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Maharashtra SSC Class 10 Algebra July 2025 question paper

Maximum marks 40 · Time 2 hours

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Q.1 (A)

1 mark each

  1. Q.1 (A) (i)1 mark
    The value of determinant ∣53−7−4∣\begin{vmatrix} 5 & 3 \\ -7 & -4 \end{vmatrix} is ____.

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  2. Q.1 (A) (ii)1 mark
    Out of the following equations which one is not a quadratic equation?

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  3. Q.1 (A) (iii)1 mark
    For given A.P. a=3.5a = 3.5, d=0d = 0, then t2=t_2 = ____.

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  4. Q.1 (A) (iv)1 mark
    From the following numbers which number cannot represent a probability?

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Q.1 (B)

1 mark each

  1. Q.1 (B) (i)1 mark
    For simultaneous equations in variables xx and yy, Dx=49D_x = 49, Dy=−63D_y = -63, D=7D = 7, then find the value of xx.
  2. Q.1 (B) (ii)1 mark
    Write the following quadratic equation in standard form: 2y=10−y22y = 10 - y^2.
  3. Q.1 (B) (iii)1 mark
    Face value of one share is ₹100 and premium is ₹10. Find the market value of the share.
  4. Q.1 (B) (iv)1 mark
    Find the class mark of the class 6–10.

Q.2 (A)

2 marks each · attempt any 2

  1. Q.2 (A) (i)2 marks
    Complete the following activity to solve the quadratic equation x2+8x−48=0x^2 + 8x - 48 = 0 by completing square method.
  2. Q.2 (A) (ii)2 marks
    Courier service agent charged total ₹590 to courier a parcel from Nashik to Nagpur. In the tax invoice taxable value is ₹500 on which CGST is ₹45 and SGST is ₹45. Complete the following activity to find the rate of GST charged for this service.
  3. Q.2 (A) (iii)2 marks
    The monthly expenditure of a family on different items is shown in the following table. Complete the following activity to calculate the related central angles.
    Different itemsPercentage of expenditure
    Food40
    Clothing20
    Education30
    Other expenditure10
    Total100

Q.2 (B)

2 marks each · attempt any 4

  1. Q.2 (B) (i)2 marks
    Find the values of (x+y)(x + y) and (x−y)(x - y) of the following given simultaneous equations: 101x+99y=501101x + 99y = 501; 99x+101y=49999x + 101y = 499.
  2. Q.2 (B) (ii)2 marks
    Solve the following quadratic equation by factorisation method: x2−15x+54=0x^2 - 15x + 54 = 0.
  3. Q.2 (B) (iii)2 marks
    Which term of the following A.P. is 560? 2,11,20,29,…2, 11, 20, 29, \ldots
  4. Q.2 (B) (iv)2 marks
    Market value of a share is ₹200. If the brokerage rate is 0.3%, then find the purchase value of the share.
  5. Q.2 (B) (v)2 marks
    If ∑fidi=10,000\sum f_i d_i = 10{,}000, ∑fi=100\sum f_i = 100 and A=2000A = 2000, then find mean (xˉ)(\bar{x}).

Q.3 (A)

3 marks each · attempt any 1

  1. Q.3 (A) (i)3 marks
    In an A.P. sum of three consecutive terms is 27 and their product is 504. Complete the following activity to find the terms.
  2. Q.3 (A) (ii)3 marks
    A card is drawn from a well shuffled pack of 52 playing cards. Complete the following activity to find the probability of the following events: (a) A red card (b) A face card.

Q.3 (B)

3 marks each · attempt any 2

  1. Q.3 (B) (i)3 marks
    In the following table the yearly investment made by 210 families is given. From this information draw the histogram.
    Investment (Thousand Rupees)Number of families
    10–2030
    20–3050
    30–4060
    40–5055
    50–6015
  2. Q.3 (B) (ii)3 marks
    Shri Shivajirao has purchased 150 shares of F.V. ₹100, for M.V. of ₹120. Company has paid 7% dividend. Find the rate of return on his investment.
  3. Q.3 (B) (iii)3 marks
    Product of Shraddha's age 2 years ago and 3 years hence is 84. Find her present age.
  4. Q.3 (B) (iv)3 marks
    Solve the following simultaneous equations graphically: x+y=6x + y = 6, x−y=4x - y = 4.

Q.4

4 marks each · attempt any 2

  1. Q.4 (i)4 marks
    In an agriculture field the ratio of salary of skilled and unskilled workers is 5 : 4. Total salary of one day of both of them is ₹900. Find daily wages of skilled and unskilled workers.
  2. Q.4 (ii)4 marks
    Two dice are thrown. Find the probability of the following events: (a) Event A: The sum of the numbers on their upper faces is at least 9. (b) Event B: The sum of the numbers on their upper faces is divisible by 5. (c) Event C: The number on the upper face of the first die is greater than the number on the upper face of the second die.
  3. Q.4 (iii)4 marks
    In the following frequency distribution table ages of 300 patients and number of patients in a hospital is given. Find the median age of the patients.
    Age (In years)Number of patients
    10–2060
    20–3042
    30–4055
    40–5070
    50–6053
    60–7020

Q.5

3 marks each · attempt any 1

  1. Q.5 (i)3 marks
    Three conditions are given below. Write the quadratic equation for each of them satisfy that condition: (a) If discriminant Δ=0\Delta = 0 (b) If discriminant Δ>0\Delta > 0 (c) If discriminant Δ<0\Delta < 0
  2. Q.5 (ii)3 marks
    If first term of an A.P. is 'p', second term is 'q' and last term is 'r', then show that the sum of all terms is (p+r)(q+r−2p)2(q−p)\dfrac{(p + r)(q + r - 2p)}{2(q - p)}.