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Q41. Choose the four-digit number where the product of the 1st and 4th digits is 40 and the middle digits is 28. The 1000s digit is as much less than the unit digit as the 100s is less than the 10s.
Digits a, b, c, d: a*d=40 and b*c=28. Possible for a,d: (5,8) or (8,5). For b,c: (4,7) or (7,4). Condition: d-a = c-b. For 5478: 8-5=3 and 7-4=3. This matches.
Q42. Write d=1 degree, r=1 radian and g=1 grad (100 grad = right angle). Then which of the following is true?
Comparing the sizes: 1 radian ≈ 57.3°, 1 grad = 0.9°, and 1 degree = 1°. So, 1° > 0.9°, and 57.3° is the largest. In the first quadrant, cosine decreases as the angle increases. Therefore, cos(1 rad) < cos(1 grad) < cos(1°).
Q43. Two runners A and B start running from diametrically opposite points on a circular track in the same direction. If A runs at a constant speed of 8 km/h and B at a constant speed of 6 km/h and A catches up with B in 30 minutes, what is the length of the track?
A runs 2 km/h faster than B. In 30 minutes (0.5 hours), A closes a distance of 2 km/h * 0.5 h = 1 km. Since they started diametrically opposite, this 1 km represents exactly half the length of the circular track. Therefore, the full track is 2 km long.