Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Determinants · Long Answer3 Marksmatrix_method_applications

Class 12 Maths · Determinants · Long Answer #93

Typing 10 English pages and 3 Hindi pages costs ₹145; typing 3 English and 10 Hindi pages costs ₹180. Using matrices, find the cost per page in each language.

✅ Step-by-Step Solution

Final Answer: English ₹10/page; Hindi ₹15/page.
  1. Let per-page costs be x,y. Then [[10,3],[3,10]][x,y]ᵀ=[145,180]ᵀ.
  2. The determinant is 100−9=91≠0 and the inverse is (1/91)[[10,−3],[−3,10]].
  3. Multiply by the right side: (1/91)[1450−540,−435+1800]ᵀ=[10,15]ᵀ.
  4. Thus the English and Hindi per-page costs are ₹10 and ₹15 respectively.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Let per-page costs be x,y. Then [[10,3],[3,10]][x,y]ᵀ=[145,180]ᵀ.
  • [1 mark] The determinant is 100−9=91≠0 and the inverse is (1/91)[[10,−3],[−3,10]].
  • [1 mark] Multiply by the right side: (1/91)[1450−540,−435+1800]ᵀ=[10,15]ᵀ.
  • [0.5 marks] Thus the English and Hindi per-page costs are ₹10 and ₹15 respectively.

Master Chapter 4: Determinants

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Determinants.
📘 Chapter Notes & All Exercises 🚀 Open in Interactive Workspace →
← Previous Question
Prove the points A(a,b+c),B(b,c+a),C(c,a+b) are collinear.
Next Question →
For real square matrices A,B of the same order, prove…

More Practice Questions in Determinants

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38Q39Q40

Related Questions in Determinants

Class 12 Determinants · Mcq Single Correct
If \(\begin{vmatrix}2 & 4\\5 & 1\end{vmatrix}\)=\(\begin{vmatrix}2x & 4\\6 &…
Class 12 Determinants · Mcq Single Correct
The area of the triangle with vertices (−3,0),(3,0),(0,k) is 9 square units. Find k.
Class 12 Determinants · Mcq Single Correct
Let f(x)=\(\begin{vmatrix}0 & x−a & x−b\\x+a & 0 & x−c\\x+b & x+c & 0\end{vmatrix}\). Which…
Class 12 Determinants · Mcq Single Correct
If \(\begin{vmatrix}2 & 3 & 2\\x & x & x\\4 & 9 & 1\end{vmatrix}\)+3=0, find x.
Class 12 Determinants · Mcq Single Correct
If x=−4 is a root of \(\begin{vmatrix}x & 2 & 3\\1 & x & 1\\3 & 2 & x\end{vmatrix}\)=0, find…
Class 12 Determinants · Mcq Single Correct
For a 3×3 real matrix A, det(Aᵀ)=−3. Find det(AAᵀ).