1
GATE CE 2009
MCQ (Single Correct Answer)
+1
-0.3
In the solution of the following set of linear equations by Gauss-elimination using partial pivoting $$$5x+y+2z=34,$$$ $$$4y-3z=12$$$ and $$$10x-2y+z=-4.$$$
The pivots for elimination of $$x$$ and $$y$$ are
A
$$10$$ and $$4$$
B
$$10$$ and $$2$$
C
$$5$$ and $$4$$
D
$$5$$ and $$-4$$
2
GATE CE 2009
MCQ (Single Correct Answer)
+1
-0.3
For a scalar function $$f(x,y,z)=$$ $${x^2} + 3{y^2} + 2{z^2},\,\,$$ the gradient at the point $$P(1,2,-1)$$ is
A
$$2\widehat i + 6\widehat j + 4\widehat k$$
B
$$2\widehat i + 12\widehat j - 4\widehat k$$
C
$$2\widehat i + 12\widehat j + 4\widehat k$$
D
$$\sqrt {56} $$
3
GATE CE 2009
MCQ (Single Correct Answer)
+2
-0.6
For a scalar function $$\,f\left( {x,y,z} \right) = {x^2} + 3{y^2} + 2{z^2},\,\,$$ the directional derivative at the point $$P(1,2,-1)$$ in the direction of a vector $$\widehat i - \widehat j + 2\widehat k\,\,$$ is
A
$$-18$$
B
$$-3\sqrt 6 $$
C
$$3\sqrt 6 $$
D
$$18$$
4
GATE CE 2009
MCQ (Single Correct Answer)
+2
-0.6
The standard normal probability function can be approximated as $$$F\left( {{X_N}} \right) = {1 \over {1 + \exp \left( { - 1.7255{X_N}{{\left| {{X_N}} \right|}^{0.12}}} \right)}}\,\,\,$$$
$$\,{X_N} = $$ standard normal deviate. If mean and standard deviation of annual precipitation are $$102$$ cm and $$27$$ cm respectively, the probability that the annual precipitation will be $$b/w$$ $$90$$ cm and $$102$$ cm is
A
$$66.7$$%
B
$$50.0$$%
C
$$33.3$$%
D
$$16.7$$%
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Graduate Aptitude Test in Engineering
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