Maharashtra SSC Class 10 Algebra March 2017 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 markState whether the following sequence is an Arithmetic Progression or not:
- Q.1 (ii)1 markIf one root of the quadratic equation is , then write another root of the equation.
- Q.1 (iii)1 markThere are 15 tickets bearing the numbers from 1 to 15 in a bag and one ticket is drawn from this bag at random. Write the sample space (S) and n(S).
- Q.1 (iv)1 markFind the class mark of the class 35-39.
- Q.1 (v)1 markWrite the next two terms of the A.P. whose first term is 3 and the common difference is 4.
- Q.1 (vi)1 markFind the values of for the quadratic equation by comparing with the standard form .
Q.2
2 marks each · attempt any 4
- Q.2 (i)2 marksFind the first two terms of the sequence for which is given below: .
- Q.2 (ii)2 marksFind the value of discriminant for the quadratic equation .
- Q.2 (iii)2 marksWrite the equation of the X-axis. Hence find the point of intersection of the graph of the equation with the X-axis.
- Q.2 (iv)2 marksFor a certain frequency distribution the values of Assumed mean , and . Find the value of mean .
- Q.2 (v)2 marksTwo coins are tossed simultaneously. Write the sample space (S), n(S), the following event A using set notation and n(A), where 'A' is the event of getting at the most one tail.
- Q.2 (vi)2 marksFind the value of k for which the given simultaneous equations have infinitely many solutions: and .
Q.3
3 marks each · attempt any 3
- Q.3 (i)3 marksHow many three digit natural numbers are divisible by 2?
- Q.3 (ii)3 marksSolve the following quadratic equation by factorization method: .
- Q.3 (iii)3 marksSolve the following simultaneous equations by using Cramer's rule: ; .
- Q.3 (iv)3 marksThe following is the frequency distribution of waiting time at an ATM centre; draw a histogram to represent the data:
Waiting time (in seconds) Number of Customers 0 - 30 10 30 - 60 54 60 - 90 68 90 - 120 28 120 - 150 20
Q.4
4 marks each · attempt any 2
- Q.4 (i)4 marksThree horses A, B and C are in a race. A is twice as likely to win as B and B is twice as likely to win as C. What are their probabilities of winning?
- Q.4 (ii)4 marksThe following is the distribution of the size of certain farms from a taluka (tehsil). Find the median size of farms.
Size of Farms (in acres) Number of Farms 5 - 15 7 15 - 25 12 25 - 35 17 35 - 45 25 45 - 55 31 55 - 65 5 65 - 75 3 - The following pie diagram represents the sectorwise loan amount in crores of rupees distributed by a bank. In the pie diagram the Agriculture sector subtends a central angle of and the Dairy sector subtends a central angle of ; the remaining sector is Industry.Q.4 (iii) (a)4 marksIf the dairy sector receives Rs 20 crores, then find the total loan disbursed.
- Q.4 (iii) (b)Find the loan amount for the agriculture sector and also for the industrial sector.
- Q.4 (iii) (c)How much additional amount did the industrial sector receive than the agriculture sector?
Q.5
5 marks each · attempt any 2
- Q.5 (i)5 marksIf the cost of bananas is increased by Rs 10 per dozen, one can get 3 dozen less for Rs 600. Find the original cost of one dozen of bananas.
- Q.5 (ii)5 marksIf the sum of first p terms of an A.P. is equal to the sum of first q terms, then show that the sum of its first terms is zero, where .
- Q.5 (iii)5 marksSolve the following simultaneous equations: and .