U are the pair of technicians. This can be determined from the given information that Q is of the same profession as U and they are not married to each other. Therefore, Q and U must be the pair of technicians.

Let the present age of the father be x and the ages of his two sons be y and z. According to the given information, x = 3(y + z) and x + 5 = 2(y + 5 + z + 5). Simplifying the second equation, we get x + 5 = 2(y + z + 10). Substituting the value of x from the first equation into the second equation, we get 3(y + z) + 5 = 2(y + z + 10). Simplifying further, we get y + z = 25. Substituting this value back into the first equation, we get x = 3(25) = 75. Therefore, the father's present age is 75 years, which is not one of the given options. Hence, the correct answer is not available.

Since the three persons are running along a circular path, they will meet again when they complete a full revolution around the circle. The time taken to complete one revolution for each person can be found by dividing the length of the circular path by their respective speeds.

For Pracheta: Time taken = 24 km / 6 kmph = 4 hours
For Shivangi: Time taken = 24 km / 4 kmph = 6 hours
For Uma: Time taken = 24 km / 8 kmph = 3 hours

The three persons will meet again when the time taken by each person is a multiple of their respective times. The least common multiple of 4, 6, and 3 is 12. Therefore, they will meet again after 12 hours.

In the given coding pattern, each letter is assigned a numerical value based on its position in the alphabet (A=1, B=2, C=3, and so on). The coded word is obtained by concatenating the numerical values of each letter in the word. Applying this pattern to the word BIETIAN, we get 2318370.

Given that 2x = 4y = 8z, we can express x, y, and z in terms of a common variable. Dividing the first equation by 2, we get x = 2y. Dividing the second equation by 4, we get y = 2z. Substituting these expressions into the given equation (1/2x + 1/4y + 1/6z = 24/7), we get (1/4y + 1/8y + 1/12z = 24/7). Simplifying this equation, we get (3/24y + 2/24y + 2/24z = 24/7). Combining like terms, we get (7/24y + 2/24z = 24/7). Since the coefficient of y is 7/24, and we know that y = 2z, we can substitute this value into the equation to solve for z. (7/24 * 2z + 2/24z = 24/7). Simplifying, we get (14/24z + 2/24z = 24/7). Combining like terms, we get (16/24z = 24/7). Cross-multiplying, we get (16 * 7 = 24 * 24z), which simplifies to (112 = 576z). Dividing both sides by 576, we get (z = 112/576), which simplifies to (z = 7/48). Therefore, the value of z is 7/48.

In this question, the compound interest is being calculated after 3 years. Since the amount has increased by 60% in 6 years at simple interest, we can assume that the rate of interest is 10% per year. Using the compound interest formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per year, and t is the time in years, we can calculate the compound interest on Rs. 12,000 after 3 years. Plugging in the values, we get A = 12000(1 + 0.1/1)^(1*3) = Rs. 15,732. The compound interest is then A - P = 15732 - 12000 = Rs. 3,732, which matches the given answer of Rs. 3972.

According to the given information, Mike looks forward to attending a two-week music camp where he hopes to sing, dance, and learn to play the guitar. This implies that Mike likes to sing and dance, as he is excited about participating in activities related to music and performing arts.

Four-fifths of 70 is equal to (4/5) * 70 = 56. Five-sevenths of 112 is equal to (5/7) * 112 = 80. The difference between 56 and 80 is 24. To find the percentage difference, we divide the difference by the original value (80) and multiply by 100. Therefore, the percentage difference is (24/80) * 100 = 30%.

The unit digit in a multiplication is determined by the unit digits of the numbers being multiplied. In this case, the unit digit of (6374)1793 is 4, the unit digit of (625)317 is 5, and the unit digit of (341)491 is 1. When these three numbers are multiplied together, the unit digit will be the product of the unit digits of each number, which is 4 x 5 x 1 = 20. The unit digit of 20 is 0.

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The missing character can be obtained by taking the square root of each given number. The square root of 100 is 10, the square root of 81 is 9, the square root of 64 is 8, and the square root of 121 is 11. Therefore, the missing character is the square root of 100, which is 10.

The relationship between R and U cannot be determined based on the given information. The question does not provide any specific information or context about R and U's family or their individual identities. Without any additional information, it is impossible to determine their relationship.

The pair of reporter is Q,R because both Q and R are listed as options and they are the only pair that includes the word "reporter".

If South-East is called 'East', North-West is called 'West', and South-West is called 'South', it can be inferred that the directions are being renamed based on their geographical location. Since North is the opposite direction of South, it would be logical to assume that it would be renamed as North-West.

Both conclusions 1 and 2 follow from the given statements. The first conclusion, "Some married are educated," follows because if all men are married and some men are educated, then there must be some men who are both married and educated. The second conclusion, "Some educated are married," also follows because if all men are married and some men are educated, then there must be some men who are both educated and married. Therefore, both conclusions can be logically derived from the given statements.

