Baja 2016-aptitude-test- 6th Sem

Explanation
The man is running in the same direction as the train, so his speed needs to be subtracted from the relative speed of the train to calculate the actual speed of the train. The length of the train is given as 125 m and the time taken to pass the man is given as 10 seconds. We can use the formula speed = distance/time to find the relative speed of the train. The relative speed is 125/10 = 12.5 m/s. To convert this to km/hr, we multiply by 18/5, which gives us 45 km/hr. However, this is the relative speed, so we need to subtract the speed of the man, which is 5 km/hr. Therefore, the speed of the train is 45 - 5 = 40 km/hr. None of the given options match this speed, so the correct answer is not available.

Explanation
The given series alternates between two numbers, 53 and 40, and then between two numbers, 40 and 27. It follows the pattern of subtracting 13 from the previous number to get the next number. Therefore, the next number in the series would be 27 - 13 = 14.

Explanation
Based on the given information, Tanya is older than Eric, and Cliff is older than Tanya. Therefore, it is not possible for Eric to be older than Cliff, making the third statement false.

Explanation
To find the speed in km per hour, we need to convert the distance from meters to kilometers and the time from minutes to hours. Since there are 1000 meters in a kilometer, the distance is 600/1000 = 0.6 km. And since there are 60 minutes in an hour, the time is 5/60 = 1/12 hours. To find the speed, we divide the distance by the time: 0.6 / (1/12) = 0.6 * 12 = 7.2 km/h. Therefore, the person's speed is 7.2 km per hour.

Explanation
The pattern in the given series is that the first letter of each group is increasing by one alphabetically, while the second letter remains the same. The third letter is decreasing by one alphabetically, and the fourth letter remains the same. Applying this pattern, the missing group should start with "K" as the first letter, have "L" as the second letter, "L" as the third letter, and "A" as the fourth letter. Therefore, the correct answer is "KLLA".

Explanation
The artificial language seems to follow a pattern where the first syllable of a word represents the second syllable of the English word and the second syllable of the artificial word represents the first syllable of the English word. Applying this pattern, "haplresbo" can be broken down into "hapl" and "resbo", which can be rearranged to form "cloud" and "nine" respectively. Therefore, "haplresbo" could mean "cloud nine".

Explanation
To find the volume of water that falls on 1.5 hectares of ground, we need to multiply the area of the ground (in square meters) by the depth of the rain (in meters). First, we convert 1.5 hectares to square meters by multiplying it by 10,000 (1 hectare = 10,000 square meters). So, the area of the ground is 15,000 square meters. Then, we multiply the area by the depth of the rain (5 cm or 0.05 meters) to get the volume of water. 15,000 square meters multiplied by 0.05 meters equals 750 cubic meters. Therefore, the correct answer is 750 cu. m.

Explanation
A prime number is a number that is only divisible by 1 and itself. 31, 61, and 71 are all prime numbers because they are only divisible by 1 and themselves. However, 91 is not a prime number because it is divisible by 1, 7, 13, and 91.

Explanation
The two numbers are respectively 20% and 50% more than a third number. To find the ratio between the two numbers, we can assume the third number to be 100. The first number would then be 120 (20% more than 100) and the second number would be 150 (50% more than 100). Simplifying the ratio, we get 120:150, which can be further reduced to 4:5.

Explanation
The hour hand of a clock completes a full rotation of 360 degrees in 12 hours. Therefore, in 6 hours (from 8 o'clock in the morning to 2 o'clock in the afternoon), the hour hand will rotate half of that, which is 180 degrees.

Explanation
One-third of one-fourth of a number is 15, which means that one-fourth of the number is 45. To find three-tenths of the number, we multiply 45 by 3/10. This calculation gives us 13.5. However, since the answer choices are all integers, we need to round up to the nearest whole number, which is 14. Therefore, the correct answer is 54.

Explanation
The man has an equal number of one-rupee notes, five-rupee notes, and ten-rupee notes. Let's assume he has x number of each denomination. Therefore, the total value of the one-rupee notes is 1x, the total value of the five-rupee notes is 5x, and the total value of the ten-rupee notes is 10x. Since the total amount of money the man has is Rs. 480, we can write the equation as 1x + 5x + 10x = 480. Simplifying the equation, we get 16x = 480. Dividing both sides by 16, we find that x = 30. Since x represents the number of notes of each denomination, the total number of notes the man has is 30 + 30 + 30 = 90.

