Maharashtra SSC Class 10 Algebra March 2016 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
1 mark each · attempt any 5
- Q.1 (i)1 markWrite the first two terms of the sequence whose nth term is .
- Q.1 (ii)1 markFind the value of , , in the following quadratic equation: .
- Q.1 (iii)1 markWrite the quadratic equation whose roots are and .
- Q.1 (iv)1 markFind the value of determinant .
- Q.1 (v)1 markWrite the sample space for selecting a day randomly of the week.
- Q.1 (vi)1 markFind the class mark of the classes 20-30 and 30-40.
Q.2
2 marks each · attempt any 4
- Q.2 (i)2 marksWrite the first three terms of the A.P. whose common difference is and first term is .
- Q.2 (ii)2 marksSolve the following quadratic equation by Factorisation method: .
- Q.2 (iii)2 marksIf the value of determinant is , find the value of .
- Q.2 (iv)2 marksA die is thrown, then find the probability of the following events: A is an Event: getting an odd number on the upper surface of the die. B is an Event: getting a perfect square on the upper surface of the die.
- Q.2 (v)2 marksBelow is the given frequency distribution of words in an essay. Find the mean number of words written.
Number of Words Number of Candidates 600 - 800 8 800 - 1000 22 1000 - 1200 40 1200 - 1400 18 1400 - 1600 12 - Q.2 (vi)2 marksSubjectwise marks obtained by a student in an examination are given below. Draw pie diagram.
Subject Marks Marathi 85 Hindi 85 Science 90 Mathematics 100 Total 360
Q.3
3 marks each · attempt any 3
- Q.3 (i)3 marksSolve the following quadratic equation by using formula method: .
- Q.3 (ii)3 marksThere are three boys and two girls. A committee of two is to be formed. Find the probability of the following events: Event A: The committee contains at least one girl. Event B: The committee contains one boy and one girl.
- Q.3 (iii)3 marksThe measurements (in mm) of the diameters of the head of the screws are given below. Calculate the mean diameter of the head of a screw by 'Assumed Mean Method'.
Diameter (in mm) No. of Screws 33 - 35 10 36 - 38 19 39 - 41 23 42 - 44 21 45 - 47 27 - Q.3 (iv)3 marksThe marks scored by students in Mathematics in a certain Examination are given below. Draw histogram for the above data.
Marks Scored Number of Students 0 - 20 3 20 - 40 8 40 - 60 19 60 - 80 18 80 - 100 6 - Q.3 (v)3 marksDraw the frequency polygon for the following frequency distribution:
Rainfall (in cm) No. of Years 20 - 25 2 25 - 30 5 30 - 35 8 35 - 40 12 40 - 45 10 45 - 50 7
Q.4
4 marks each · attempt any 2
- Q.4 (i)4 marksThe term and the term of an A.P. are and respectively, then find: (a) The first term and common difference (b) The term (c) '' such that
- Q.4 (ii)4 marksSolve the following simultaneous equations: , .
- Q.4 (iii)4 marksIn a certain race, there are three boys A, B, C. The winning probability of A is twice than B and the winning probability of B is twice than C. If , then find the probability of win for each boy.
Q.5
5 marks each · attempt any 2
- Q.5 (i)5 marksThe divisor and quotient of the number are same and the remainder is half the divisor. Find the divisor.
- Q.5 (ii)5 marksFind the sum of all numbers from to which are divisible by . Hence find the term of that A.P.
- Q.5 (iii)5 marksA three digit number is equal to times the sum of its digits. If is added to the number, the digits are interchanged. The addition of first and third digit is less than middle digit. Find the number.