Other Maths · JEE Main previous year questions

2012 6 questions

1. Q22012 · 26 May 2012 · Shift 1

   $|z_1+z_2{|}^2+|z_1-z_2{|}^2$ is equal to

   1. A.$2(|z_1|+|z_2|)$
   2. B.$2(|z_1{|}^2+|z_2{|}^2)$
   3. C.$|z_1||z_2|$
   4. D.$|z_1{|}^2+|z_2{|}^2$
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   Answer: B

2. Q102012 · 26 May 2012 · Shift 1

   If $A=\left[\begin{array}{ccc}1& 0& 0\\ 2& 1& 0\\ -3& 2& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}1& 0& 0\\ -2& 1& 0\\ 7& -2& 1\end{array}\right]$ then $AB$ equals

   1. A.$I$
   2. B.$A$
   3. C.$B$
   4. D.0
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   Answer: A

3. Q232012 · 26 May 2012 · Shift 1

   The line parallel to $x$-axis and passing through the point of intersection of lines $ax+2by+3b=0$ and $bx-2ay-3a=0$, where $(a,b)\ne (0,0)$ is

   1. A.above $x$-axis at a distance $2/3$ from it
   2. B.above $x$-axis at a distance $3/2$ from it
   3. C.below $x$-axis at a distance $3/2$ from it
   4. D.below $x$-axis at a distance $2/3$ from it
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   Answer: C

4. Q152012 · 12 May 2012 · Shift 1

   If $f(x)=x{e}^{x(1-x)},x\in R$, then $f(x)$ is

   1. A.decreasing on $[-1/2,1]$
   2. B.decreasing on $R$
   3. C.increasing on $[-1/2,1]$
   4. D.increasing on $R$
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   Answer: C

5. Q212012 · 12 May 2012 · Shift 1

   The coordinates of the foot perpendicular from the point $(1,0,0)$ to the line $\frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+10}{8}$ are

   1. A.$(2,-3,8)$
   2. B.$(1,-1,-10)$
   3. C.$(5,-8,-4)$
   4. D.$(3,-4,-2)$
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   Answer: D

6. Q62012 · 7 May 2012 · Shift 1

   The point of intersection of the lines $(a^3+3)x+ay+a-3=0$ and $(a^5+2)x+(a+2)y+2a+3=0$ ($a$ real) lies on the $y$-axis for

   1. A.no value of $a$
   2. B.more than two values of $a$
   3. C.exactly one value of $a$
   4. D.exactly two values of $a$
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   Answer: A