PART III: MATHEMATICS
SECTION 1 (Maximum Marks: 18)
• This section contains SIX (06) questions.
• Each question has FOUR options. ONLY ONE of these four options is the correct answer.
• For each question, choose the option corresponding to the correct answer.
• Answer to each question will be a evaluated according to the following marking scheme:
Full Marks : +3 if ONLY the correct option is chosen;
Zero Marks : 0 if none of these of the options is chosen (i.e. the question is unanswered);
Negative Marks : -1 in all other cases.
Suppose a, b denote the distinct real roots of the quadratic polynomial x 2 + 20x - 2020 and suppose c, d denote the distinct complex roots of the quadratic polynomial x 2 - 20x + 2020. Then the value of ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d)
Text Solution
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Given a + b = -20, ab = -2020, c + d = 20, cd = 2020-09-28
a 2 c - ac 2 + a 2 d - ad 2 + b 2 c - b 2 c - be 2 + b 2 d - bd 2
= (a 2 + b 2 )(c + d) - (a + b)(c 2 + d 2 )
= ((a + b) 2 - 2ab)(c + d) - (a + b)((c + d) 2 - 2cd)
= (400 - 2 x 2020)(20) - (-20)(400 - 2 x 2020)
= 20x800=16000
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