1
GATE CE 2015 Set 1
Numerical
+1
-0
For what value of $$'p'$$ the following set of equations will have no solutions? $$2x+3y=5$$$$$3x+py=10$$$
2
GATE CE 2015 Set 1
Numerical
+2
-0
The directional derivative of the field $$u(x, y, z)=$$ $${x^2} - 3yz$$ in the direction of the vector $$\left( {\widehat i + \widehat j - 2\widehat k} \right)\,\,$$ at point $$(2, -1, 4)$$ is _______.
3
GATE CE 2015 Set 1
Numerical
+2
-0
Consider the following probability mass function (p.m.f) of a random variable $$X.$$ $$p\left( {x,q} \right) = \left\{ {\matrix{ q & {if\,X = 0} \cr {1 - q} & {if\,X = 1} \cr 0 & {otherwise} \cr } } \right.$$\$
$$q=0.4,$$ the variance of $$X$$ is _______.
4
GATE CE 2015 Set 1
+2
-0.6
Consider the following differential equation
$$x\left( {y\,dx + x\,dy} \right)\cos \left( {{y \over x}} \right)$$
$$\,\,\,\,\,\,\,\,\,\, = y\left( {x\,dy - y\,dx} \right)\sin \left( {{y \over x}} \right)$$

Which of the following is the solution of the above equation ($$C$$ is an arbitrary constant)

A
$${x \over y}\cos {y \over x} = C$$
B
$${x \over y}\sin {y \over x} = C$$
C
$$xy\,\cos {y \over x} = C$$
D
$$xy\,\sin {y \over x} = C$$
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