About this HOTS set
Students call the most important, most-likely-to-come questions of a chapter its HOTS or IMP questions. This page collects them for Linear Equations in Two Variables (Maharashtra SSC Class 10 Algebra) for the 2027 board exam. Part 1 has the questions the board has actually repeated in its recent papers; Part 2 has new questions in the same board style, covering the patterns that keep coming back and the parts of the chapter not yet asked, with a few harder thinking-type questions.
The board questions are taken from the official MSBSHSE SSC Algebra question papers of March 2024, July 2024, March 2025, July 2025, March 2026 and June 2026. All step-by-step answers and all the new questions are written by Doubtly.
Marks from this chapter in recent board papers
| Board paper | Marks (including internal options) |
|---|---|
| March 2024 | 12 |
| July 2024 | 12 |
| March 2025 | 12 |
| July 2025 | 11 |
| March 2026 | 12 |
| June 2026 | 12 |
Question types that repeat most
- Cramer’s rule: finding \(D\), \(D_x\), \(D_y\) and the 3-mark “solve by Cramer’s rule” sum (in 4 of the 6 papers).
- 1-mark determinant value, or \(x = \dfrac{D_x}{D}\) from given values.
- Equations with swapped coefficients (like \(17x + 15y\) and \(15x + 17y\)): add and subtract to get \(x + y\) and \(x - y\).
- Completing a table of points to draw the graph of a line (almost every paper), and graph questions on the area of the triangle formed with an axis.
- Simple 2-mark “solve the simultaneous equations” and word problems on numbers, groups, wages and rectangles.
Exam tips
- In determinants, write each product in brackets first, e.g. \((5)(1) - (-2)(-3)\); most lost marks come from sign mistakes.
- Always number your equations (I), (II) and check your answer in both equations; it takes 20 seconds.
- For graphs, plot at least three points per line, label each line, and read the intersection point clearly.
- In word problems, write “Let … be \(x\) and … be \(y\)” first; method marks are given for forming the equations correctly.