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Maharashtra SSC Class 10 Algebra March 2023 question paper

Maximum marks 40 · Time 2 hours

Try each question first, then open its model answer. Where the paper offers a choice, both questions are shown with OR between them.

Q.1 (A)

1 mark each

  1. Q.1 (A) (i)1 mark
    To draw the graph of 4x+5y=194x + 5y = 19, find yy when x=1x = 1:

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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 the given A.P., a=3.5a = 3.5, d=0d = 0, then tn=t_n = ______

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  4. Q.1 (A) (iv)1 mark
    If n(A)=2n(A) = 2, P(A)=15P(A) = \dfrac{1}{5}, then n(S)=n(S) = ?

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Q.1 (B)

1 mark each

  1. Q.1 (B) (i)1 mark
    Find the value of the following determinant: ∣4327∣\begin{vmatrix} 4 & 3 \\ 2 & 7 \end{vmatrix}
  2. Q.1 (B) (ii)1 mark
    Find the common difference of the following A.P.: 2,4,6,8,…2, 4, 6, 8, \ldots
  3. Q.1 (B) (iii)1 mark
    On a certain article if the rate of CGST is 9%, then what is the rate of SGST?
  4. Q.1 (B) (iv)1 mark
    If one coin is tossed, write the sample space SS.

Q.2 (A)

2 marks each · attempt any 2

  1. Q.2 (A) (i)2 marks
    Complete the following activity to find the value of xx: 5x+3y=95x + 3y = 9 ...... (I) 2x−3y=122x - 3y = 12 ...... (II) Add equations (I) and (II) and hence find xx.
  2. Q.2 (A) (ii)2 marks
    Complete the following activity to determine the nature of the roots of the quadratic equation x2+2x−9=0x^2 + 2x - 9 = 0.
  3. Q.2 (A) (iii)2 marks
    Complete the following table using the given information:
    Sr. No.FVShare is atMV
    1₹100Par?
    2?Premium ₹500₹575
    3₹10?₹5
    4₹200Discount ₹50?

Q.2 (B)

2 marks each · attempt any 4

  1. Q.2 (B) (i)2 marks
    Solve the following simultaneous equations: x+y=4x + y = 4; 2x−y=22x - y = 2.
  2. Q.2 (B) (ii)2 marks
    Write the following equation in the form ax2+bx+c=0ax^2 + bx + c = 0, then write the values of aa, bb, cc: 2y=10−y22y = 10 - y^2.
  3. Q.2 (B) (iii)2 marks
    Write an A.P. whose first term is a=10a = 10 and common difference d=5d = 5.
  4. Q.2 (B) (iv)2 marks
    A courier service agent charged a total of ₹590 to courier a parcel from Nashik to Nagpur. In the tax invoice the taxable value is ₹500, on which CGST is ₹45 and SGST is ₹45. Find the rate of GST charged for this service.
  5. Q.2 (B) (v)2 marks
    Observe the following table and find the Mean (Assumed mean A=300A = 300):
    ClassClass mark xix_idi=xi−300d_i = x_i - 300Frequency fif_ifidif_i d_i
    200–240220-805-400
    240–280260-4010-400
    280–3203000150
    320–3603404012480
    360–400380808640
    Total∑fi=50\sum f_i = 50∑fidi=320\sum f_i d_i = 320

Q.3 (A)

3 marks each · attempt any 1

  1. Q.3 (A) (i)3 marks
    Form a 'Road Safety Committee' of two, from 2 boys B1,B2B_1, B_2 and 2 girls G1,G2G_1, G_2. Complete the following activity to write the sample space: (a) Committee of 2 boys (b) Committee of 2 girls (c) Committee of one boy and one girl (d) Sample space SS
  2. Q.3 (A) (ii)3 marks
    Fill in the boxes of the following sample tax invoice of services provided with the help of the given information (Food Junction, Khed-Shivapur, Pune; GSTIN 27AAAAA5555B1ZA; CGST rate 2.5% and SGST rate 2.5% on each item):
    SACFood ItemsQtyRate (₹)Taxable amountCGST %CGSTSGST %SGST
    9963Coffee12020.002.5%₹0.502.5%?
    9963Masala Tea11010.00?₹0.252.5%?
    9963Masala Dosa260?2.5%?2.5%₹3.00
    Total150.00?₹3.75
    Grand Total == ₹157.50.

Q.3 (B)

3 marks each · attempt any 2

  1. Q.3 (B) (i)3 marks
    Solve the following simultaneous equations using Cramer's rule: 4m+6n=544m + 6n = 54; 3m+2n=283m + 2n = 28.
  2. Q.3 (B) (ii)3 marks
    Solve the following quadratic equation by the formula method: x2+10x+2=0x^2 + 10x + 2 = 0.
  3. Q.3 (B) (iii)3 marks
    A two digit number is formed with the digits 2, 3, 5, 7, 9 without repetition. What is the probability of the following events? Event A: The number formed is an odd number. Event B: The number formed is a multiple of 5.
  4. Q.3 (B) (iv)3 marks
    The frequency distribution table shows the number of mango trees in a grove and their yield of mangoes. Find the median of the data:
    No. of MangoesNo. of Trees
    50–10033
    100–15030
    150–20090
    200–25080
    250–30017

Q.4

4 marks each · attempt any 2

  1. Q.4 (i)4 marks
    If the first term of an A.P. is pp, the second term is qq and the last term is rr, then show that the sum of all the terms is (q+r−2p)×(p+r)2(q−p)(q + r - 2p) \times \dfrac{(p + r)}{2(q - p)}.
  2. Q.4 (ii)4 marks
    Show the following data by a frequency polygon:
    Electricity bill (₹)Families
    200–400240
    400–600300
    600–800450
    800–1000350
    1000–1200160
  3. Q.4 (iii)4 marks
    The sum of the squares of five consecutive natural numbers is 1455. Find the numbers.

Q.5

3 marks each · attempt any 1

  1. Q.5 (i)3 marks
    Draw the graph of the equation x+2y=4x + 2y = 4. Find the area of the triangle formed by the line intersecting the X-axis and the Y-axis.
  2. Q.5 (ii)3 marks
    A survey was conducted for 180 people in a city. 70 ate pizza, 60 ate burgers and 50 ate chips. Draw a pie diagram for the given information.