1
GATE EE 2022
MCQ (Single Correct Answer)
+2
-0.67

Let $$f(x) = \int\limits_0^x {{e^t}(t - 1)(t - 2)dt} $$. Then f(x) decreases in the interval.

A
x $$\in$$ (1, 2)
B
x $$\in$$ (2, 3)
C
x $$\in$$ (0, 1)
D
x $$\in$$ (0.5, 1)
2
GATE EE 2022
MCQ (Single Correct Answer)
+2
-0.67

Let R be a region in the first quadrant of the xy plane enclosed by a closed curve C considered in counter-clockwise direction. Which of the following expressions does not represent the area of the region R?

GATE EE 2022 Engineering Mathematics - Calculus Question 5 English

A
$$\int\!\!\!\int\limits_R {dxdy} $$
B
$$\oint\limits_C {xdy} $$
C
$$\oint\limits_C {ydx} $$
D
$${1 \over 2}\oint\limits_C {(xdy - ydx)} $$
3
GATE EE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Let $$g\left( x \right) = \left\{ {\matrix{ { - x} & {x \le 1} \cr {x + 1} & {x \ge 1} \cr } } \right.$$ and
$$f\left( x \right) = \left\{ {\matrix{ {1 - x,} & {x \le 0} \cr {{x^{2,}}} & {x > 0} \cr } } \right..$$
Consider the composition of $$f$$ and $$g,$$ i.e., $$\left( {f \circ g} \right)\left( x \right) = f\left( {g\left( x \right)} \right).$$ The number of discontinuities in $$\left( {f \circ g} \right)\left( x \right)$$ present in the interval $$\left( { - \infty ,0} \right)$$ is
A
$$0$$
B
$$1$$
C
$$2$$
D
$$4$$
4
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 $$b.$$
GATE EE Subjects
EXAM MAP