Number Nexus

123456789101112
Across
  1. 2. A dog after travelling 50 km meets a swami who counsels him to go slower. He then proceeds at ¾ of his former speed and arrives at his destination 35 minutes late. Had the meeting ocurred 24 km further the dog would have reached its destination 25 minutes late. The speed of the dog is?
  2. 4. "Though ancient, my rule still stands tall, I work with three but not with all. If one is square and two combine, The longest side will match just fine. What am I?" Answer: Pythagoras theorem (name o
  3. 8. Seven sports awardees- A, B, C, D, E, F and G are to be honoured at a special luncheon. The players will be seated on the dias in a row. A and G have to catch the flight for their Cricket Match and so must be seated at extreme right. B, the Rajiv Gandhi Khel Ratna recipient must be in the centre. C and D are bitter rivals and therefore, must be seated as far apart as possible. What can be the position of C from the right side? (there are two possible answers, try either)
  4. 9. For any real number etc.
  5. 10. A jar contains 50 red marbles, 50 blue marbles, and 50 green marbles. You are blindfolded and allowed to pick 10 marbles at random. What is the minimum number of marbles you need to guarantee that you have at least 3 marbles of the same color?
  6. 11. Suppose f(x,y) is a real-valued function such that f(3x+2y, 2x-5y) = 19x, for all real numbers x and y, The value of x for which f(x,2x) = 27 is
  7. 12. Find the last two digits of 7^2024
Down
  1. 1. In a certain code, ‘BISNU’ is written as ‘YRHMF’. What should be the code for ‘PINK’ in the same coding system?
  2. 3. Let ABC be an isosceles triangle such that AB and AC are of equal length. AD is the altitude from A on BC and BE is the altitude from B on AC. If AD and BE intersect at O such that angle AOB = 105 degrees, then AD/BE equals
  3. 5. "I help you find the unknown with ease Using symbols, I aim to please. Equations and variables are my art, Balancing both sides is just the start. What am I?"
  4. 6. In a six-digit number, the sixth, that is, the rightmost, digit is the sum of the first three digits, the fifth digit is the sum of first two digits, the third digit is equal to the first digit, the second digit is twice the first digit and the fourth digit is the sum of fifth and sixth digits. Then, the largest possible value of the fourth digit is
  5. 7. The value of this integral