JEE Main 2022 Physics Question Paper July 29 Shift 2- Download Paper with Solution PDF Here

JEE Main Questions

• 1.

  Let \(a_1, a_2, a_3, \dots\) be a G.P. of increasing positive terms such that \(a_2 \cdot a_3 \cdot a_4=64\) and \(a_1 + a_3 + a_5 = \frac{813}{7}\). Then \(a_3 + a_5 + a_7\) is equal to:

  • 3256
  • 3248
  • 3244
  • 3252
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• 2.

  Let O be the vertex of the parabola \(x^2=4y\) and Q be any point on it. Let the locus of the point P, which divides the line segment OQ internally in the ratio 2:3 be the conic C. Then the equation of the chord of C, which is bisected at the point (1, 2), is:

  • \(5x-4y+3=0\)
  • \(x-2y+3=0\)
  • \(5x-y-3=0\)
  • \(4x-5y+6=0\)
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• 3.

  One side of an equilateral prism is painted by a transparent material of refractive index \( n_2 \). The refractive index of prism is 1.6. The minimum value of \( n_2 \) required for total internal reflection from the painted face is _______.

  

  • \( \frac{\sqrt{3}}{1.6} \)
    
  • \( \sqrt{3} \)
    
  • \( \frac{3.2}{\sqrt{3}} \)
    
  • \( \frac{4\sqrt{3}}{5} \)
    
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• 4.

  Let \(f: R \to (0, \infty)\) be a twice differentiable function such that \(f(3) = 18\), \(f'(3)=0\) and \(f''(3) = 4\). Then \(\lim_{x \to 1} \log_e \left[ \frac{f(2+x)}{f(3)} \right]^{\frac{18}{(x-1)^2}}\) is equal to:

  • 2
  • 1
  • 18
  • 9
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• 5.

  In the given figure, the blocks $A$, $B$ and $C$ weigh $4\,\text{kg}$, $6\,\text{kg}$ and $8\,\text{kg}$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is ___ N.
  (Given: $g = 10\,\text{m s}^{-2}$) 
  

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• 6.

  The value of $\lim_{x \to 0} \frac{x^2 \sin^2 x}{x^2 - \sin^2 x}$ is:

  • 2
  • 3
  • 4
  • 5
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