1
GATE ECE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The values of the integrals $$\int\limits_0^1 {\left( {\int\limits_0^1 {{{x - y} \over {{{\left( {x + y} \right)}^3}}}dy} } \right)} dx\,\,$$ and $$\,\,\int\limits_0^1 {\left( {\int\limits_0^1 {{{x - y} \over {{{\left( {x + y} \right)}^3}}}dx} } \right)} dy\,\,$$ are
A
same and equal to $$0.5$$
B
same and equal to $$-0.5$$
C
$$0.5$$ and $$-05,$$ respectively
D
$$-0.5$$ and $$-0.5,$$ respectively
2
GATE ECE 2017 Set 2
Numerical
+2
-0
The minimum value of the function $$f\left( x \right) = {1 \over 3}x\left( {{x^2} - 3} \right)\,\,$$ in the interval $$ - 100 \le x \le $$ $$100$$ occurs at $$x=$$ __________.
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3
GATE ECE 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Let $$\,\,f\left( x \right) = {e^{x + {x^2}}}\,\,$$ for real $$x.$$ From among the following. Choose the Taylor series approximation of $$f$$ $$(x)$$ around $$x=0,$$ which includes all powers of $$x$$ less than or equal to $$3.$$
A
$$1 + x + {x^2} + {x^3}$$
B
$$\,1 + x + {3 \over 2}{x^2} + {x^3}$$
C
$$\,1 + x + {3 \over 2}{x^2} + {7 \over 6}{x^3}$$
D
$$1 + x + 3{x^2} + 7{x^3}$$
4
GATE ECE 2017 Set 1
Numerical
+2
-0
A three dimensional region $$R$$ of finite volume is described by $$\,\,{x^2} + {y^2} \le {z^3},\,\,\,0 \le z \le 1$$
Where $$x, y, z$$ are real. The volume of $$R$$ correct to two decimal places is __________.
Your input ____
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