Explanation
To find the value of ab, we can use the given equations. We are given that a - b = 3 and a^2 + b^2 = 29. We can square the first equation to get a^2 - 2ab + b^2 = 9. Subtracting this equation from the second equation, we get 3ab = 20. Dividing both sides by 3, we find that ab = 20/3, which is approximately 6.67. However, none of the answer choices match this value, so the correct answer is not available.

Explanation
Isometric drawings are a type of 3D representation that shows an object from multiple angles. They are commonly used by mechanical engineers, piping drafters, and aerospace engineers to visually communicate complex designs. These drawings provide a clear and detailed view of the object, allowing engineers to analyze and understand the various components and their relationships. Therefore, the correct answer is "all of the above" as all three professions can benefit from using isometric drawings in their work.

Explanation
Given that the average weight of A and B is 40 kg and the average weight of B and C is 43 kg, we can set up the equations: A + B = 80 and B + C = 86. Subtracting the first equation from the second equation, we get C - A = 6. Since A + B + C = 135 (since the average weight of A, B, and C is 45 kg), we can substitute the value of A from the first equation into this equation to get C - 80 + B = 6. Simplifying, we get C + B = 86. Subtracting the second equation from this equation, we get C - B = 0, which means C = B. Therefore, the weight of B is 31 kg.

Explanation
To find the smallest number that should be added to 4456 so that the sum is completely divisible by 6, we need to find the remainder when 4456 is divided by 6. By performing the division, we find that the remainder is 2. To make the sum divisible by 6, we need to add the smallest number that will result in a remainder of 4 when divided by 6. Since 2 satisfies this condition, it is the correct answer.

Explanation
Let's assume the two numbers as x and y. We are given that x + y = 25 and x - y = 13. By solving these two equations simultaneously, we can find the values of x and y. Adding the two equations, we get 2x = 38, which gives us x = 19. Substituting this value in either of the equations, we find y = 6. The product of x and y is 19 * 6 = 114.

Explanation
The given expression can be simplified using the formula (a + b)² = a² + b² + 2ab. Applying this formula to the expression, we get (397 + 104)² = 397² + 104² + 2(397)(104). Simplifying further, we get 501² = 157609 + 10816 + 82688. Combining like terms, we get 251001. Therefore, the answer is 251001.

Explanation
The expression (xn - an) can be factored as (x - a)(xn-1 + xn-2a + xn-3a^2 + ... + a^(n-2)x + a^(n-1)). This means that if (xn - an) is completely divisible by (x - a), then (xn - an) can be divided by (x - a) without any remainder. Since (x - a) is a linear factor, it will divide (xn - an) for any value of n, whether n is natural, even, odd, or prime. Therefore, the correct answer is that n can be any natural number.

Explanation
To reach a target of 282 runs in 50 overs, the team would need to score at a run rate of 5.64 runs per over. Since the run rate in the first 10 overs was only 3.2, the team would need to score at a higher run rate in the remaining 40 overs to compensate for the slower start. To calculate the required run rate, we subtract the runs scored in the first 10 overs (32 runs) from the target (282 runs) and divide it by the remaining 40 overs. Therefore, the required run rate is 250 runs divided by 40 overs, which equals 6.25 runs per over.

Explanation
To calculate the speed in km per hour, we need to convert the distance from meters to kilometers and the time from minutes to hours. Since there are 1000 meters in a kilometer, the distance is 0.6 km. And since there are 60 minutes in an hour, the time is 1/12 hours. Dividing the distance by the time, we get a speed of 7.2 km/h.

Explanation
Dandia is a popular dance that originated in the state of Gujarat. It is traditionally performed during the festival of Navratri and involves dancers holding sticks called dandiyas and striking them together in a rhythmic pattern. The dance is characterized by its energetic and vibrant movements, and it is often accompanied by traditional Gujarati music. Dandia has gained popularity not only in Gujarat but also in other parts of India and even internationally, making it a well-known dance form associated with Gujarat.

Explanation
The first statement states that the fruit basket contains more apples than lemons. The second statement states that there are more lemons in the basket than there are oranges. Based on these two statements, it can be inferred that there are more apples than lemons and more lemons than oranges in the basket. Therefore, it is logical to conclude that the third statement, which states that the basket contains more apples than oranges, is true.

Explanation
The given sequence follows a pattern where each term starts with 'B', followed by a number, then 'C', another number, and finally 'D'. The numbers in the sequence are increasing by 1 each time. Therefore, the missing term in the sequence would be 'BC3D', as it follows the pattern of the previous terms.

Explanation
The word "pound" does not belong with the others because it is a unit of weight, while the rest of the words are units of length.