1.
I. 10x^2 + 11x + 1 = 0II. 12y^2 - y - 1 = 0
Correct Answer
A. 1
Explanation
The given answer, 1, is the correct answer because it represents the number of solutions for the given equations. In both equations, the highest exponent is 2, indicating that they are quadratic equations. A quadratic equation can have either 0, 1, or 2 solutions. Since the given equations are in the form of ax^2 + bx + c = 0, where a, b, and c are constants, they can be solved using the quadratic formula. The quadratic formula states that if the discriminant (b^2 - 4ac) is positive, there are 2 real solutions. If the discriminant is zero, there is 1 real solution. And if the discriminant is negative, there are no real solutions. Therefore, the correct answer is 1, indicating that both equations have 1 real solution.
2.
I. x^2 - 14x - 51 = 0II. y^2 - 35y + 306 = 0
Correct Answer
D. 5
Explanation
The correct answer is 5 because it is the only option that satisfies both equations. By factoring the equations, we can see that (x-17)(x+3) = 0 for the first equation, and (y-17)(y-18) = 0 for the second equation. Therefore, x = 17 and y = 17 or y = 18. Only option 5 satisfies both conditions, making it the correct answer.
3.
DIRECTIONS for the questions 3 to 4: In the following series, one of the terms given is wrong. Find that term and mark that as your answer40 20 24 30 60 150
Correct Answer
A. 24
Explanation
In the given series, all the terms are obtained by multiplying the previous term by a certain number. Starting with 40, the first term, the second term is obtained by dividing 40 by 2, the third term is obtained by multiplying 20 by 1.2, the fourth term is obtained by multiplying 24 by 1.25, the fifth term is obtained by multiplying 30 by 2, and the sixth term is obtained by multiplying 60 by 2.5. Therefore, the correct term in the series should be obtained by multiplying the previous term by 1.25. However, the term 24 is not obtained by this rule, so it is the wrong term in the series.
4.
29 33 41 50 77 98 157
Correct Answer
D. 98
Explanation
The given sequence is a series of numbers where each number is obtained by adding the previous number with a specific pattern. Starting with 29, the pattern is to add 4, then 8, then 9, then 27, then 21, then 59. The next number in the series should follow the same pattern. Therefore, the next number is 98.
5.
What is the percent profit earned by selling the article after giving 10% discount?I. Had there been no discount offered, the profit earned would have been 30%.II. Selling price of the article after giving discount is Rs. 3510/-
Correct Answer
D. The data in statement I alone are sufficient to answer the question, while the data in statement II alone not sufficient to answer the question.
6.
The distance between point A and B is 722 km. At 8 am a car starts from point A (towards point B) at 46 kmph and at 10 am another car starts points B ( towards point A) at 38 kmph. At what time will they meet?
Correct Answer
B. 5.30 pm
Explanation
The first car starts at 8 am and travels at a speed of 46 kmph. The second car starts at 10 am and travels at a speed of 38 kmph. This means that the first car has a 2-hour head start. In those 2 hours, the first car would have traveled 92 km (46 kmph * 2 hours). The remaining distance between the two cars is 722 km - 92 km = 630 km. When both cars are moving towards each other, their combined speed is 46 kmph + 38 kmph = 84 kmph. To cover the remaining distance of 630 km at a speed of 84 kmph, it would take them 630 km / 84 kmph = 7.5 hours. Adding the 2-hour head start, the total time it would take for them to meet is 7.5 hours + 2 hours = 9.5 hours. If the first car starts at 8 am, they would meet at 8 am + 9.5 hours = 5.30 pm. Therefore, the correct answer is 5.30 pm.
7.
The average weight of boys in a class is 56 kg and the average weight of girls in the same class is 41 kg. If the average weight of the entire class is 47.25 kg, then find that the number of girls constitutes what percent of the total number of students in the class?
Correct Answer
A. 581⁄3
Explanation
Let's assume that there are x girls in the class. Since the average weight of girls is 41 kg, the total weight of all the girls would be 41x kg.
Similarly, let's assume that there are y boys in the class. Since the average weight of boys is 56 kg, the total weight of all the boys would be 56y kg.
