IIT JEE Examination is held to give admission to various prestigious engineering colleges such as IITs, NITs and various others prestigious engineering institutions.

This examination is held at two levels: JEE Main and JEE Advanced

**About Paper**

The **JEE Main Solved Mathematics Sample Paper Set-XII **in this article consists of 30 questions from Mathematics. The questions in this paper have been asked from the complete syllabus. Each question of this paper is very important from examination point of view and has been developed very carefully by Subject Experts at Jagranjosh.

**Importance of Sample Paper**

Practicing sample papers and previous years’ question papers help in assessing your preparation and time management. It will also help in increasing your marks in examination.

**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.

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