Maharashtra Board Class 10 Algebra Guess Paper 2027
A full practice paper on the official Algebra pattern, built from the most-likely questions by repetition analysis. Not an official or leaked paper.
Maharashtra Board Class 10 Algebra — Guess Paper 2027
Time: 2 hours · Maximum marks: 40 · Practice paper
Section 1Q1(A) MCQs (choose the correct alternative) and Q1(B) short one-mark subquestions
Q1.1 mark
One of the roots of the equation x2 + mx - 5 = 0 is 2, find the value of m. (a) -2 (b) -1/2 (c) 1/2 (d) 2
Why this question: Quadratic Equations → Find the value of an unknown coefficient given that a value is a root of the qua — appeared 5× Board 2022Board 2024Board 2026
Q2.1 mark
From the following numbers which number cannot represent a probability ? (A) 0.6 (B) 2.0 (C) 0.15 (D) 0.75
Why this question: Probability → Identify which value cannot represent a probability — appeared 4× Board 2022Board 2024Board 2025
Q3.1 mark
To draw the graph of 4x + 5y = 19, find the value of y when x = 1. (A) 4 (B) 3 (C) 2 (D) -3
Why this question: Linear Equations in Two Variables → Find the value of one variable in a linear equation in two variables given the o — appeared 4× Board 2022Board 2023Board 2024Board 2026
Q4.1 mark
Out of the following equations which one is not a quadratic equation ? (A) x2 + 4x = 11 + x2 (B) x2 = 4x (C) 5x2 = 90 (D) 2x - x2 = x2 + 5
Why this question: Quadratic Equations → Identify which of the given equations is not a quadratic equation — appeared 3× Board 2023Board 2025Board 2026
Q5.1 mark
When two coins are tossed simultaneously, write the sample space 'S'.
Why this question: Probability → Write the sample space for a given random experiment — appeared 5× Board 2022Board 2023Board 2024Board 2025Board 2026
Q6.1 mark
If 15x + 17y = 21 and 17x + 15y = 11, then find the value of x + y.
Why this question: Linear Equations in Two Variables → Find a linear combination of variables from a pair of simultaneous equations — appeared 3× Board 2024Board 2025Board 2026
Q7.1 mark
Find the first term and common difference of the given A.P. 5, 1, -3, -7, ......
Why this question: Arithmetic Progression → Find the first term and common difference of a given A.P. — appeared 2× Board 2024Board 2026
Q8.1 mark
Face value of one share is `100 and premium is `10. Find the market value of the share.
Why this question: Financial Planning → Find the market value of a share given face value and premium — appeared 2× Board 2024Board 2025
Section 2Q2(A) complete-the-activity (any two of three) and Q2(B) two-mark subquestions (any four of five)
Q9.2 marks
Solve the following quadratic equation by factorisation method: 25m2 = 9.
Why this question: Quadratic Equations → Solve a quadratic equation by factorisation — appeared 6× Board 2022Board 2024Board 2025Board 2026
Q10.2 marks
Solve the following simultaneous equations: 5x + 3y = 9; 2x - 3y = 12.
Why this question: Linear Equations in Two Variables → Solve a pair of simultaneous linear equations — appeared 5× Board 2023Board 2024Board 2025Board 2026
Q11.2 marks
Complete the following table to draw the graph of the equation x - y = 1 (find missing x, y and (x, y) values).
Why this question: Linear Equations in Two Variables → Complete a table of values for drawing the graph of a linear equation — appeared 4× Board 2024Board 2025Board 2026
Q12.2 marks
Given A.P. is 12, 16, 20, 24, ................. Find the 24th term of this progression.
Why this question: Arithmetic Progression → Find the nth term of a given A.P. — appeared 4× Board 2024Board 2025Board 2026
Q13.2 marks
Form the quadratic equation whose roots are 3 and -10.
Why this question: Quadratic Equations → Form a quadratic equation given its two roots — appeared 3× Board 2024Board 2025Board 2026
Q14.2 marks
If one die is rolled, complete the activity to find the probability of the event that the number on the upper face is prime.
Why this question: Probability → Complete an activity to find the probability of an event when a die is rolled — appeared 3× Board 2022Board 2024Board 2026
Section 3Q3(A) three-mark activity (any one of two) and Q3(B) three-mark subquestions (any two of four)
Q15.3 marks
Solve the following quadratic equation by formula method: x2 - 3x - 2 = 0.
Why this question: Quadratic Equations → Solve a quadratic equation by the formula method — appeared 6× Board 2022Board 2023Board 2024Board 2025Board 2026
Q16.3 marks
Solve the following simultaneous equations by Cramer's rule: x + 2y = -1; 2x - 3y = 12.
Why this question: Linear Equations in Two Variables → Solve simultaneous equations using Cramer's rule — appeared 5× Board 2023Board 2024Board 2025Board 2026
Q17.3 marks
The table shows the funds collected by 105 students for flood affected people (classes 10-20 ... 70-80). Find the median of the data.
Why this question: Statistics → Find the median of given grouped frequency data — appeared 4× Board 2023Board 2025Board 2026
Section 4Q4 four-mark problems (any two of three)
Q18.4 marks
Draw a histogram of the following data: Height of Students (cm) 135-140, 140-145, 145-150, 150-155 with number of students 4, 12, 16, 8.
Why this question: Statistics → Draw a histogram for given grouped data — appeared 3× Board 2024Board 2025Board 2026
Q19.4 marks
Two numbers differ by 3. The sum of twice the smaller number and thrice the greater number is 19. Find the numbers.
Why this question: Linear Equations in Two Variables → Solve a word problem reducing to simultaneous linear equations — appeared 2× Board 2025Board 2026
Section 5Q5 three-mark challenge problem (any one of two)
Q20.3 marks
A two digit number is formed using digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is (a) an odd number (b) a multiple of 5 ?
Why this question: Probability → Find the probability of events when a number is formed from given digits — appeared 2× Board 2023Board 2026