JEE Main Solved Mathematics Sample Paper Set-XII
Various famous engineering colleges, including IITs, NITs, and other prestigious engineering institutes, provide admission through the IIT JEE Exam.
JEE Main and JEE Advanced are the two levels at which this exam is given.
This article’s JEE Main Solved Mathematics Sample Paper Set-XII has 30 math questions. This paper’s questions were drawn from the entire syllabus. Each question on this test has been meticulously crafted by subject experts and is very significant from the perspective of the examination.
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1. If a and b are roots of the equation x2 + x + 1 = 0. The equation whose roots are a19, b7 is
(A) x2 – x -1 = 0 (B) x2 – x + 1 = 0 (C) x2 + x -1 = 0 (D) x2 + x + 1 = 0
(A) cos x + i sin x (B) m/2 (C) 1 (D) (m + 1)/2
3. If two roots of the equation x3 + mx2 + 11x – n = 0 are 2 and 3, then value of m + n is
(A) -1 (B) -2 (C) -3 (D) none of these
Hints and Solutions
We know that the roots of x2 + x + 1 = 0 are w, w2. Let a = w, b = w2, then
a+b=w + w2 = -1 and ab = w.w2 = w3 = 1
Now, a19 = w19 = (w3)6 w = w and b7 = (w2)7 = w14 = (w3)4w2 = w2.
Hence the equation whose roots are a19, b7 is x2 + x + 1 = 0
We have 23 + m(22) + 11(2) – n = 0 and 33 + m(32) + 11(3) – n = 0
4m – n = – 30 and 9m – n = -60
Solving we get m = -6, n = 6 Thus m + n = 0.