CAT Exam Numerical Ability Trigonometry

Figure shows an equilateral triangle of side of length 5 which is divided into several unit triangles. A valid path is a path from the triangle in the top row to the middle triangle in the bottom row such that the adjacent triangles in our path share a common edge and the path never travels up (from a lower row to a higher row) or revisits a triangle. An example is given below. How many such valid paths are there?

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CAT Other Question

A number when divided by 296 leaves 75 as remainder.When the same number is divided by 37,the remainder will be: how many divisors of 86400 are there?