Integral Calculus & Area · JEE Main previous year questions

2002 4 questions

1. Q302002 · 27 Apr 2002 · Shift 1

   ${\int }_{-\pi }^{\pi }\frac{2x(1+\sin x)}{1+{\cos }^{2}x}dx$ is

   1. A.$\frac{{\pi }^2}{4}$
   2. B.${\pi }^2$
   3. C.zero
   4. D.$\frac{\pi }{2}$
   Show answer

   Answer: B

2. Q322002 · 27 Apr 2002 · Shift 1

   The area bounded by the curves $y=\ln x$, $y=\ln |x|$, $y=|\ln x|$ and $y=|\ln |x||$ is :

   1. A.$4$ sq. units
   2. B.$6$ sq. units
   3. C.$10$ sq. units
   4. D.none of these
   Show answer

   Answer: A

3. Q392002 · 27 Apr 2002 · Shift 1

   If $|\vec{a}|=5,|\vec{b}|=4,|\vec{c}|=3$ thus what will be the value of $|\vec{a}.\vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a}|$, given that $\vec{a}+\vec{b}+\vec{c}=0$ :

   1. A.$25$
   2. B.$50$
   3. C.$-25$
   4. D.$-50$
   Show answer

   Answer: A

4. Q712002 · 27 Apr 2002 · Shift 1

   If the pair of lines $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ intersect on the $y$-axis then :

   1. A.$2fgh=b{g}^2+c{h}^2$
   2. B.$b{g}^2\ne c{h}^2$
   3. C.$abc=2fgh$
   4. D.none of these
   Show answer

   Answer: A