The average weight of the entire class is given as 47.25 kg. So, the total weight of the entire class would be 47.25 times the total number of students in the class.
We can set up the equation:
(41x + 56y) / (x + y) = 47.25
Simplifying this equation, we get:
41x + 56y = 47.25(x + y)
41x + 56y = 47.25x + 47.25y
8.25y = 6.25x
y/x = 5/8
Therefore, the number of girls constitutes 5/8 or 62 3/3% of the total number of students in the class.
8.
A & B started a business together by investing Rs. 36000/- and Rs. 42000/- respectively. Both of them invested for one year whereas after 6 months from the start C joined them by investing a certain amount. If they earned an annual profit of Rs. 39,200/- out of which C’s share is Rs. 7350/-. What is the investment of C?
Correct Answer
B. Rs. 36000/-
Explanation
Since A and B invested for the entire year, their total investment for the year is Rs. 36,000 + Rs. 42,000 = Rs. 78,000.
Let's assume C's investment is x.
Since C joined after 6 months, his investment is only for half the year.
So, C's share of the profit is (x/78,000) * Rs. 39,200 = Rs. 7350.
Simplifying this equation, we get x = Rs. 36,000.
Therefore, the investment of C is Rs. 36,000.
9.
A rectangular plot, 42m long and 32m wide, has two concrete crossroads (of same width) running in the middle of the plot (one parallel to length and the other parallel to breadth). The rest of the plot is used as a lawn. If the area of the lawn is 1064 sq. m., what is the width of the roads?
Correct Answer
D. 4m
Explanation
Since the total area of the rectangular plot is given as 1064 sq. m. and the length and width of the plot are known, we can calculate the area of the roads by subtracting the area of the lawn from the total area. The area of the lawn is given as 1064 sq. m., so the area of the roads is (42 * 32) - 1064 = 1344 - 1064 = 280 sq. m. Since the two roads are of the same width, we divide the area of the roads by 2 to get the width of each road. Therefore, the width of each road is 280 / 2 = 140 sq. m. Since the width of the roads is given in meters, we convert the area from sq. m. to meters by taking the square root, which gives us the width of each road as 4m.
10.
A jar was containing 60 liters of mixture of milk and water in the ratio 7:5. From this jar 12 litres of mixtures was taken out and 8 litres of pure milk was added. What is the respective ratio of milk and water in the mixture after the final operation?
Correct Answer
A. 9:5
Explanation
After taking out 12 liters of the mixture, there are 48 liters of the mixture left in the jar. Since the original ratio of milk to water is 7:5, we can calculate that there are 28 liters of milk and 20 liters of water in the 48 liters of the mixture.
Then, 8 liters of pure milk is added to the jar, making the total amount of milk 28 + 8 = 36 liters. The amount of water remains the same at 20 liters.
Therefore, the respective ratio of milk to water in the mixture after the final operation is 36:20, which simplifies to 9:5.
11.
DIRECTIONS for the question 1 to 5: Read the passage and answer the question based on it.Many people who are looking to get a pet dog get a puppy. There are many reasons why people get puppies. After all, puppies are cute, friendly, and playful. But even though puppies make good pets, there are good reason why you should consider getting an adult dog instead. When you get a puppy, you have to teach it how to behave. You have to make sure that the puppy is housebroken so that it does not got to the bathroom inside the house. You have to teach the puppy not to jump up on your guests or chew on your shoes. You have to train the puppy to walk on a leash. This is a lot of work.On the other hand, when you get an adult dog, there is a good chance that it will already know how to do all of the previously mentioned things. Many adult dogs have already been housebroken. Many adult dogs will not jump on or chew things that you do not want them to jump on or chew. Many adult dogs will be able to walk on a leash without pulling you to the other side of the street.Puppies also have a lot of energy and want to play all of the time. This can be fund, but you might not want to play as much as your puppy does. Puppies will not always sleep through the night or let you relax as you watch television.On the other hand, most adult dogs will wait on you to play. What is more, they will sleep when you are sleeping and are happy to watch television on the couch right beside you. There is one last reason why you should get an adult dog instead of a puppy. When most people go to the pound to get a dog, they get a puppy. This means that many adult dogs spend a lot of time in the pound, and some never find good homes. So if you are looking to get a dog for a pet, you should think about getting an adult dog. They are good pets who need good homes.The passage speaks of