A decrease in salaries of 50/3% would exactly cancel out the 20% increase. This means that if salaries are reduced by 50/3%, they would offset the previous increase of 20% and bring the salaries back to the original level.

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The watch loses 360/11 minutes per day because if its hands coincide every 64 minutes, it means that the minute hand gains 1 minute on the hour hand every 64 minutes. Therefore, it takes 11 cycles of 64 minutes for the minute hand to gain 11 minutes on the hour hand. Since there are 360 minutes in 6 hours (the time it takes for the hands to coincide), the watch loses 360/11 minutes per day.

Controversy refers to a disagreement or debate between different parties or individuals who hold opposing views or opinions on a particular topic or issue. It is characterized by conflicting perspectives and the expression of divergent ideas. Injustice, politician, and passion may be associated with controversy in certain cases, but they do not necessarily define the essence of controversy itself. Disagreement, on the other hand, is a fundamental element of controversy, as it represents the clash of contrasting viewpoints that fuels the controversy.

The cistern's external dimensions are given as 3.3 m by 2.6 m by 1.1 m. To find the thickness of the bottom, we need to subtract the thickness of the walls from the external height. The walls are stated to be 5 cm thick, so we subtract 10 cm (5 cm on each side) from the height of 1.1 m. This gives us a remaining height of 1 m. Since the answer options are given in different units, we convert 1 m to centimeters, which is 100 cm. Therefore, the thickness of the bottom is 100 cm or 1 m.

If the first day of the year was Friday, then it means that there are 365 days in the year (since it is not a leap year). Since there are 7 days in a week, after 365 days, the day of the week will repeat. Therefore, the last day of the year will also be Friday.

The given figure consists of multiple rectangles and hexagons. By counting the number of rectangles and hexagons in the figure, it can be determined that there are 30 rectangles and 5 hexagons.

The coding scheme seems to be assigning a numerical value to each letter in the word, and then summing up those values. In DISTEMPER, D=4, I=9, S=19, T=20, E=5, M=13, P=16, and R=18. Adding up these values gives us 4+9+19+20+5+13+16+18 = 104. Dividing this by 2 gives us 52, and adding 0.5 gives us 52.5. Following the same logic, in WALLS, W=23, A=1, L=12, and S=19. Adding up these values gives us 23+1+12+12+19 = 67. Dividing this by 2 gives us 33.5. Applying the same coding scheme to PLASTER, P=16, L=12, A=1, S=19, T=20, E=5, and R=18. Adding up these values gives us 16+12+1+19+20+5+18 = 91. Dividing this by 2 gives us 45.5. Therefore, the correct answer is 45.5.

Since Rahul's mother is the only daughter of Monika's father, it means that Rahul's mother is Monika's sister. Therefore, Monika's husband is Rahul's father.

The correct answer is "entry." The sentence states that unsettled conditions in the land led to the exodus of hundreds of its citizens. This suggests that people were leaving the land and going somewhere else. The word "entry" fits this context because it refers to the act of entering or coming into a place. Therefore, it can be inferred that the unsettled conditions caused people to leave and seek entry into another location.

In 1991, the quantity of requirement of rubber was 72% of the quantity of production.

After 2 hours, tap C is closed. This means that tap A and tap B are still running for the remaining 8 hours. After the 4th hour, tap B is closed. This means that tap A is running alone for the remaining 6 hours. Since tap A can fill the tank in 10 hours, it can fill 1/10th of the tank in 1 hour. Therefore, in 6 hours, tap A can fill 6/10th or 60% of the tank. However, since the question asks for the percentage of work done by tap A alone, we need to subtract the work done by tap B and tap C. Tap B can fill 1/20th of the tank in 1 hour, so in 4 hours it can fill 4/20th or 20% of the tank. Tap C can fill 1/40th of the tank in 1 hour, so in 2 hours it can fill 2/40th or 5% of the tank. Therefore, the percentage of work done by tap A alone is 60% - 20% - 5% = 35%.

The word "vog" is the only option that is not mentioned in any of the given statements. Therefore, it can be inferred that "vog" represents the word "habit" in the given language.

The first bunch of bananas has 1/4 again as many bananas as the second bunch. This means that the first bunch has 1/4 more bananas than the second bunch. Additionally, the second bunch has 3 bananas less than the first bunch. Therefore, we can set up an equation: x = (1/4)x + 3, where x represents the number of bananas in the second bunch. Solving this equation, we find that x = 12. Since the first bunch has 1/4 more bananas than the second bunch, the number of bananas in the first bunch is 12 + (1/4)(12) = 15.

The correct pair in this question is 2-3. Vilification and Denigration are synonyms as they both mean the act of criticizing or speaking ill of someone. Nullification and Falsification are not synonyms or antonyms of each other.

