PSEB CLASS 10 MATHEMATICS SEPTEMBER SAMPLE PAPER SET 1 ( ENGLISH MEDIUM)

 

Class 10th (Mathematics)

September Exam 2026-27 M.M. 80

Section A(1 Marks) — 20 × 1 = 20

1. Choose the correct option:

1. 5ⁿ, where n is a natural number, end with the digit:
   A) 0 B) 5 C) 2 D) 9
2. If L.C.M. of two prime number p and q(p > q) is 22, then the value of 3p − q is:
   A) 4 B) 28 C) 38 D) 48
3. The product of a non-zero rational and an irrational number is:
   A) Always irrational B) Always Rational C) Rational or irrational D) None of these
4. The graph of the quadratic polynomial ax² + bx + c is always:
   A) Straight line B) Curve C) Parabola D) None of these
5. If α and β are the zeroes of x² − 8x + 12, then α + β equals:
   A) 12 B) 8 C) -8 D) -12
6. The value of c for which the system of linear equations 2x + cy − 7 = 0 and 4x + 6y − 11 = 0 has no solution:
   A) 3 B) -3 C) 2 D) -2
7. One equation of a pair of coincident linear equations is 3x − 4y + 5 = 0, the second equation can be:
   A) 6x + 8y − 10 = 0 B) -6x − 8y + 10 = 0 C) -6x + 8y − 10 = 0 D) 6x − 8y + 10 = 0
8. The pair of equations y = 0 and y = -7 has:
   A) One solution B) Two solutions C) Infinitely many solution D) No solution
9. Which of following is not a quadratic equation?
   A) x + ¹/_x = 4 B) x² + ¹/_x = 4 C) x² − 5x + 6 = 0 D) 2x² − 4 = x² − 7
10. If the discriminant of a quadratic equation is positive and non-zero, then the equation has:
    A) Two distinct real roots B) Two equal real roots C) No real roots D) One real root
11. In an A.P. T₁ + T₂₄ = 100, then what is the value of T₂ + T₂₃?
    A) 300 B) 200 C) 100 D) -100
12. Common difference of A.P. -17, -10, -3, ... is:
    A) 7 B) -7 C) -17 D) None of these
13. If ΔABC ~ ΔDEF, then which of following is not true?
    A) AB/DE = BC/EF B) ∠C = ∠F C) AC/DF = BC/DE D) All of these are true
14. Two triangular flags are similar. The first has sides 4, 5 and 6. If the longest side of the second flag is 18, what is its shortest side?
    A) 12 B) 10 C) 15 D) 8
15. In a frequency distribution, the class marks of a class interval is 32 and the class width is 10. What is the lower limit of the class?
    A) 37 B) 35.5 C) 27 D) 29.5
16. Class size of 50-100 is:
    A) 50 B) 100 C) 75 D) None of these
17. Relationship between mean, median and mode is:
    A) Mode = 3 Median − 2 Mean B) Mode = 2 Median − 3 Mean C) Mode = 3 Median + 2 Mean D) Mode = 2 Median − Mean
18. What is probability of getting 53 Mondays in a leap year?
    A) ¹/₇ B) ²/₇ C) ³/₇ D) 0
19. Which of following cannot be the probability of an event?
    A) 1 B) ²/₃ C) ³/₂ D) 0
20. The probability of a certain event is:
    A) 0 B) 1 C) 1½ D) between 0 and 1

Section B(2 Marks)

2. 2. Two numbers are in ratio 4:5. If their H.C.F is 18 then find L.C.M of the numbers.
3. 3. Find a quadratic polynomial with √2 as sum and ¹/₃ as the product of its zeroes.
4. 4. How many 3 digits numbers are divisible by 9?
5. 5. Find sum of 51 terms of A.P. 10, 14, 18, 22,........
6. 6. In the given figure, DE||BC if AD = x, DB = x − 2, AE = x + 2, EC = x − 1, Find the value of x. 

   

   
   
   
   
7. 7. A number is selected at random from the integers between 0 and 50. Find the probability that the selected number is a) multiple of 5 b) not a multiple of 5.
8. 8. One card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting i) a red face card ii) black card of queen

Section: C(4 Marks)

9. 9. Solve the following pair of linear equations 3x − 5y = 4 and 9x − 2y = 7
10. 10. Is it possible to design a rectangular park of perimeter 80m and the area 400m²? If so, find its length and breadth.
    OR
    The product of two consecutive multiples of 5 is 750. Form the quadratic equation and find the two multiples.
11. 11. Find the nature of roots of the quadratic equation 3x² − 5x + 2 = 0 If real roots exists, find them.
12. 12. Find two consecutive positive integers sum of whose squares is 365.
13. 13. How many terms of A.P 3, 5, 7, 9 ... must be added to get the sum 99?
    OR
    Which term of A.P 3, 15, 27, 39... will be 132 more than its 54th term?
14. 14. Find 31st term of an A.P whose 11th term is 38 and 16th term is 73.
15. 15. Find three consecutive terms in A.P whose sum is 21 and product is 231.
    OR
    Find the sum 34 + 32 + 30 + ..... + 10

Section: D(6 Marks)

16. 16. Check whether the pair of equations 2x + y − 6 = 0 and 4x − 2y − 4 = 0 is consistent. If so solve graphically.
    OR
    The sum of present ages of a father and his son is 50 years. Five years ago, the father's age was 7 times the age of son. Find their present age.
17. 17. a) In a triangle, a line drawn parallel to one side to intersect the other sides in distinct points divides the two sides in the same ratio. Prove it.
    b) In fig, if PQ || RS, prove that ΔPOQ ~ ΔSOR 
    
    
    OR
    The diagonals of a quadrilateral ABCD intersect each other at the point O such that ^AO/_BO = ^CO/_DO. Show that ABCD is a trapezium.

16. 18. Find the mode of data given below :-

    Age (in years)	5-15	15-25	25-35	35-45	45-55	55-65
    No. of Patients	6	11	21	23	14	5

    OR
    Find the median weight of following students :-

    Weight (in kg)	40-45	45-50	50-55	55-60	60-65	65-70	70-75
    No. of Students	2	3	8	6	6	3	2

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