PYQ Vault

Maharashtra SSC Class 10 Algebra March 2024 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
    If 3 is one of the roots of the quadratic equation kx2−7x+12=0kx^2 - 7x + 12 = 0, then k=k = ______

    Tap an option to check your answer.

  2. Q.1 (A) (ii)1 mark
    To draw the graph of x+2y=4x + 2y = 4, find xx when y=1y = 1:

    Tap an option to check your answer.

  3. Q.1 (A) (iii)1 mark
    For an A.P., t7=4t_7 = 4, d=−4d = -4, then a=a = ______

    Tap an option to check your answer.

  4. Q.1 (A) (iv)1 mark
    In the format of GSTIN, there are ______ alpha-numerals.

    Tap an option to check your answer.

Q.1 (B)

1 mark each

  1. Q.1 (B) (i)1 mark
    If 17x+15y=1117x + 15y = 11 and 15x+17y=2115x + 17y = 21, then find the value of x−yx - y.
  2. Q.1 (B) (ii)1 mark
    Find the first term of the sequence tn=3n−2t_n = 3n - 2.
  3. Q.1 (B) (iii)1 mark
    If the face value of a share is ₹100 and the market value is ₹150. If the rate of brokerage is 2%, find the brokerage paid on one share.
  4. Q.1 (B) (iv)1 mark
    Two digit numbers are formed using the digits 2, 3 and 5 without repeating a digit. Write the sample space.

Q.2 (A)

2 marks each · attempt any 2

  1. Q.2 (A) (i)2 marks
    If (0,2)(0, 2) is the solution of 2x+3y=k2x + 3y = k, then complete the activity to find the value of kk.
  2. Q.2 (A) (ii)2 marks
    If 2 and 5 are the roots of a quadratic equation, then complete the activity to form the quadratic equation.
  3. Q.2 (A) (iii)2 marks
    Two coins are tossed simultaneously. Complete the activity to write the sample space and the given events A and B in the set form. Event A: To get at least one head. Event B: To get no head.

Q.2 (B)

2 marks each · attempt any 4

  1. Q.2 (B) (i)2 marks
    □ABCD\square ABCD is a rectangle. Write two simultaneous equations using the information given in the diagram, in the form ax+by=cax + by = c.
  2. Q.2 (B) (ii)2 marks
    Solve the following quadratic equation using the factorisation method: x2+x−20=0x^2 + x - 20 = 0.
  3. Q.2 (B) (iii)2 marks
    Find the 19th term of the following A.P.: 7, 13, 19, 25, ...
  4. Q.2 (B) (iv)2 marks
    A card is drawn from a well shuffled pack of 52 playing cards. Find the probability that the card drawn is a face card.
  5. Q.2 (B) (v)2 marks
    The following table shows the classification of the number of workers and the number of hours they work in a software company. Prepare a 'less than' upper limit type cumulative frequency distribution table:
    Number of hours dailyNumber of workers
    8–10150
    10–12500
    12–14300
    14–1650

Q.3 (A)

3 marks each · attempt any 1

  1. Q.3 (A) (i)3 marks
    The following frequency distribution table shows the classification of the number of vehicles and the volume of petrol filled in them. Complete the activity to find the mode of the volume of petrol filled.
    Class (Petrol filled in Liters)Frequency (Number of Vehicles)
    0.5–3.533
    3.5–6.540
    6.5–9.527
    9.5–12.518
    12.5–15.512
  2. Q.3 (A) (ii)3 marks
    The total value (with GST) of a remote controlled toy car is ₹2360. The rate of GST is 18% on toys. Complete the activity to find the taxable value for the toy car.

Q.3 (B)

3 marks each · attempt any 2

  1. Q.3 (B) (i)3 marks
    Solve the following quadratic equation by the formula method: 3m2−m−10=03m^2 - m - 10 = 0.
  2. Q.3 (B) (ii)3 marks
    Solve the following simultaneous equations using Cramer's rule: 3x−4y=103x - 4y = 10, 4x+3y=54x + 3y = 5.
  3. Q.3 (B) (iii)3 marks
    50 shares of face value ₹10 were purchased for the market value of ₹25. The company declared a 30% dividend on the shares, then find: (1) Sum invested (2) Dividend received (3) Rate of return.
  4. Q.3 (B) (iv)3 marks
    One coin and a die are thrown simultaneously. Find the probability of the following events: Event A: To get a head and a prime number. Event B: To get a tail and an odd number.

Q.4

4 marks each · attempt any 2

  1. Q.4 (i)4 marks
    A tank can be filled up by two taps in 6 hours. The smaller tap alone takes 5 hours more than the bigger tap alone. Find the time required by each tap to fill the tank separately.
  2. Q.4 (ii)4 marks
    The following table shows the classification of the percentage of marks of students and the number of students. Draw the frequency polygon from the table without drawing a histogram:
    Result (Percentage)Number of Students
    20–4025
    40–6065
    60–8080
    80–10015
  3. Q.4 (iii)4 marks
    In a 'Mahila Bachat Gat', Kavita invested from the first day of the month ₹20 on the first day, ₹40 on the second day and ₹60 on the third day. If she saves like this, then what would be her total saving in the month of February 2020?

Q.5

3 marks each · attempt any 1

  1. Q.5 (i)3 marks
    In the given figure, the pie diagram represents the amount spent on different sports by a school administration in a year. If the money spent on football is ₹9,000, answer the following questions: (a) What is the total amount spent on sports? (b) What is the amount spent on cricket?
  2. Q.5 (ii)3 marks
    Draw the graph of the equation x+y=4x + y = 4 and answer the following questions: (a) Which type of triangle is formed by the line with the X and Y-axes based on its sides? (b) Find the area of that triangle.