1
GATE EE 2009
+2
-0.6
If $$(x, y)$$ is continuous function defined over $$\left( {x,y} \right) \in \left[ {0,1} \right] \times \left[ {0,1} \right].\,\,\,$$ Given two constants, $$\,x > {y^2}$$ and $$\,y > {x^2},$$ the volume under $$f(x, y)$$ is
A
$$\,\,\int\limits_{y = 0}^{y = 1} {\int\limits_{x = {y^2}}^{x = \sqrt y } {f\left( {x,y} \right)dx\,dy\,\,} }$$
B
$$\int\limits_{y = {x^2}}^{y = 1} {\int\limits_{x = {y^2}}^{x = 1} {f\left( {x,y} \right)dx\,dy\,\,} }$$
C
$$\int\limits_{y = 0}^{y = 1} {\int\limits_{x = 0}^{x = 1} {f\left( {x,y} \right)dx\,dy\,\,} }$$
D
$$\int\limits_{x = 0}^{y = \sqrt x } {\int\limits_{x = 0}^{x = \sqrt y } {f\left( {x,y} \right)dx\,dy\,\,} }$$
2
GATE EE 2009
+2
-0.6
$$F\left( {x,y} \right) = \left( {{x^2} + xy} \right)\,\widehat a{}_x + \left( {{y^2} + xy} \right)\,\widehat a{}_y.\,\,$$ Its line integral over the straight line from $$(x, y)=(0,2)$$ to $$(x,y)=(2,0)$$ evaluates to
A
$$-8$$
B
$$4$$
C
$$8$$
D
$$0$$
3
GATE EE 2009
+1
-0.3
Assume for simplicity that $$N$$ people, all born in April (a month of $$30$$ days) are collected in a room, consider the event of at least two people in the room being born on the same date of the month (even if in different years e.g. $$1980$$ and $$1985$$). What is the smallest $$N$$ so that the probability of this exceeds $$0.5$$ is ?
A
$$20$$
B
$$7$$
C
$$15$$
D
$$16$$
4
GATE EE 2009
+1
-0.3
Let $$\,{x^2} - 117 = 0.\,\,$$ The iterative steps for the solution using Newton -Raphson's method is given by
A
$${x_{k + 1}} = {1 \over 2}\left( {{x_k} + {{117} \over {{x_k}}}} \right)$$
B
$${x_{k + 1}} = {x_k} - {{117} \over {{x_k}}}$$
C
$${x_{k + 1}} = {x_k} - {{{x_k}} \over {117}}$$
D
$${x_{k + 1}} = {x_k} - {1 \over 2}\left( {{x_k} + {{117} \over {{x_k}}}} \right)$$
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