1
GATE EE 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
A function $$f(x)$$ is defined as
$$f\left( x \right) = \left\{ {\matrix{ {{e^x},x < 1} \cr {\ln x + a{x^2} + bx,x \ge 1} \cr } \,\,,\,\,} \right.$$ where $$x \in R.$$

Which one of the following statements is TRUE?

A
$$f(x)$$ is NOT differentiable at $$x=1$$ for any values of $$a$$ and $$b.$$
B
$$f(x)$$ is differentiable at $$x=1$$ for the unique values of $$a$$ and $$b.$$
C
$$f(x)$$ is differentiable at $$x=1$$ for all values of $$a$$ and $$b$$ such that $$a+b=c.$$
D
$$f(x)$$ is differentiable at $$x=1$$ for all values of $$a$$ and $$b.$$
2
GATE EE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The value of the integral $$\,\,2\int_{ - \infty }^\infty {\left( {{{\sin \,2\pi t} \over {\pi t}}} \right)} dt\,\,$$ is equal to
A
$$0$$
B
$$0.5$$
C
$$1$$
D
$$2$$
3
GATE EE 2016 Set 1
Numerical
+2
-0
Let $$\,\,S = \sum\limits_{n = 0}^\infty {n{\alpha ^n}} \,\,$$ where $$\,\,\left| \alpha \right| < 1.\,\,$$ The value of $$\alpha $$ in the range $$\,\,0 < \alpha < 1,\,\,$$ such that $$\,\,S = 2\alpha \,\,$$ is ___________.
Your input ____
4
GATE EE 2015 Set 2
Numerical
+2
-0
The volume enclosed by the surface $$f\left( {x,y} \right) = {e^x}$$ over the triangle bounded by the lines $$x=y;$$ $$x=0;$$ $$y=1$$ in the $$xy$$ plane is ________.
Your input ____
GATE EE Subjects
EXAM MAP