#### 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.

**About Paper**

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.

**The value of a sample paper**

Examine your preparation and time management by practising sample papers and previous years’ question papers. Additionally, it will improve your test-taking performance and score.

Questions

**1.** If a and b are roots of the equation x^{2} + x + 1 = 0. The equation whose roots are a^{19}, b^{7} is

**(A)** x^{2} – x -1 = 0 **(B)** x^{2} – x + 1 = 0 **(C)** x^{2} + x -1 = 0 **(D)** x^{2} + 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 x^{3} + mx^{2} + 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**

**1. D**

We know that the roots of x^{2} + x + 1 = 0 are w, w^{2}. Let a = w, b = w^{2}, then

a+b=w + w^{2} = -1 and ab = w.w^{2} = w^{3} = 1

** **Now, a^{19} = w^{19} = (w^{3})^{6} w = w and b^{7} = (w^{2})^{7} = w^{14} = (w^{3})^{4}w^{2} = w^{2}.

Hence the equation whose roots are a^{19}, b^{7} is x^{2} + x + 1 = 0

**2. C**

**3. A**

We have 2^{3} + m(2^{2}) + 11(2) – n = 0 and 3^{3} + m(3^{2}) + 11(3) – n = 0

4m – n = – 30 and 9m – n = -60

Solving we get m = -6, n = 6 Thus m + n = 0.