1.
1. How many students of MCGS school played the game of Athletics in 2003?
Correct Answer
D. 40
Explanation
In 2003, a total of 40 students from MCGS school played the game of Athletics.
2.
2. How many students of MCGS school played more than one game in 2003?
Correct Answer
B. 10
Explanation
The answer is 10 because it states that there were students from MCGS school who played more than one game in 2003.
3.
What is the ratio of students playing only Hockey to those playing Volleyball in 2003?
Correct Answer
B. 16:9
Explanation
The ratio of students playing only Hockey to those playing Volleyball in 2003 is 16:9. This means that for every 16 students playing only Hockey, there are 9 students playing Volleyball.
4.
4. If 50% of those playing Hockey also played one other game, how many students of MCGS school played both Hockey and Volleyball in 2003?
Correct Answer
D. Data Insufficient
5.
Thirteen pirates put their treasure in a safe. They decide that the safe should be able to be opened if any majority of pirates agree but not be able to be opened if any minority agree. The pirates don’t trust each other so they consult a locksmith. The locksmith puts a specific number of locks on the safe such that every lock must be opened to open the safe. Then he distributes keys to the pirates such that every pirate has some but not all of the keys. Any given lock can have multiple keys but any given key can only open one lock. What is the least number of locks required?
a)
b)
c)
Correct Answer
C. Option c
Explanation
In order to satisfy the condition that any majority of pirates should be able to open the safe, the number of locks should be greater than or equal to the number of pirates divided by 2 and rounded up to the nearest integer. For example, if there are 13 pirates, the number of locks required would be 7 (13/2 = 6.5, rounded up to 7). Therefore, the correct answer is option c.
6.
A, B,C,D,E are 5 points on a plane. AE = 19.5, BC = 15, CE = 5, AB = 15, BD = 6.5, DC = 8.5, BE = 19.5.How many triangles can be formed using the 5 points ?
Correct Answer
B. 9
Explanation
There are 5 points on a plane, labeled A, B, C, D, and E. To form a triangle, we need to choose 3 points from these 5.
We can form a triangle using points A, B, and C because AB = 15, BC = 15, and AC = 30.
We can form a triangle using points A, B, and D because AB = 15, BD = 6.5, and AD = 21.5.
We can form a triangle using points A, C, and D because AC = 30, CD = 8.5, and AD = 21.5.
We can form a triangle using points A, B, and E because AB = 15, BE = 19.5, and AE = 19.5.
We can form a triangle using points A, C, and E because AC = 30, CE = 5, and AE = 19.5.
We can form a triangle using points B, C, and D because BC = 15, CD = 8.5, and BD = 6.5.
We can form a triangle using points B, C, and E because BC = 15, CE = 5, and BE = 19.5.
We can form a triangle using points B, D, and E because BD = 6.5, DE = 13, and BE = 19.5.
We can form a triangle using points C, D, and E because CD = 8.5, DE = 13, and CE = 5.
Therefore, a total of 9 triangles can be formed using the 5 points.
7.
An infinite GP has first term ‘X’ and sum ‘5’ , then X belongs to
Correct Answer
A. X< -10
Explanation
In an infinite geometric progression (GP), the sum of the series is given by the formula S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio. In this case, the sum is given as 5. Since the sum is finite (5), it implies that the common ratio (r) must be between -1 and 1 (exclusive). If the common ratio is between -1 and 1, the series will converge and have a finite sum. Therefore, if X is the first term and the sum is 5, X must be less than -10 in order for the series to converge and have a finite sum. Hence, X < -10 is the correct answer.
8.
Find the coefficient of in the expression (x – 1) (x – 2) (x – 3) ... (x – 50).
Correct Answer
B. 1275
Explanation
To find the coefficient of x, we need to expand the given expression. The expression is a product of factors (x - 1), (x - 2), (x - 3), ..., (x - 50). When we expand this expression, we will get terms of the form x^n multiplied by constants. The coefficient of x will be the sum of all the constants multiplied by x. Since all the constants are negative, when we add them up, we get a positive value. Therefore, the coefficient of x is 1275.
9.
What is the approximate compounded annual growth rate in the book value per equity share of CRBC Bank during the given period 2001-02 to 2003-04, as per Indian GAAP?
Correct Answer
B. 29%
Explanation
The approximate compounded annual growth rate in the book value per equity share of CRBC Bank during the given period 2001-02 to 2003-04 is 29%.
10.
What is the approximate percentage change in difference in net profit between Indian and US GAAP in 2003-04 as compared to the same difference in the previous year for CRBC Bank?
Correct Answer
C. 23.5%
Explanation
The approximate percentage change in the difference in net profit between Indian and US GAAP in 2003-04 as compared to the same difference in the previous year for CRBC Bank is 23.5%.
11.
Which year showed the highest net profit as a percentage of the shareholder’s equity and as per which accounting principle for CRBC Bank?
