IISER Aptitude Test Question Paper 2026: Download Answer Key with Solutions PDF

IISER 2026 Questions

• 1.

  Three infinite plane sheets which have uniform positive surface charge densities $\sigma$, $\sigma$ and $2\sigma$, are arranged parallel to each other with a separation of $d$ as shown in the figure. A spherical Gaussian surface $S$ of radius $d/2$ has its center on the middle sheet. Which of the following statements regarding the electric flux $\Phi_L$ through the left hemisphere and the electric flux $\Phi_R$ through the right hemisphere of the Gaussian surface is correct?
  

  

  • $\Phi_L > \Phi_R$
    
  • $\Phi_L < \Phi_R$
    
  • $\Phi_L = \Phi_R$
    
  • $\Phi_L = 2\Phi_R$
    
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• 2.

  Consider two Carnot engines of efficiencies $\eta_1$ and $\eta_2$. The first engine absorbs heat $Q_1$ from a heat reservoir A and releases heat $Q_2$ to a heat reservoir B. The second engine takes heat $Q_2$ from B and releases heat $Q_3$ to a heat reservoir C. If $Q_1 > Q_2 > Q_3$, what is the net efficiency of this combination of the two Carnot engines?
  

  • $\eta_1 + \eta_2 - \eta_1\eta_2$
    
  • $\eta_1 + \eta_2 + \eta_1\eta_2$
    
  • $\eta_1\eta_2$
    
  • $\eta_1 + \eta_2$
    
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• 3.

  An experimental study of the photoelectric effect involves a metal of work function $\phi_0$. What is the smallest wavelength of the incident photon to photoemit an electron of mass $m$ which has the same de Broglie wavelength as that of the incident photon? [Given $h$ is the Planck's constant, $c$ is the speed of light, and $\phi_0 \ll mc^2$]
  

  • $\frac{h}{mc} \left( 1 + \sqrt{1 - \frac{2\phi_0}{mc^2}} \right)^{-1}$
    
  • $\frac{h}{mc} \left( 1 - \sqrt{1 - \frac{2\phi_0}{mc^2}} \right)^{-1}$
    
  • $\frac{h}{mc} \left( 1 - \sqrt{1 - \frac{\phi_0}{mc^2}} \right)^{-1}$
    
  • $\frac{h}{mc} \left( 1 + \sqrt{1 - \frac{\phi_0}{mc^2}} \right)^{-1}$
    
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• 4.

  The acceleration of a point particle is given by the equation \[ \frac{d^2\mathbf{x}}{dt^2} = \alpha \frac{\mathbf{x}}{|\mathbf{x}|^7} + \beta \frac{d\mathbf{x}}{dt} \] where $\mathbf{x}$ denotes position and $t$ denotes time. Which of the following relations show the correct dimensions for $\alpha$ and $\beta$?
  

  • $[\alpha] = [\text{M}^0\text{L}^7\text{T}^{-2}]$, $[\beta] = [\text{M}^0\text{L}^0\text{T}^{-1}]$
    
  • $[\alpha] = [\text{M}^1\text{L}^6\text{T}^{-2}]$, $[\beta] = [\text{M}^0\text{L}^0\text{T}^{-3}]$
    
  • $[\alpha] = [\text{M}^0\text{L}^6\text{T}^{-1}]$, $[\beta] = [\text{M}^0\text{L}^1\text{T}^{-2}]$
    
  • $[\alpha] = [\text{M}^0\text{L}^7\text{T}^{-2}]$, $[\beta] = [\text{M}^0\text{L}^0\text{T}^0]$
    
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• 5.

  A jar is filled with two monoatomic non-interacting gases A and B with total masses $M_A$ and $M_B$, respectively. The molar mass of A is double the molar mass of B. If the jar is kept at temperature $T$, what is the ratio of the total pressure of the combined gas to the partial pressure due to the gas A?
  

  • $1 + 2 \frac{M_B}{M_A}$
    
  • $1 + \frac{1}{2} \frac{M_B}{M_A}$
    
  • $1 + \frac{1}{2} \frac{M_A}{M_B}$
    
  • $1 + 2 \frac{M_A}{M_B}$
    
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