Engineering Mathematics GATE-2017

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

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

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

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

$F(x,y)=x^3+y^2$

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

A) $3x^2\;i-2y\;j$
B) $6x^2y$
C) $3x^2\;i+2y\;j$
D) $2y\;i-3x^2\;j$

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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

A) 45 and 75
B) 55 and 48
C) 60 and 60
D) 60 and 70

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Q 6: For the initial value problem

$\frac{dy}{dt}=\sin\left(t\right),\;\;x(0)=0$

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

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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.

A) P-II, Q-I, R-III, S-IV
B) P-I, Q-II, R-IV, S-III
C) P-IV, Q-III, R-II, S-I
D) P-II, Q-I, R-IV, S-III

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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 ________.

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