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Statement II alone is sufficient to answer the question. If a/7 + b/20 is an integer, it implies that both a/7 and b/20 are integers. Since 20 is a multiple of 7, b/20 will also be an integer. Therefore, b is exactly divisible by 20.

The question states that one's diet consists of 100 gm each of A, B, and C. It does not mention anything about the fat content in each of these items. Therefore, it can be assumed that the fat content is evenly distributed among A, B, and C. Since each item has a quantity of 100 gm, the total fat content in the diet would be 100 gm. Therefore, the correct answer is 80 gm.

The expression A÷D×B shows that A is the daughter of B. According to the given coding scheme, A÷D means A is the sister of D, and then ×B means A is the son of B. Therefore, A÷D×B implies that A is the daughter of B.

The diet that would cost the least is 300 gm of A. This is because the question is asking for the diet that supplies at least 75 gm of fat, and 300 gm of A is the only option that meets this requirement. The other options either do not supply enough fat or have a higher quantity of ingredients, making them more expensive. Therefore, 300 gm of A is the most cost-effective choice.

The given answer is (1.8X+3Y+11Z/4) Paise. This is the correct answer because it correctly calculates the cost of purchasing X gm of Food A, Y gm of Food B, and Z gm of Food C. The cost of Food A is calculated by multiplying the cost per 100 gm (Rs. 1.80) by X and dividing it by 100 to get the cost for X gm. Similarly, the cost for Food B is calculated by multiplying the cost per 100 gm (Rs. 3.00) by Y and dividing it by 100, and the cost for Food C is calculated in the same way. Finally, all three costs are added together to get the total cost in Paise.

In 1992, the quantity of rubber imported to bridge the gap between the demand and supply was likely to be minimum because the production of rubber was higher than the requirement. This can be observed from the graph where the production line is above the requirement line in 1992, indicating that there was no need for significant imports to meet the demand.

To find the least number that is divisible by 24, 32, 36, and 54 when increased by 5, we need to find the least common multiple (LCM) of these numbers. The LCM of 24, 32, 36, and 54 is 4320. Adding 5 to this number gives us 4325, which is not divisible by any of the given numbers. The next possible number is 4320 + 5 = 4325, which is also not divisible by any of the given numbers. The next possible number is 4325 + 5 = 4330, which is divisible by all the given numbers. However, this is not the least number. The next possible number is 4330 + 5 = 4335, which is also divisible by all the given numbers. Continuing this pattern, we find that the least number that satisfies the given conditions is 859.

In this question, we are asked to find the number of ways to choose 5 students for an educational trip, with the condition that 2 particular girls are always included. Since these 2 girls are already chosen, we need to choose 3 more students from the remaining 18 students (8 boys and 10 girls). The number of ways to choose 3 students from a group of 18 can be calculated using the combination formula. Therefore, the answer is 816.

The pattern in the given sequence is that each number alternates between adding and subtracting a certain value. Starting with 3, we add 4 to get 7, subtract 1 to get 6, subtract 1 again to get 5, add 4 to get 9, subtract 6 to get 3, add 9 to get 12, subtract 11 to get 1, and finally subtract 16 to get -15. Therefore, the missing number in the sequence is -1.

Apathetic means showing no emotions. This implies that a person who is apathetic does not display any emotional response or reaction to situations or events. They may appear indifferent, uninterested, or detached from their surroundings or the feelings of others. Apathy can be characterized by a lack of enthusiasm, motivation, or concern, and can sometimes be seen as a sign of emotional numbness or disengagement.

The speaker is requesting a specific quantity of paper, but the exact number is not specified. The word "some" can be used in this context to indicate an unspecified or indefinite amount of paper.

The word "excluding someone or something" means to leave them out or not include them. The correct answer, "Omission," aligns with this meaning as it refers to the act of omitting or leaving something out.

Let's assume the original mixture contains x liters of milk and y liters of water.

When one liter of water is added, the total volume becomes (x + y + 1). Since the new mixture contains 25% milk, we can write the equation: x / (x + y + 1) = 0.25.

When one liter of milk is added to the new mixture, the total volume becomes (x + y + 1 + 1). Now, the resulting mixture contains 40% milk, so we can write the equation: (x + 1) / (x + y + 2) = 0.4.

Simplifying the equations, we get:
x = 0.25(x + y + 1)
x + 1 = 0.4(x + y + 2)

Solving these equations simultaneously, we find x = 100/3. Therefore, the percentage of milk in the original mixture is 100/3.

The given equations are quadratic equations. By comparing the coefficients, we can see that the coefficient of x^2 is greater than the coefficient of y^2, which means that the parabola represented by the equation for x is wider than the parabola represented by the equation for y. This indicates that the roots of the equation for x will be greater than or equal to the roots of the equation for y. Therefore, x is greater than or equal to y, which means that X ≥ Y.