Date: July 2016

If 3x + 2y = 10 and 2x + 3y = 15, then find the value of x + y.

Chapter: [0.01] Linear equations in two variables

Find the common difference of the A.P 3, 5, 7, ..........

Chapter: [0.03] Arithmetic Progression

Two coins are tossed simultaneously. Write the sample space S.

Chapter: [0.05] Probability

Write the following quadratic equation in standard form ax^{2} + bx + c = 0 : x (x + 3) = 7

Chapter: [0.02] Quadratic Equations

If Σf_{i} = 25 and Σf_{i}x_{i} = 100, then find the mean (`bar"x"`)

Chapter: [0.06] Statistics

Find the value of a, b, c in the following quadratic equation: 2x^{2} + 18 = 6x

Chapter: [0.02] Quadratic Equations

Find the eighteenth term of the A.P: 1, 7, 13, 19, ............

Chapter: [0.03] Arithmetic Progression

Form the quadratic equation if the roots are 3 and 8.

Chapter: [0.02] Quadratic Equations

Solve the following simultaneous equation using Cramer's rule

4x + 3y = 4

6x + 5y = 8

Chapter: [0.01] Linear equations in two variables

In the following experiment write the sample space S, Number of sample points n(S), write the event P in set form and find n(P):

Form two-digit numbers using the digit 0, 1, 2, 3, 4, without repeating the digits, P is the event, that the number so formed is even.

Chapter: [0.05] Probability

Find a certain frequency distribution, the value of mean and mode are 54.6 and 54 respectively. Find the value of median.

Chapter: [0.06] Statistics

Subjective marks obtained by a student in an examination are given below:

Subject |
Marks |

Marathi | 85 |

English | 90 |

Science | 85 |

Mathematics | 100 |

Total | 360 |

Draw a pie diagram to represent the above data.

Chapter: [0.06] Statistics [0.06] Statistics

Represent the following data by histogram:

Price of sugar Per kg (in Rs) | Number of weeks |

28-30 | 4 |

30-32 | 8 |

32-34 | 22 |

34-36 | 12 |

36-38 | 6 |

Chapter: [0.06] Statistics [0.06] Statistics

A coin is tossed three time then find the probablity of the following events:

A is an event of getting a head on middle coin.

B is an event of getting exactly one tail.

Chapter: [0.05] Probability

The following table shows ages of 3000 patients getting medical treatment in a hospital on a particular day :

Age (in years) | No. of Patients |

10-20 | 60 |

20-30 | 42 |

30-40 | 55 |

40-50 | 70 |

50-60 | 53 |

60-70 | 20 |

Find the median age of the patients.

Chapter: [0.06] Statistics

Solve the following quadratic equation by using formula method :

7y^{2} - 5y - 2 = 0

Chapter: [0.02] Quadratic Equations

Draw histogram and hence 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 |

Chapter: [0.06] Statistics [0.06] Statistics

The 11^{th} term and the 21^{st} term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term.

Chapter: [0.03] Arithmetic Progression

If the point of intersection of ax + by = 7 and bx + ay = 5 is (3,1), then find the value of a and b.

Chapter: [0.01] Linear equations in two variables

In 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 P(A) + P(B) + P(C) = 1, then find the probabilities of their winning.

Chapter: [0.05] Probability [0.05] Probability

Find the sum of all members from 50 to 250 which divisible by 6 and find t13.

Chapter: [0.03] Arithmetic Progression

Solve `9("x"^2 + 1/"x"^2) -3("x" - 1/"x") - 20 = 0`

Chapter: [0.02] Quadratic Equations

A three digit number is equal to 17 times the sum of its digits. If 198 is added to the number, the digits are interchanged. The addition of first and third digit is 1 less than middle digit. Find the number.

Chapter: [0.01] Linear equations in two variables

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