1
GATE ME 2016 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The condition for which the eigenvalues of the matrix $$A = \left[ {\matrix{ 2 & 1 \cr 1 & k \cr } } \right]$$ are positive, is
A
$$k > 1/2$$
B
$$k > -2$$
C
$$k > 0$$
D
$$k < - 1/2$$
2
GATE ME 2016 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The values of $$x$$ for which the function $$f\left( x \right) = {{{x^2} - 3x - 4} \over {{x^2} + 3x - 4}}$$ is NOT continuous are
A
$$4$$ and $$-1$$
B
$$4$$ and $$1$$
C
$$-4$$ and $$1$$
D
$$-4$$ and $$-1$$
3
GATE ME 2016 Set 2
Numerical
+2
-0
A scalar potential $$\,\,\varphi \,\,$$ has the following gradient: $$\,\,\nabla \varphi = yz\widehat i + xz\widehat j + xy\widehat k.\,\,$$ Consider the integral $$\,\,\int_C {\nabla \varphi .d\overrightarrow r \,\,} $$ on the curve $$\overrightarrow r = x\widehat i + y\widehat j + z\widehat k.\,\,$$ The curve $$C$$ is parameterized as follows: $$\,\,\left\{ {\matrix{ {x = t} \cr {y = {t^2}} \cr {z = 3{t^2}} \cr } \,\,\,\,\,\,\,} \right.$$ and $$1 \le t \le 3.\,\,\,\,\,$$
The value of the integral is _________.
Your input ____
4
GATE ME 2016 Set 2
Numerical
+2
-0
The probability that a screw manufactured by a company is defective is $$0.1$$. The company sells screws in packets containing $$5$$ screws and gives a guarantee of replacement if one or more screws in the packet are found to be defective. The probability that a packet would have to be replaced is _________.
Your input ____
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