CBSE Class 12 Mathematics Set 3- (65/4/3) Question Paper 2026 with Solution PDF

CBSE CLASS XII Questions

• 1.

  Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]

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• 2.

  Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.
  

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• 3.

  Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while 120 out of 1000 females who smoke develop lung related problems. In a colony, 50 people were found to be smokers of which 30 are males. A person is selected at random from these 50 people and tested for lung related problems. Based on the given information answer the following questions: 
  
  (i) What is the probability that selected person is a female? 
  (ii) If a male person is selected, what is the probability that he will not be suffering from lung problems? 
  (iii)(a) A person selected at random is detected with lung complications. Find the probability that selected person is a female. 
  OR 
  (iii)(b) A person selected at random is not having lung problems. Find the probability that the person is a male. 
   

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• 4.

  Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).

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• 5.

  Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

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• 6.

  Find the domain of \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).
  

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