CBSE Class 12 2026 English Core Set 2 Question Paper with Solutions (Available)

CBSE CLASS XII Questions

• 1.

  Arora and Gurmeet were partners in a firm sharing profits and losses in the ratio of 3 : 2. Starting from 1st October, 2024 Arora withdrew ₹ 30,000 at the beginning of each quarter for his personal use. Interest on drawings was to be charged @ 12% per annum. Interest on Arora's drawings for the year ended 31st March, 2025 was:

  • ₹ 1,800
    
  • ₹ 2,700
    
  • ₹ 450
    
  • ₹ 3,600
    
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• 2.

  Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]

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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.

  In a Young's double-slit experiment, two waves each of intensity I superpose each other and produce an interference pattern. Prove that the resultant intensities at maxima and minima are 4I and zero respectively.
  

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• 5.

  If \[ P = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix} \quad \text{and} \quad Q = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 1 & -1 & 5 \end{bmatrix} \] find \( QP \) and hence solve the following system of equations using matrix method:
  \[ x - y = 3,\quad 2x + 3y + 4z = 13,\quad y + 2z = 7 \]

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• 6.

  A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
  
  (i) Express \(y\) as a function of \(x\) from the given equation of ellipse. 
  (ii) Integrate the function obtained in (i) with respect to \(x\). 
  (iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration. 
  OR 
  (iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\). 
   

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