1
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
2
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
3
GATE ECE 2016 Set 3
Numerical
+1
-0
The integral $$\int\limits_0^1 {{{dx} \over {\sqrt {\left( {1 - x} \right)} }}}$$ is equal ________.
4
GATE ECE 2016 Set 1
+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
EXAM MAP
Medical
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