Correct Answer
B. 2003-04, Indian GAAP
Explanation
In 2003-04, according to Indian GAAP, CRBC Bank showed the highest net profit as a percentage of the shareholder's equity.
12.
If the number of equity shares is given by the ratio of shareholder’s equity to that of the book value per equity share, find the approximate difference in the number of shares of CRBC Bank as per Indian GAAP and US GAAP in the year 2003-04.
Correct Answer
A. No difference
13.
Correct Answer
D. Figure Not possible.
Explanation
The given answer "Figure Not possible" indicates that there is no figure that can be formed using the given numbers 3.732, 0.267, and 0.866. Without any context or additional information, it is not possible to determine what kind of figure or calculation is being referred to. Therefore, the answer suggests that the given numbers cannot be used to form a figure.
14.
[x] is defined as the greatest integer less than or equal to x and {x} is defined as the least integer greater than or equal to x, for all real values of x. Consider the four statements.I. [x] + [–x] = –1II. {x} + [–x] = 0III. {[x]} – [{x}] = –1IV. [2x] +{3x} ≤ 5xHow many of the above statements are always true for all real values of x ?
Correct Answer
D. None of these.
15.
Correct Answer
B. [-0.25,0.33]
16.
Several goods wagons were commissioned to transport animals. At station Q1, 12 animals were placed in each wagon. At station Q2, some animals were taken out and 2 wagons detached. All the animals were now equally distributed among the remaining wagons. It was noted that the number of animals in each wagon was a prime number, and the number of wagons was now 14 less than the number of animals in each wagon. How many animals were in the Wagons that left from station Q1?
Correct Answer
B. 60
Explanation
At station Q1, there were an equal number of animals in each wagon, and the number of wagons was 14 less than the number of animals in each wagon. This means that the number of wagons must be a prime number. If we subtract 14 from each of the answer choices and check if the resulting number is a prime number, we find that only 60 satisfies this condition. Therefore, the number of animals in the wagons that left from station Q1 must be 60.
17.
What are the total number of sets (p, q, r) such that p < q < r, where p, q, r ∈ N and ≤ 10 ?
Correct Answer
D. None of these
18.
The total profit per trip made by running a train between Kolkata & Haldia consist of two parts, one of which is a constant amount of Rs. 24 lakh per trip and the other varies as the square of the number of wagons attached to the engine and amounts to Rs. 7n 2 , where n is the number of wagons attached to the engine in the trip. If the average profit per wagon per trip should not fall below Rs.169 lakh, then what is the minimum number of wagons that have to be attached to the engine?
Correct Answer
B. 24
Explanation
The total profit per trip consists of a constant amount of Rs. 24 lakh and a variable amount that depends on the square of the number of wagons attached to the engine. To find the minimum number of wagons that have to be attached to the engine, we need to determine the point at which the average profit per wagon per trip falls below Rs. 169 lakh. By setting up the equation 24 + 7n^2/n = 169, we can solve for n. Simplifying the equation gives us n^3 - 24n + 169 = 0. By trial and error, we find that n = 24 satisfies the equation, so the minimum number of wagons that have to be attached to the engine is 24.
19.
In âˆ† ABC, the points P, Q and R divide the side AB, BC and CA in the ratio 1 : 2, 3 : 1 and 2 : 3 respectively.Find the ratio of the areas of âˆ† PQR and âˆ† ABC.
Correct Answer
D. 0.2
Explanation
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. In this case, the sides of triangle PQR are in the ratio 1:3:2, which is the same as the sides of triangle ABC. Therefore, the ratio of the areas of triangle PQR and triangle ABC is equal to (1/3)^2 = 1/9. However, since the question asks for the ratio of the areas, we need to take the reciprocal of 1/9, which is 9/1. Simplifying this ratio gives us 9:1, which is equivalent to 0.2.
20.
A hare and a tortoise start running simultaneously clockwise around an oval lake. First time they meet at an apple tree, next time at a mango tree and third time at a banyan tree and fourth time again at the apple tree. Which of the following is not a possible ratio of their speed?
Correct Answer
D. 4:8
Explanation
The given answer, 4:8, is not a possible ratio of their speed because it can be simplified to 1:2. If the hare and the tortoise have a ratio of 1:2, they would meet at the apple tree every other time they complete a lap around the lake, which contradicts the information given in the question.
21.
If a process is a combination of (1, 2); (2, 3); (3, 4) and (4, 1) in succession, which letter will be at the position 3 when the process is executed 100 times successively?
Correct Answer
D. D
Explanation
The given process consists of four steps: (1, 2), (2, 3), (3, 4), and (4, 1). When this process is executed successively, the letter at position 3 will always be "d". This is because the process forms a cycle, where each step leads to the next step in the cycle. After completing the cycle once, the process will repeat again, and the letter at position 3 will remain the same. Therefore, regardless of how many times the process is executed, the letter at position 3 will always be "d".
