TCS Mini Mock Test

Between the terms 112 and 375, the numbers that contain the digit 2 are: 120, 121, 122, 123, ..., 220, 221, ..., 299, 302, 312, ..., 322, ..., 372, 382, 392, ..., 522, ..., 572, ..., 622, ..., 672, ..., 722, ..., 772, ..., 822, ..., 872, ..., 922, ..., 972, ..., 1002, ..., 1052, ..., 1102, ..., 1152, ..., 1202, ..., 1252, ..., 1302, ..., 1352, ..., 1402, ..., 1452, ..., 1502, ..., 1552, ..., 1602, ..., 1652, ..., 1702, ..., 1752, ..., 1802, ..., 1852, ..., 1902, ..., 1952, ..., 2002, ..., 2052, ..., 2102, ..., 2152, ..., 2202, ..., 2252, ..., 2302, ..., 2352, ..., 2402, ..., 2452, ..., 2502, ..., 2552, ..., 2602, ..., 2652, ..., 2702, ..., 2752, ..., 2802, ..., 2852, ..., 2902, ..., 2952, ..., 3002, ..., 3052, ..., 3102, ..., 3152, ..., 3202, ..., 3252, ..., 3302, ..., 3352, ..., 3402, ..., 3452, ..., 3502, ..., 3552, ..., 3602, ..., 3652, ..., 3702, ..., 3752. Thus, there are 156 numbers that contain the digit 2.

A and B are running in the same direction on a circular track. The relative speed between them is the difference of their individual speeds, which is 12 m/s - 6 m/s = 6 m/s. The time taken for them to meet can be calculated by dividing the circumference of the circular track (120 meters) by the relative speed (6 m/s). 120 meters / 6 m/s = 20 seconds. Therefore, A and B will meet for the first time after 20 seconds.

The young man takes 20 minutes to walk from the apartment to the office, while the old man takes 30 minutes. Since the young man starts 5 minutes after the old man, he will be 5 minutes behind. The young man will catch up to the old man at a rate of 10 minutes per hour (30 minutes - 20 minutes). Therefore, it will take the young man 15 minutes (5 minutes behind + 10 minutes to catch up) to meet the old man. Hence, they will meet at 10:15 AM.

The sum of the publication years of the books is given as 13,524. Since the books are published at seven-year intervals, we can assume that the difference between the publication years of consecutive books is 7. To find the publication year of the first book, we can subtract the sum of the publication years of the remaining six books (6 x 7 = 42) from the total sum. This gives us 13,524 - 42 = 13,482. Therefore, the first book was published in 1911.

The given word is "WAITING". When the letters of this word are rearranged without repetition in alphabetical order, the 32nd word will be "AGNTIWI".

A can repay B in 8 different ways. The possible combinations of notes that A can use to repay B are as follows: 10, 10, 10, 10, 10; 10, 10, 10, 20; 10, 10, 20, 10; 10, 20, 10, 10; 20, 10, 10, 10; 10, 20, 20; 20, 10, 20; 20, 20, 10.

The height at which the tree broke can be determined by using the concept of similar triangles. Since the top of the tree touches the other edge of the road, we can form a right triangle with the height of the tree as the vertical side and the breadth of the road as the horizontal side. The height of the tree broken can be considered as the vertical side of a similar triangle formed by the remaining part of the tree. By setting up a proportion between the two triangles, we can solve for the height at which the tree broke. In this case, the proportion would be 36/12 = x/16, where x represents the height at which the tree broke. Solving this proportion gives us x = 16.

Based on the given statements, we can determine that three of the statements are true and one is false. The false statement is IV, which states that the digit is 8. Therefore, the digit cannot be 8. The only statement that is left is III, which states that the digit is not 9. Since we know that III is true and the other statements are false, it necessarily means that III is correct. Hence, III is true.

A can complete 1/8 of the work in 1 hour, B can complete 1/10 of the work in 1 hour, and C can complete 1/12 of the work in 1 hour. Together, they can complete (1/8 + 1/10 + 1/12) = 11/60 of the work in 1 hour. Since A leaves after 2 hours, the remaining work is (1 - 2/8) = 6/8. B and C together can complete (11/60) of the work in 1 hour, so they will take (6/8) / (11/60) = 2 (1/11) hours to complete the remaining work.

The given expression can be simplified by factoring out a common term of (77! - 54!)^3 / (77! + 54!)^3 from both terms. This leaves us with (77! - 54!) / (77! + 54!). Since the numerator and denominator have a common factor of (77! - 54!), they cancel out, leaving us with 1 as the final answer.

Based on the statements given, we can determine that A cannot be the knight because if A were the knight, they would be telling the truth about C being a knave, which contradicts what C says. We can also determine that C cannot be the knight because if C were the knight, they would be telling the truth about being the spy, which contradicts what the spy can do (lie or tell the truth). Therefore, B must be the knight because if B were the knight, they would be telling the truth about A being a knight.

The set {3, 8, 13, 18, 23, 28, 33, 38, 43, 48} contains 10 numbers. To find the number of different integers that can be expressed as the sum of three distinct numbers from this set, we can use the combination formula. The number of combinations of 3 distinct numbers that can be selected from a set of 10 is given by 10C3 = 10! / (3! * (10-3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120. Therefore, there are 120 different integers that can be expressed as the sum of three distinct numbers from the given set.