Date & Time: 8th March 2016, 11:00 am

Duration: 2h

Write the first two terms of the sequence whose nth term is t_{n} = 3n ‒ 4.

Chapter: [0.03] Arithmetic Progression

Find the value of a, b, c in the following quadratic equation : 2x^{2} ‒ x ‒ 3 = 0

Chapter: [0.02] Quadratic Equations

Write the quadratic equation whose roots are ‒2 and ‒3.

Chapter: [0.02] Quadratic Equations

Find the value of the determinate:

`|(4,-2),(3,1)|`

Chapter: [0.03] Arithmetic Progression

Write the sample space for selecting a day randomly of the week.

Chapter: [0.05] Probability

Find the class mark of the classes 20-30 and 30-40.

Chapter: [0.05] Probability [0.05] Probability

If for an A.P. the first term is 2 and the common difference is 3, then find first three-term of A.P.

Chapter: [0.03] Arithmetic Progression

Solve the following quadratic equation using factorization method:

`"x"^2-11"x"+24=0`

Chapter: [0.02] Quadratic Equations

If the value of determinants `|(3, 4),(-2, "x")|` is 23, then find the value of` x.

Chapter: [0.02] Quadratic Equations

A die is thrown, then find the probability of the following events:

A is an event: getting a perfect square.

B is an event: getting a prime number.

Chapter: [0.05] Probability [0.05] Probability

Below is the given frequency distribution of words in an essay:

Number of words | Number of Candidates |

600 - 800 | 12 |

800 - 1000 | 14 |

1000 - 1200 | 40 |

1200 - 1400 | 15 |

1400 - 1600 | 19 |

Find the mean number of words written.

Chapter: [0.06] Statistics

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

Subject | Marks |

Marathi | 85 |

Hindi | 80 |

English | 95 |

Mathematics | 100 |

Total | 360 |

Represent the data using pie diagram.

Chapter: [0.06] Statistics [0.06] Statistics

Solve the equation by using the formula method. 3y^{2} +7y + 4 = 0

Chapter: [0.02] Quadratic Equations

There 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

Chapter: [0.05] Probability [0.05] Probability

The measurements (in mm) of the diameters of the head of the screws are given below :

Diameter (in mm) | no. of screws |

33 - 35 | 9 |

36 - 38 | 21 |

39 - 41 | 30 |

42 - 44 | 22 |

45 - 47 | 18 |

Calculate the mean diameter of the head of a screw by the ' Assumed Mean Method'.

Chapter: [0.06] Statistics

The marks scored by students in Mathematics in a certain examination are given below :

Marks Scored |
Number of Students |

0 - 20 | 6 |

20 - 40 | 9 |

40 - 60 | 14 |

60 - 80 | 16 |

80 - 100 | 5 |

Draw histogram for the above data.

Chapter: [0.06] Statistics [0.06] Statistics

Draw 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:

(a) The first term and common difference

(b) The 34^{th} term

(c) ‘n’ such that t_{n} = 55

Chapter: [0.03] Arithmetic Progression

Solve the following simultaneous equations.

\[\frac{7}{2x + 1} + \frac{13}{y + 2} = 27 ; \frac{13}{2x + 1} + \frac{7}{y + 2} = 33\]

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 probability of win for each boy.

Chapter: [0.05] Probability [0.05] Probability

The divisor and quotient of the number 6123 are same and the remainder is half the divisor. Find the divisor.

Chapter: [0.02] Quadratic Equations

Find the sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15^{th} term of that A.P.

Chapter: [0.03] Arithmetic Progression

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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