22.
If a process is a combination of (1, 2); (2, 3); (3, 4); (4, 2); (4, 1); (3, 1); (3, 2); (2, 4) and (1, 4) in succession, the intermediate processes are redundant except the exchange of letters at the positions 1. (1, 2) 2. (1, 3) 3. (1, 4) 4. (3, 4)
Correct Answer
B. (1,3)
Explanation
The given process is a combination of multiple steps, each represented by a pair of numbers. The intermediate processes are considered redundant if they do not result in any change except for the exchange of letters at a specific position. In this case, the intermediate processes (1,2), (2,3), (4,2), (4,1), (3,1), (3,2), and (2,4) do not result in any change except for the exchange of letters at position 1. However, the intermediate process (1,3) does result in a change in the letters at position 1. Therefore, the answer is (1,3).
23.
Correct Answer
D. 2:3
24.
What is the sum of all the 5 digit numbers formed using 1, 2, 3, 4, 5 such that there is no repetition of digits. The sum of all such numbers as represented in base 6 is
Correct Answer
B. 155554000
Explanation
To find the sum of all the 5-digit numbers formed using the digits 1, 2, 3, 4, and 5 without repetition, we can use the concept of permutations. Since there are 5 digits to choose from for each position, there are 5 choices for the first digit, 4 choices for the second digit, 3 choices for the third digit, 2 choices for the fourth digit, and 1 choice for the fifth digit. Therefore, the total number of 5-digit numbers without repetition is 5! = 120.
To find the sum of these numbers, we can use the formula for the sum of an arithmetic series. The first term is 11111 (formed by arranging the digits in increasing order) and the last term is 55555 (formed by arranging the digits in decreasing order). The common difference is 11111, as each subsequent term is obtained by adding 11111 to the previous term.
Using the formula, the sum of the arithmetic series is (120/2) * (11111 + 55555) = 155554000.
Therefore, the sum of all the 5-digit numbers formed using 1, 2, 3, 4, 5 without repetition, represented in base 6, is 155554000.
25.
Correct Answer
B. 4.2
26.
In an LCD display some numbers when viewed upside down, are images of other numbers. (e.g., 1995 becomes 5661). The 5th number that can read upside down is 8, and the 15th is 21, which is 12 when viewed upside down. What is the millionth number that is meaningful upside down?
Correct Answer
B. 11, 555, 511
Explanation
The given answer, 11, 555, 511, is the millionth number that is meaningful upside down. This can be determined by analyzing the pattern of the numbers. The numbers are arranged in a sequence where the first number is 55, the second number is 666, and the third number is 515. This pattern continues, with each number having one more digit than the previous number. When the numbers are viewed upside down, they form different numbers. By following this pattern, the millionth number would have 7 digits and would be 11, 555, 511.
27.
A milk man diluted milk to an extent of 25 % of the original volume of pure milk with water and priced it same as the cost price of milk. Part of the water evaporated and the volume was reduced to 23/25th of the diluted volume. The profit % to the milk man is
Correct Answer
C. 15%
Explanation
The milk man diluted the milk to 25% of its original volume with water. This means that 75% of the diluted mixture is pure milk. When the water evaporated, the volume reduced to 23/25th of the diluted volume. This means that the final volume is 92% of the diluted volume. Since 75% of the diluted mixture is pure milk, the final volume is 69% pure milk. Therefore, the milk man made a profit of 69% - 25% = 44%. To calculate the profit percentage, we divide the profit by the cost price and multiply by 100, which gives us 44%/25% * 100 = 176%. However, since none of the answer choices match this calculation, the correct answer must be "None of these."
28.
Correct Answer
B. 8.92%
29.
The tenth’s place of the number 39^78 is
Correct Answer
D. 8
Explanation
When we raise 39 to the power of 78, we are essentially multiplying 39 by itself 78 times. To determine the tenth's place of the result, we only need to consider the last two digits of each multiplication. We can observe that the last two digits of 39 raised to any power greater than 1 will always end in 21. Therefore, the tenth's place of the number 39^78 is 8.
30.
A man is running on a circular track with uniform speed and a source of light is placed on the ground at the centre of the circular track. The shadow of a man appears on a wall tangential to the circular track at the point of start. The height of the shadow was found to be twice the height of the man 30 min after the man had started running. It was found that the man was yet to complete one round of the circle. The time (hrs) taken by the man to complete 10 rounds is
Correct Answer
C. Either (a) or (b)
Explanation
The height of the shadow being twice the height of the man indicates that the angle of elevation of the source of light from the man is 30 degrees. Since the man is yet to complete one round of the circle in 30 minutes, it means that he completes one round in 60 minutes or 1 hour. Therefore, the time taken to complete 10 rounds would be 10 hours. So, the correct answer is either (a) or (b), which are 6 and 30 respectively.