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Maharashtra SSC Class 10 Algebra March 2020 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
    In the format of GSTIN there are _______ alpha-numerals.

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  2. Q.1 (A) (ii)1 mark
    From the following equations, which one is the quadratic equation?

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  3. Q.1 (A) (iii)1 mark
    For simultaneous equations in variables xx and yy, if Dx=49D_x = 49, Dy=−63D_y = -63, D=7D = 7, then what is the value of xx?

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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 second and third term of an A.P. whose first term is −2-2 and common difference is −2-2.
  2. Q.1 (B) (ii)1 mark
    'Pawan Medicals' supplies medicines. On some medicines the rate of GST is 12%, then what is the rate of CGST and SGST?
  3. Q.1 (B) (iii)1 mark
    Find the values of aa and bb from the quadratic equation 2x2−5x+7=02x^{2} - 5x + 7 = 0.
  4. Q.1 (B) (iv)1 mark
    If 15x+17y=2115x + 17y = 21 and 17x+15y=1117x + 15y = 11, then find the value of x+yx + y.

Q.2 (A)

2 marks each · attempt any 2

  1. Q.2 (A) (i)2 marks
    Complete the following table to draw the graph of 2x−6y=32x - 6y = 3:
    xx−5-5
    yy00
    (x,y)(x, y)
  2. Q.2 (A) (ii)2 marks
    First term and common difference of an A.P. are 6 and 3 respectively. Find S27S_{27}.
  3. Q.2 (A) (iii)2 marks
    A card is drawn from a well shuffled pack of 52 playing cards. Find the probability of the event that the card drawn is a red card.

Q.2 (B)

2 marks each · attempt any 4

  1. Q.2 (B) (i)2 marks
    Find the value of the determinant: ∣73533212∣\begin{vmatrix} \frac{7}{3} & \frac{5}{3} \\ \frac{3}{2} & \frac{1}{2} \end{vmatrix}
  2. Q.2 (B) (ii)2 marks
    Solve the quadratic equation by factorisation method: x2−15x+54=0x^{2} - 15x + 54 = 0
  3. Q.2 (B) (iii)2 marks
    Decide whether the following sequence is an A.P. If so, find the 20th term of the progression: −12,−5,2,9,16,23,30,…-12, -5, 2, 9, 16, 23, 30, \ldots
  4. Q.2 (B) (iv)2 marks
    A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is an odd number?
  5. Q.2 (B) (v)2 marks
    If L=10L = 10, f1=70f_1 = 70, f0=58f_0 = 58, f2=42f_2 = 42, h=2h = 2, then find the mode by using formula.

Q.3 (A)

3 marks each · attempt any 1

  1. Q.3 (A) (i)3 marks
    Complete the following activity to find the measures of the central angles for drawing a pie diagram of the given data (Total number of persons = 200; measure of central angle =No. of persons200×360= \dfrac{\text{No. of persons}}{200} \times 360):
    Age group (in years)No. of PersonsMeasure of central angle
    20 - 258080200×360\frac{80}{200} \times 360
    25 - 306060200×360\frac{60}{200} \times 360
    30 - 353535200×360=63∘\frac{35}{200} \times 360 = 63^\circ
    35 - 402525200×360\frac{25}{200} \times 360
    Total200
  2. Q.3 (A) (ii)3 marks
    Shri Shantilal has purchased 150 shares of FV Rs. 100\text{Rs.}\,100, for MV of Rs. 120\text{Rs.}\,120. The company has paid dividend at 7%. Find the rate of return on his investment.

Q.3 (B)

3 marks each · attempt any 2

  1. Q.3 (B) (i)3 marks
    A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets: (1) a red balloon, (2) a blue balloon?
  2. Q.3 (B) (ii)3 marks
    The denominator of a fraction is 4 more than twice its numerator. The denominator becomes 12 times the numerator, if both the numerator and the denominator are reduced by 6. Find the fraction.
  3. Q.3 (B) (iii)3 marks
    A milk centre sold milk to 50 customers. The table below gives the number of customers and the milk they purchased. Find the mean of the milk sold by the direct method:
    Milk Sold (litre)No. of Customers
    1 - 217
    2 - 313
    3 - 410
    4 - 57
    5 - 63
  4. Q.3 (B) (iv)3 marks
    In an A.P. the sum of three consecutive terms is 27 and their product is 504. Find the terms. (Assume that the three consecutive terms in an A.P. are a−d, a, a+da - d,\ a,\ a + d.)

Q.4

4 marks each · attempt any 2

  1. Q.4 (i)4 marks
    Represent the following data by a histogram:
    Price of Sugar (per kg in Rs.\text{Rs.})Number of Weeks
    18 - 204
    20 - 228
    22 - 2422
    24 - 2612
    26 - 286
    28 - 308
  2. Q.4 (ii)4 marks
    One person borrows Rs. 4,000\text{Rs.}\,4{,}000 and agrees to repay it with a total interest of Rs. 500\text{Rs.}\,500 in 10 instalments, each instalment being less than the preceding instalment by Rs. 10\text{Rs.}\,10. What should be the first and the last instalments?
  3. Q.4 (iii)4 marks
    The sum of the areas of two squares is 400 sq.m. If the difference between their perimeters is 16 m, find the sides of the two squares.

Q.5

3 marks each · attempt any 1

  1. Q.5 (i)3 marks
    Convert the following equations into simultaneous equations and solve: xy=4,1x+1y=1xy\sqrt{\dfrac{x}{y}} = 4,\quad \dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{xy}
  2. Q.5 (ii)3 marks
    A dealer sells a toy for Rs. 24\text{Rs.}\,24 and gains as much percent as the cost price of the toy. Find the cost price of the toy.