1
GATE IN 2013
+1
-0.3
While numerically solving the differential equation $$\,{{dy} \over {dx}} + 2x{y^2} = 0,y\left( 0 \right) = 1\,\,$$ using Euler's predictor corrector (improved Euler- Cauchy) method with a step size of $$0.2,$$ the value of $$y$$ after the first step is
A
$$1.00$$
B
$$1.03$$
C
$$0.97$$
D
$$0.96$$
2
GATE IN 2008
+1
-0.3
It is known that two roots of the non-linear equation $$\,{x^3} - 6{x^2} + 11x - 6 = 0\,\,$$ are $$1$$ and $$3.$$ The third root will be
A
$$j$$
B
$$-j$$
C
$$2$$
D
$$4$$
3
GATE IN 2007
+1
-0.3
The polynomial $$\,p\left( x \right) = {x^5} + x + 2\,\,$$ has
A
all real roots
B
$$3$$ real and $$2$$ complex roots
C
$$1$$ real and $$4$$ complex roots
D
all complex roots
4
GATE IN 2007
+1
-0.3
Identity the Newton $$-$$ Raphson iteration scheme for the finding the square root of $$2$$
A
$${x_{n + 1}} = {1 \over 2}\left( {{x_n} + {2 \over {{x_n}}}} \right)$$
B
$${x_{n + 1}} = {1 \over 2}\left( {{x_n} - {2 \over {{x_n}}}} \right)$$
C
$${x_{n + 1}} = {2 \over {{x_n}}}$$
D
$${x_{n + 1}} = \sqrt {2 + {x_n}}$$
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