1
GATE CE 1995
MCQ (Single Correct Answer)
+1
-0.3
The function $$f\left( x \right) = {x^3} - 6{x^2} + 9x + 25$$ has
A
a maxima at $$x=1$$ and a minima at $$x=3$$
B
a maxima at $$x=3$$ and a minima at $$x=1$$
C
no maxima, but a minima at $$x=3$$
D
a maxima at $$x=1,$$ but no minima
2
GATE CE 1995
MCQ (Single Correct Answer)
+1
-0.3
The function $$f\left( x \right) = \left| {x + 1} \right|$$ on the interval $$\left[ { - 2,0} \right]$$ is __________.
A
continuous and differentiable
B
continuous on the interval but not differentiable at all points
C
Neither continuous nor differentiable
D
Differentiable but not continuous
3
GATE CE 1995
MCQ (Single Correct Answer)
+1
-0.3
The derivative of $$f(x, y)$$ at point $$(1, 2)$$ in the direction of vector $$\overrightarrow i + \overrightarrow j $$ is $$2\sqrt 2 $$ and in the direction of the vector $$ - 2\overrightarrow j $$ is $$-3.$$ Then the derivative of $$f(x,y)$$ in direction $$ - \overrightarrow i - 2\overrightarrow j $$ is
A
$$2\sqrt 2 + 3/2$$
B
$$ - 7/\sqrt 5 $$
C
$$ - 2\sqrt 2 - 3/2$$
D
$$ 1/\sqrt 5 $$
4
GATE CE 1995
MCQ (Single Correct Answer)
+1
-0.3
The differential equation $${y^{11}} + {\left( {{x^3}\,\sin x} \right)^5}{y^1} + y = \cos {x^3}\,\,\,\,$$ is
A
homogeneous
B
non-linear
C
$$2$$nd order linear
D
non-homogeneous with constant coefficients
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