JEE Main B.E./B.Tech 2014 Question Paper with Answer Key PDFs - April 11

JEE Main Questions

• 1.

  In a microscope of tube length $10\,\text{cm}$ two convex lenses are arranged with focal lengths $2\,\text{cm}$ and $5\,\text{cm}$. Total magnification obtained with this system for normal adjustment is $(5)^k$. The value of $k$ is ___.
  

  • $4$
  • $5$
  • $3.5$
  • $2$ 

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• 2.

  The number of relations defined on the set \( \{a, b, c, d\} \) that are both reflexive and symmetric is equal to:

  • 1024
  • 64
  • 16
  • 256
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• 3.

  For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index \(n\) of the prism satisfies:

  • \(\sqrt{2}<n<2\)
    
  • \(\sqrt{2}<n<2\sqrt{2}\)
    
  • \(n\ge 2\)
    
  • \(1<n<2\)
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• 4.

  Let $a_1,a_2,a_3,a_4$ be an A.P. of four terms such that each term of the A.P. and its common difference are integers. If $a_1+a_2+a_3+a_4=48$ and $a_1^2a_2a_3a_4+1^4=361$, then the largest term of the A.P. is equal to
  

  • 27
    
  • 23
    
  • 24
    
  • 21
    
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• 5.

  The solubility product constants of \(Ag_2CrO_4\) and \(AgBr\) are \(32x\) and \(4y\) respectively at 298 K. The value of} \[ \left(\frac{\text{molarity of } Ag_2CrO_4}{\text{molarity of } AgBr}\right) \] can be expressed as:

  • \(\dfrac{2\sqrt[3]{x}}{y}\)
    
  • \(2\sqrt{\dfrac{x}{y}}\)
    
  • \(\sqrt{\dfrac{x}{y}}\)
    
  • \(\dfrac{\sqrt[3]{x}}{\sqrt{y}}\)
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• 6.

  Two wires \(A\) and \(B\) made of different materials have lengths \(6.0\) cm and \(5.4\) cm, and areas of cross-sections \(3.0\times10^{-5}\,\text{m}^2\) and \(4.5\times10^{-5}\,\text{m}^2\), respectively. They are stretched by the same magnitude under the same load. If the ratio of Young’s modulus of \(A\) to that of \(B\) is \(x:3\), find the value of \(x\).

  • \(5\)
  • \(4\)
  • \(2\)
  • \(1\)
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