BITSAT 2025 Question Paper June 25 Shift 2 (Available): Download Solutions with Answer Key

BITSAT Questions

• 1.

  If the roots of the quadratic equation \( ax^2 + bx + c = 0 \) are real and equal, then:

  • \( b^2 - 4ac < 0 \)
    
  • \( b^2 - 4ac = 0 \)
    
  • \( b^2 - 4ac > 0 \)
    
  • \( a + b + c = 0 \)
    
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• 2.

  Evaluate the integral: $$ \int_0^{\pi/4} \frac{\ln(1 + \tan x)}{\cos x \sin x} \, dx $$

  • \( \frac{\pi}{4} \ln 2 \)
    
  • \( \frac{\pi}{8} \ln 2 \)
    
  • \( \ln 2 \)
    
  • \( \frac{1}{2} \ln 2 \)
    
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• 3.

  The work done by a gas during an isothermal expansion from 2 L to 4 L at a constant temperature, with pressure initially at 2 atm, is: (Use R = 8.314 J/mol·K, T = 300 K).

  • 281 J
     

  • 831.4 J
    
  • 1247.1 J
    
  • 1662.8 J
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• 4.

  The escape velocity from the surface of a planet is \(v_e\). What will be the escape velocity from a planet whose mass and radius are twice that of the original planet?

  • \(v_e\)
    
  • \(2v_e\)
    
  • \(\sqrt{2}v_e\)
    
  • \(4v_e\)
    
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• 5.

  Statement: All flowers are beautiful. Some beautiful things are fragile.
  Conclusion I: Some flowers are fragile. 
  Conclusion II: All beautiful things are flowers.

  • Only I follows
    
  • Only II follows
    
  • Both follow
    
  • Neither follows
    
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• 6.

  A source supplies heat to a system at the rate of 1000 W. If the system performs work at a rate of 200 W, what is the rate at which internal energy of the system increases?

  • 1200 W
    
  • 600 W
    
  • 500 W
    
  • 800 W
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