# Engineering Mathematics GATE-2017

**Q 1: **The value of \lim\limits_{x \to 0}\frac{\tan\left(x\right)}x is ______________.

**Q 2:** The real part of 6e^{i\pi/3} is ________.

**Q 3:** The number of positive roots of the function f(x) shown in the range 0 < x < 6 is _____.

**Q 4:** Let i and j be the unit vectors in the x and y directions, respectively. For the function

the gradient of the function i.e. ∇F is given by

**Q 5: **The marks obtained by a set of students are 38, 84, 45,70, 75, 60, 48. The mean and median marks, respectively, are

**Q 6:** For the initial value problem

The value of x at t = π/3, is ________________.

**Q 7:** Match the problem type in Group 1 with the numerical method in Group 2.

Group 1 | Group 2 |

(P) System of linear algebraic equations | (I) Newton-Raphson |

(Q) Non-linear algebraic equations | (II) Gauss-seidel |

(R) Ordinary differential equations | (III) Simphson’s Rule |

(S) Numerical integrations | (IV) Runge-Kutta |

Choose the correct set of combinations.

**Q 8: **A box has 6 red balls and 4 white balls. A ball is picked at random and replaced in the box, after which a second ball is picked. The probability of both the balls being red, rounded to 2 decimal places, is ________.