JEE Main Question Paper 2014 (Available): Check Previous Year Question Paper with Solution PDF

JEE Main 2014 Questions

• 1.

  Given point \( P(6, 4\sqrt{5}) \) satisfies the hyperbola \[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \] where eccentricity is a root of the equation \( 9e^2 - 21e + 10 = 0 \). Then find the length of latus rectum of the hyperbola \[ \frac{x^2}{a^2} - \frac{y^2}{2(1+b^2)} = 1. \]
  

  • \( \frac{56}{3} \)
    
  • \( \frac{68}{3} \)
    
  • \( \frac{52}{3} \)
    
  • \( \frac{70}{3} \)
  View Solution

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• 2.

  Let $P=[p_{ij}]$ and $Q=[q_{ij}]$ be two square matrices of order $3$ such that $q_{ij}=2^{(i+j-1)}p_{ij}$ and $\det(Q)=2^{10}$. Then the value of $\det(\operatorname{adj}(\operatorname{adj} P))$ is
  

  • 81
    
  • 16
    
  • 32
    
  • 124
    
  View Solution

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• 3.

  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 ___.
  

  • $4$
  • $5$
  • $3.5$
  • $2$ 

  View Solution

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• 4.

  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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• 5.

  If $\cot x=\dfrac{5}{12}$ for some $x\in\left(\pi,\dfrac{3\pi}{2}\right)$, then \[ \sin 7x\left(\cos\frac{13x}{2}+\sin\frac{13x}{2}\right) +\cos 7x\left(\cos\frac{13x}{2}-\sin\frac{13x}{2}\right) \] is equal to:

  • $\dfrac{1}{\sqrt{13}}$
  • $\dfrac{5}{\sqrt{13}}$
  • $-\dfrac{1}{\sqrt{13}}$
  • $\dfrac{8}{\sqrt{13}}$
    
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