Maharashtra SSC Class 10 Algebra March 2018 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 markFind next two terms of an A.P.
- Q.1 (ii)1 markState whether the given equation is quadratic or not. Give reason.
- Q.1 (iii)1 markIf , are the values of the determinants for certain simultaneous equations in and , find .
- Q.1 (iv)1 markIf and , find .
- Q.1 (v)1 markWrite any one solution of equation .
- Q.1 (vi)1 markIf and , find .
Q.2
2 marks each · attempt any 4
- Q.2 (i)2 marksFind if the th term of the following A.P. is 64:
- Q.2 (ii)2 marksIf one of the roots of the quadratic equation is 2, then find the value of .
- Q.2 (iii)2 marksA box contains 20 cards marked with the numbers 1 to 20. One card is drawn at random, where the event A is such that the number on the card is multiple of 3. Write , , and .
- Q.2 (iv)2 marksFind the value of if , .
- Q.2 (v)2 marksIf the roots of quadratic equation are 5 and , form the quadratic equation.
- Q.2 (vi)2 marksFor a certain frequency distribution mean is 72 and median is 78, find the mode.
Q.3
3 marks each · attempt any 3
- Q.3 (i)3 marksFor an A.P., find if and .
- Q.3 (ii)3 marksSolve the following quadratic equation by formula method:
- Q.3 (iii)3 marksSolve the following simultaneous equations by using Cramer's rule: ;
- Q.3 (iv)3 marksA die is thrown, find the probability of the event of getting a square number.
- Q.3 (v)3 marksThe marks obtained by a student in an examination out of 100 are given below. The total marks obtained in various subjects are as follows. Represent the above data using a pie diagram.
Subject Marks Marathi 80 English 80 Science 100 Mathematics 100 Total 360
Q.4
4 marks each · attempt any 2
- Q.4 (i)4 marksIf and , find the quadratic equation whose roots are and .
- Q.4 (ii)4 marksTwo dice are thrown. Find the probability of getting: (a) The sum of the numbers on their upper faces is at least 9. (b) The sum of the numbers on their upper faces is 15. (c) The number on the upper face of the second die is greater than the number on the upper face of the first die.
- Q.4 (iii)4 marksFrequency distribution of daily commission received by 100 salesmen is given below. Find the mean daily commission received by salesmen, by assumed mean method.
Daily commission (in Rs.) No. of Salesmen 100 - 120 20 120 - 140 45 140 - 160 22 160 - 180 9 180 - 200 4
Q.5
5 marks each · attempt any 2
- Q.5 (i)5 marksA boat takes 10 hours to travel 30 km upstream and 44 km downstream, but it takes 13 hours to travel 40 km upstream and 55 km downstream. Find the speed of the boat in still water and the speed of the stream.
- Q.5 (ii)5 marksIf the 9th term of an A.P. is zero, then prove that 29th term is double of 19th term.
- Q.5 (iii)5 marksDraw histogram and frequency polygon on the same graph paper for the following frequency distribution:
Class Frequency 15 - 20 20 20 - 25 30 25 - 30 50 30 - 35 40 35 - 40 25 40 - 45 25