Infosys Company Numerical Ability Quadratic Equations

What should be the value of a, in the polynomials x2 - 11x + a and x2 - 14x + 2a, so that these two polynomials have common factors.
A. 24
B. 1
C. -1
D. 1/2

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Infosys Other Question

Each of the followed paired numbers have a relationship that's the same for all of the paired numbers. What is the missing number?

{4, 100} {7, 111} {8, 1000} {1, 1} {12, 1100} {2, ?}
While traveling at uniform speed. U read a two digit no. after one hr the number is reversed order. After another hour the number read is same two digit number. What is the average speed?