JEE MAIN Definite Integration Previous Year Questions (PYQs) – Page 13 of 17
A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations
Study Stuff for MCA Examinations
Let $f:\mathbb{R}\to(0,\infty)$ be a strictly increasing function such that
$\displaystyle \lim_{x\to\infty}\frac{f(7x)}{f(x)}=1$.
Then the value of $\displaystyle \lim_{x\to\infty}\Big[\frac{f(5x)}{f(x)}-1\Big]$ is:
1
2
3
4
Solution
$\int_0^5 {\cos \left( {\pi \left( {x - \left[ {{x \over 2}} \right]} \right)} \right)dx} $,
where [t] denotes greatest integer less than or equal to t, is equal to:
1
2
3
4
Solution
The value of the integral \(\displaystyle \int_{1}^{2} \left(\frac{t^{4}+1}{t^{6}+1}\right) dt\) is:
1
2
3
4
Solution
Let $(a, b)$ be the point of intersection of the curve $x^2 = 2y$ and the straight line $y - 2x - 6 = 0$ in the second quadrant.
Then the integral $I = \int_a^b \dfrac{9x^2}{1 + 5x^4},dx$ is equal to:
1
2
3
4
Solution
The value of the integral \(\displaystyle \int_{1/2}^{2} \frac{\tan^{-1}x}{x}\,dx\) is equal to:
1
2
3
4
Solution
If [x] is the greatest integer $\le$ x, then ${\pi ^2}\int\limits_0^2 {\left( {\sin {{\pi x} \over 2}} \right)(x - [x]} {)^{[x]}}dx$ is equal to :
1
2
3
4
Solution
$\displaystyle 4 \int_0^1 \left(\dfrac{1}{\sqrt{3 + x^2} + \sqrt{1 + x^2}}\right) dx - 3 \log_e(\sqrt{3})$ is equal to:
1
2
3
4
Solution
If $\int\limits_0^2 {\left( {\sqrt {2x} - \sqrt {2x - {x^2}} } \right)dx = \int\limits_0^1 {\left( {1 - \sqrt {1 - {y^2}} - {{{y^2}} \over 2}} \right)dy + \int\limits_1^2 {\left( {2 - {{{y^2}} \over 2}} \right)dy + I} } } $, then I equals
1
2
3
4
Solution
Let $f\left( x \right) = \int {{{\sqrt x } \over {{{\left( {1 + x} \right)}^2}}}dx\left( {x \ge 0} \right)} $. Then f(3) – f(1) is eqaul to :
1
2
3
4
Solution
$ \text{If [t] denotes the greatest integer } \le t, \text{ then the value of } \frac{3(e-1)}{e} \int_{1}^{2} x^2 e^{\lfloor x \rfloor + \lfloor x^3 \rfloor} dx \text{ is:} $
1
2
3
4
Solution
JEE MAIN
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
JEE MAIN
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Ask Your Question or Put Your Review.
