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For an A.P. t_{3 =} 8 and t_{4} =12, find the common difference d.

Write the following quadratic equation in a standard form:

3x^{2} =10x + 7.

State whether the following sequence is an AP or not:

1, 3, 6, 10………

Solve the following quadratic equation by factorization method:

9x^{2}-25 = 0

If the point (3, 2) lies on the graph of the equation 5x + ay = 19, then find a.

A die is thrown. Write the sample space (S) and number of sample points n(S) and also write event A of getting even number on the upper surface and write n(A).

For a certain frequency distribution, the value of mean is 20 and mode is 11. Find the value of median.

Solve the equation by using the formula method.

3y^{2} +7y + 4 = 0

Solve the following simultaneous equations by using Cramers’s rule:

3x-y =7

x +4y =11

Two coins are tossed simultaneously. Write the sample space ‘S’ and the number of sample points n(S). Write the following events using set notation and mention the number of elements in each of them:-

(a) A is the event of getting at least one head.

(b) B is the event of getting exactly one head

The following table gives the frequency distribution of trees planted by different Housing Societies in a particular locality:

No. of Trees | No. of Housing Societies |

10-15 | 2 |

15-20 | 7 |

20-25 | 9 |

25-30 | 8 |

30-35 | 6 |

35-40 | 4 |

Find the mean number of trees planted by Housing Societies by using ‘Assumed Means Method’

Represent the following data by Histogram:

Price of Sugar per kg (in Rs.) | Number of Weeks |

18-20 | 4 |

20-22 | 8 |

22-24 | 22 |

24-26 | 12 |

26-28 | 8 |

28-30 | 6 |

A farmer borrows Rs.1,000 and agrees to repay with a total interest of Rs. 140 in 12 installments, each installment being less that the preceding installment by Rs. 10. What should be his first installment?

There are three boys and two girls. A committee of two is to be formed. Find the probability of events that the committee contains:

a) At least one girl.

b) One boy and one girl

c) Only boys

If m times m^{th} term of an A.P. is equal to n times its n^{th} term, then show that (m + n)^{th} term of the A.P. is zero.

Draw the graphs representing the equations 4x + 3y = 24 and 3y=4x+24 on the same graph paper. Write the co-ordinates of the point of intersection of these lines

and find the area of triangle formed by these lines and the X-axis.