Integral Calculus & Area · JEE Main previous year questions

2004 5 questions

1. Q222004 · 24 Apr 2004 · Shift 1

   If $x=e^{y+e^{y+\dots \infty }},x>0$, then $\frac{dy}{dx}$ is

   1. A.$\frac{1+x}{x}$
   2. B.$\frac{1}{x}$
   3. C.$\frac{1-x}{x}$
   4. D.$\frac{x}{1+x}$
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   Answer: C

2. Q272004 · 24 Apr 2004 · Shift 1

   If $\int \frac{\sin x}{\sin (x-\alpha )}dx=Ax+B\log \sin (x-\alpha ),+C$, then value of $(A,B)$ is

   1. A.$(-\cos \alpha ,\sin \alpha )$
   2. B.$(\cos \alpha ,\sin \alpha )$
   3. C.$(-\sin \alpha ,\cos \alpha )$
   4. D.$(\sin \alpha ,\cos \alpha )$
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   Answer: B

3. Q322004 · 24 Apr 2004 · Shift 1

   If $f(x)=\frac{e^x}{1+e^x},I_1={\int }_{f(-a)}^{f(a)}xg\{x(1-x)\}dx$ and $I_2={\int }_{f(-a)}^{f(a)}g\{x(1-x)\}dx$, then the value of $\frac{I_2}{I_1}$ is

   1. A.$1$
   2. B.$-3$
   3. C.$-1$
   4. D.$2$
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   Answer: D

4. Q332004 · 24 Apr 2004 · Shift 1

   The area of the region bounded by the curves $y=|x-2|,x=1,x=3$ and the $x$-axis is :

   1. A.$4$
   2. B.$2$
   3. C.$3$
   4. D.$1$
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   Answer: D

5. Q622004 · 24 Apr 2004 · Shift 1

   If $2a+3b+6c=0$, then at least one root of the equation $a{x}^2+bx+c=0$ lies in the interval

   1. A.$(1,3)$
   2. B.$(1,2)$
   3. C.$(2,3)$
   4. D.$(0,1)$
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   Answer: D