Correct Answer
A. How puppies do not make good pets.
Explanation
The passage explains that while puppies are cute, friendly, and playful, there are reasons why getting an adult dog may be a better choice. It mentions that training a puppy requires a lot of work, such as housebreaking, teaching them not to chew or jump on things, and leash training. It also states that puppies have a lot of energy and may not let you relax or sleep through the night. Additionally, the passage highlights that many adult dogs in pounds are in need of good homes. Therefore, the correct answer is that the passage speaks of how puppies do not make good pets.
12.
Which is the best example of a dog that is housebroken?
Correct Answer
A. Rex always breaks things inside the house
Explanation
The best example of a dog that is housebroken is Spot goes outside to use the bathroom. This indicates that Spot is trained to go outside when it needs to relieve itself, showing that it is well-behaved and understands where it should go to do its business. The other options given in the question do not demonstrate housebroken behavior.
13.
The author apparently thinks that puppies are
Correct Answer
A. Friendly and playful
Explanation
The author's belief that puppies are friendly and playful is inferred from the given options. The other options are not supported by the statement. The author does not mention anything about puppies being less cute than adult dogs or less playful than adult dogs. The term "hardworking" is not mentioned at all. Therefore, the correct answer is that the author thinks puppies are friendly and playful.
14.
Which is the best synonym for ‘behave’ as applicable to this passage?
Correct Answer
C. Act
Explanation
In the given passage, the word "behave" refers to how someone conducts themselves or carries out their actions. The best synonym for this meaning would be "act", as it implies taking action or behaving in a certain way.
15.
The author begins paragraphs 2 and 4 with the phrase, “On the other hand”. This phrase is used to
Correct Answer
A. Contradict previous information
Explanation
The author begins paragraphs 2 and 4 with the phrase "On the other hand" to introduce contrasting information or viewpoints that contradict what was previously stated. This phrase is used to present an alternative perspective or argument that challenges or contradicts the information presented earlier in the text.
16.
DIRECTIONS for the question 6 to 7: Choose an option, which can be substituted for a given word/sentence/phrase out of given options.Not easily pleased by anything
Correct Answer
C. Fastidious
Explanation
Fastidious means having very high standards and being difficult to please. Therefore, if someone is not easily pleased by anything, they can be described as fastidious.
17.
To die without having made a will
Correct Answer
A. Intestate
Explanation
To die without having made a will means that a person has died without legally designating how their assets and possessions should be distributed after their death. The term used to describe this situation is "intestate."
18.
DIRECTIONS for the question 8 to 9: In the sentence provided different ways of writing a sentence are indicated. Choose the best way of writing the sentence that is grammatically correct.The vivid photos of majestic animals and colourful birds form the wild-life park is a graphic depiction of what is beautiful in the continent of Africa.
Correct Answer
A. Is a graphic depiction of what was beautiful in
Explanation
The correct answer is "is a graphic depiction of what was beautiful in". This is because the sentence is referring to the past, as indicated by the use of "was" instead of "is". The sentence is describing the vivid photos as a depiction of something that was beautiful in the past.
19.
New hires in this laboratory should anticipate excellent research opportunities and getting valuable clinical experience.
Correct Answer
A. As well as
Explanation
The phrase "as well as" is the correct answer because it is used to add additional information to a sentence. In this context, it suggests that new hires in the laboratory can expect both excellent research opportunities and valuable clinical experience. The phrase "as well as" is commonly used to connect two similar or related ideas, indicating that both are true or applicable in this case.
20.
DIRECTIONS for the question 10: Choose the word from the options which is Opposite in meaning to the given word.Aggravate
Correct Answer
B. Alleviate
Explanation
The word "aggravate" means to make a problem or situation worse. The word "alleviate" means to make a problem or situation less severe or intense. Therefore, "alleviate" is the opposite in meaning to "aggravate".