1
GATE ECE 2016 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Given the following statements about a function $$f:R \to R,$$ select the right option:
$$P:$$ If $$f(x)$$ is continuous at $$x = {x_0},$$ then it is also differentiable at $$x = {x_0},$$
$$Q:$$ If $$f(x)$$ is continuous at $$x = {x_0},$$ then it may not be differentiable at $$x = {x_0},$$
$$R:$$ If $$f(x)$$ is differentiable at $$x = {x_0},$$ then it is also continuous at $$x = {x_0},$$
A
$$P$$ is true, $$Q$$ is false, $$R$$ is false
B
$$P$$ is false, $$Q$$ is true, $$R$$ is true
C
$$P$$ is false, $$Q$$ is true, $$R$$ is false
D
$$P$$ is true, $$Q$$ is false, $$R$$ is true
2
GATE ECE 2015 Set 3
Numerical
+1
-0
The value of $$\sum\limits_{n = 0}^\infty {n{{\left( {{1 \over 2}} \right)}^n}\,\,}$$ is _______.
Your input ____
3
GATE ECE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
The contour on the $$x-y$$ plane, where the partial derivative of $${x^2} + {y^2}$$ with respect to $$y$$ is equal to the partial derivative of $$6y+4x$$ with respect to $$'x',$$ is
A
$$y=2$$
B
$$x=2$$
C
$$x+y=4$$
D
$$x-y=0$$
4
GATE ECE 2015 Set 1
MCQ (Single Correct Answer)
+1
-0.3
A function $$f\left( x \right) = 1 - {x^2} + {x^3}\,\,$$ is defined in the closed interval $$\left[ { - 1,1} \right].$$ The value of $$x,$$ in the open interval $$(-1,1)$$ for which the mean value theorem is satisfied, is
A
$$- {1 \over 2}$$
B
$$- {1 \over 3}$$
C
$${1 \over 3}$$
D
$${1 \over 2}$$
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