IIT JAM 2006 Mathematics Question Paper with Answer Key PDF (March 26)

IIT JAM Questions

• 1.

  Consider a vector \(\mathbf{F} = \frac{1}{\pi}[-\sin y \hat{i} + x(1 - \cos y)\hat{j}]\). The value of the integral \(\oint \mathbf{F} \cdot d\mathbf{r}\) over a circle \(x^2 + y^2 = 1\) evaluated in the anti-clockwise direction is _____. (in integer)
  

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• 2.

  Consider a volume V enclosed by a closed surface S having unit surface normal \(\hat{n}\). For \(\mathbf{r} = x\hat{i} + y\hat{j} + z\hat{k}\), the value of the surface integral \(\frac{1}{9} \oint_{S} \mathbf{r} \cdot \hat{n} \,dS\) is

  • \(V\)
  • \(3V\)
  • \(\frac{V}{3}\)
  • \(\frac{V}{9}\)
    
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• 3.

  If \(\left(\frac{1-i}{1+i}\right)^{n/2} = -1\), where \(i = \sqrt{-1}\), one possible value of n is

  • 2
  • 4
  • 6
  • 8
    
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• 4.

  The shortest distance between an object and its real image formed by a thin convex lens of focal length 20 cm is _____ cm. (in integer)
  

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• 5.

  The ratio of the density of atoms between the (111) and (110) planes in a simple cubic (sc) lattice is ____. (up to two decimal places)
  

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• 6.

  In an orthorhombic crystal, the lattice constants are 3.0 \AA, 3.2 \AA, and 4.0 \AA. The distance \(d_{101}\) between the successive (101) planes is \rule{1cm{0.15mm} \AA. (up to one decimal place)}
  

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