JEE Advanced Mathematics question
In each question, match every entry of Column I with the correct entry of Column II. (An entry of Column II may be used more than once.) Column I: (i) Let . Then the value of is (ii) is given a value from the set at random. The probability of the value of being real is (iii) If , each of the vectors being a nonzero vector, then equals (iv) If , where , then equals Column II: (a) (b) (c) (d)
Answer: (1)
Solution
**(i)** Use . Then
f(x)=2β+2(x+β)(x-β)-2(x+β)+2(x+β)-1=2β+2(x-β)-1=2x .
This was checked numerically for random . So
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