1
GATE ECE 2018
+1
-0.33
Let $$f\left( {x,y} \right) = {{a{x^2} + b{y^2}} \over {xy}}$$, where $$a$$ and $$b$$ are constants. If $${{\partial f} \over {\partial x}} = {{\partial f} \over {\partial y}}$$ at x = 1 and y = 2, then the relation between $$a$$ and $$b$$ is
A
$$a = {b \over 4}$$
B
$$a = {b \over 2}$$
C
$$a = 2b$$
D
$$a = 4b$$
2
GATE ECE 2018
Numerical
+1
-0.33
Taylor series expansion of $$f\left( x \right) = \int\limits_0^x {{e^{ - \left( {{{{t^2}} \over 2}} \right)}}} dt$$ around 𝑥 = 0 has the form

f(x) = $${a_0} + {a_1}x + {a_2}{x^2} + ...$$

The coefficient $${a_2}$$ (correct to two decimal places) is equal to _______.
3
GATE ECE 2016 Set 2
+1
-0.3
As $$x$$ varies from $$- 1$$ to $$3,$$ which of the following describes the behavior of the function $$f\left( x \right) = {x^3} - 3{x^2} + 1?$$
A
$$f(x)$$ increases monotonically
B
$$f(x)$$ increases, then decreases and increases again
C
$$f(x)$$ decreases, then increases and decreases again
D
$$f(x)$$ increases and then decreases
4
GATE ECE 2016 Set 2
+1
-0.3
How many distinct values of $$x$$ satisfy the equation $$sin(x)=x/2,$$ where $$x$$ is in radians ?
A
$$1$$
B
$$2$$
C
$$3$$
D
$$4$$ or more
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