If the roots of the quadratic equation x²-4x-log N=0 are all real,then the minimum value of N is

In a race,A B and C take part.A beats B by 30m,B beats C by 20m and A beats C by 48m.Which of the following is correct?

1.The length of the race is 300m.

2.The speeds of A,B and C are in the ratio 50:45:42

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Let x and y be positive integers such that x>y.The expressions 3x+2y and 2x+3y when divided by 5 leaves remainders 2 and 3 reapectively.What is the remainder when (x-y) is divided by 5?

Let x and y be positive integers such that x is prime and y is composite.Which of the following statements are correct?

1.(y-x) can be an even integer

2.xy can be an even integer

3.0.5(x+y) can be an even integer

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The number of pairs (x,y) where x,y are integers satisfying the equation 21x+48y=5 is

If k=x-y+2z where -2<=x<=1,-1<=y<=2 and 3<=z<=6,then which one of the following is correct?