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Maharashtra SSC Class 10 Algebra March 2022 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. Four alternative answers are given for every subquestion. Choose the correct alternative and write its alphabet with subquestion number.
    Q.1 (A) (i)1 mark
    Which one is the quadratic equation?

    Tap an option to check your answer.

  2. Q.1 (A) (ii)1 mark
    First four terms of an A.P. are ________, whose first term is −2-2 and common difference is −2-2.

    Tap an option to check your answer.

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

    Tap an option to check your answer.

  4. Q.1 (A) (iv)1 mark
    Which number cannot represent a probability?

    Tap an option to check your answer.

Q.1 (B)

1 mark each

  1. Solve the following subquestions:
    Q.1 (B) (i)1 mark
    To draw a graph of 4x+5y=194x + 5y = 19, find yy when x=1x = 1.
  2. Q.1 (B) (ii)1 mark
    Determine whether 22 is a root of the quadratic equation 2m2−5m=02m^2 - 5m = 0.
  3. Q.1 (B) (iii)1 mark
    Write the second and third term of an A.P. whose first term is 66 and common difference is −3-3.
  4. Q.1 (B) (iv)1 mark
    Two coins are tossed simultaneously. Write the sample space 'S'.

Q.2 (A)

2 marks each · attempt any 2

  1. Complete the following activities and rewrite it (any two):
    Q.2 (A) (i)2 marks
    Find the value of the determinant ∣239233∣\begin{vmatrix} 2\sqrt{3} & 9 \\ 2 & 3\sqrt{3} \end{vmatrix}.
  2. Q.2 (A) (ii)2 marks
    Find the 19th term of the A.P. 7, 13, 19, 25, …7,\ 13,\ 19,\ 25,\ \ldots
  3. Q.2 (A) (iii)2 marks
    If one die is rolled, find the probability of the event of getting a prime number on the upper face.

Q.2 (B)

2 marks each · attempt any 4

  1. Solve the following subquestions (any four):
    Q.2 (B) (i)2 marks
    To solve the following simultaneous equations by Cramer's rule, find the value of DxD_x and DyD_y. 3x+5y=263x + 5y = 26 x+5y=22x + 5y = 22
  2. Q.2 (B) (ii)2 marks
    A box contains 5 red, 8 blue and 3 green pens. Rutuja wants to pick a pen at random. What is the probability that the pen is blue?
  3. Q.2 (B) (iii)2 marks
    Find the sum of the first 'n' even natural numbers.
  4. Q.2 (B) (iv)2 marks
    Solve the following quadratic equation by factorisation method: x2+x−20=0x^2 + x - 20 = 0.
  5. Q.2 (B) (v)2 marks
    Find the values of (x+y)(x + y) and (x−y)(x - y) of the following simultaneous equations: 49x−57y=17249x - 57y = 172 57x−49y=25257x - 49y = 252

Q.3 (A)

3 marks each · attempt any 1

  1. Complete the following activity and rewrite it (any one):
    Q.3 (A) (i)3 marks
    One of the roots of the equation kx2−10x+3=0kx^2 - 10x + 3 = 0 is 33. Find the value of kk.
  2. Q.3 (A) (ii)3 marks
    A card is drawn at random from a pack of well shuffled 52 playing cards. Find the probability that the card drawn is (A) an ace, (B) a spade.

Q.3 (B)

3 marks each · attempt any 2

  1. Solve the following subquestions (any two):
    Q.3 (B) (i)3 marks
    Solve the simultaneous equations by using the graphical method: x+3y=7x + 3y = 7 2x+y=−12x + y = -1
  2. Q.3 (B) (ii)3 marks
    There is an auditorium with 27 rows of seats. There are 20 seats in the first row, 22 seats in the second row, 24 seats in the third row and so on. Find how many total seats are there in the auditorium.
  3. Q.3 (B) (iii)3 marks
    Sum of the present ages of Manish and Savita is 31 years. Manish's age 3 years ago was 4 times the age of Savita at that time. Find their present ages.
  4. Q.3 (B) (iv)3 marks
    Solve the following quadratic equation using the formula: x2+10x+2=0x^2 + 10x + 2 = 0.

Q.4

4 marks each · attempt any 2

  1. Solve the following subquestions (any two):
    Q.4 (i)4 marks
    If 460 is divided by a natural number, then the quotient is 2 more than nine times the divisor and the remainder is 5. Find the quotient and the divisor.
  2. Q.4 (ii)4 marks
    If the 9th term of an A.P. is zero, then prove that the 29th term is double the 19th term.
  3. Q.4 (iii)4 marks
    The perimeter of an isosceles triangle is 24 cm. The length of its congruent sides is 13 cm less than twice the length of its base. Find the lengths of all sides of the triangle.

Q.5

3 marks each · attempt any 1

  1. Solve the following subquestions (any one):
    Q.5 (i)3 marks
    A bag contains 8 red and some blue balls. One ball is drawn at random from the bag. If the ratio of the probability of getting a red ball to that of getting a blue ball is 2:52 : 5, then find the number of blue balls.
  2. Q.5 (ii)3 marks
    The measures of angles of a triangle are in A.P. The measure of the smallest angle is five times the common difference. Find the measures of all angles of the triangle. (Assume the measures of angles as a, a+d, a+2da,\ a + d,\ a + 2d.)