Integral Calculus & Area · JEE Main previous year questions

2014 5 questions

1. Q32014 · 6 Apr 2014 · Shift 1

   If $a\in R$ and the equation $-3(x-[x]{)}^2+2(x-[x])+a^2=0$ (where $[x]$ denotes the greater integer $\le x$) has no integral solution, then all possible values of a lie in the interval :

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

2. Q72014 · 6 Apr 2014 · Shift 1

   Let $a,b,c$ and $d$ be non-zero numbers. If the point of intersection of the lines $4ax+2ay+c=0$ and $5bx+2by+d=0$ lies in the fourth quadrant and is equidistant from the two axes then :

   1. A.$3bc-2ad=0$
   2. B.$3bc+2ad=0$
   3. C.$2bc-3ad=0$
   4. D.$2bc+3ad=0$
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   Answer: A

3. Q132014 · 6 Apr 2014 · Shift 1

   The integral $\int (1+x-\frac{1}{x})e^{x+\frac{1}{x}}dx$ is equal to

   1. A.$(x+1)e^{x+\frac{1}{x}}+c$
   2. B.$-x{e}^{x+\frac{1}{x}}+c$
   3. C.$(x-1)e^{x+\frac{1}{x}}+c$
   4. D.$x{e}^{x+\frac{1}{x}}+c$
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   Answer: D

4. Q142014 · 6 Apr 2014 · Shift 1

   The area of the region described by $A=\{(x,y):x^2+y^2\le 1\text{ and }{y}^2\le 1-x\}$ is :

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

5. Q152014 · 6 Apr 2014 · Shift 1

   The integral ${\int }_0^{\pi }\sqrt{1+4{\sin }^2\frac{x}{2}-4\sin \frac{x}{2}}dx$ equals:

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