JEE Main 2015 B.E./B.Tech Question Paper with Answer Key PDF Code B- April 04 (Forenoon)

JEE Main Questions

• 1.

  The first and second ionization constants of $H_{2X}$ are $2.5 \times 10^{-8}$ and $1.0 \times 10^{-13}$ respectively. The concentration of $X^{2-}$ in $0.1$ M $H_{2}X$ solution is ____________\( \times 10^{-13}\) M. (Nearest Integer)

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• 2.

  Let \(S\) and \(S'\) be the foci of the ellipse \[ \frac{x^2}{25} + \frac{y^2}{9} = 1 \] and \(P(\alpha,\beta)\) be a point on the ellipse in the first quadrant. If \[ (SP)^2 + (S'P)^2 - SP \cdot S'P = 37, \] then \(\alpha^2 + \beta^2\) is equal to

  • 17
  • 13
  • 15
  • 11
    
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• 3.

  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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• 4.

  Which logic gate is given in the figure?
  

  

  • XOR
  • NOR
  • NAND
  • OR
    
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• 5.

  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
    
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• 6.

  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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