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State whether the following sequence is an A.P. or not?

1, 4, 7, 10, ………………..

A card is drawn from the pack of 25 cards labeled with numbers 1 to 25. Write the sample space for this random experiment.

Verify whether 1 is the root of the quadratic equation :

`x^2+3x-4=0`

Solve the following quadratic equation by factorization method :

`x^2-5x+6=0`

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

A die is thrown. If A is the event that the number on upper face is less than 5, then write sample space and event A in set notation.

For a certain frequency distribution, the value of Mean is 101 and Median is 100. Find the value of Mode.

If one root of the quadratic equation kx^{2} – 7x + 12 = 0 is 3, then find the value of k.

Area under different crops in a certain village is given below. Represent it by a pie diagram :

Corps | Area (in Hectares) |

Jowar | 80 |

Wheat | 20 |

Sugarcane | 60 |

Vegetables | 20 |

If two coins are tossed, then find the probability of the event that at least one head turns up.

Solve the following simultaneous equations by using graphical method :

x + y = 6;

x – y = 4.

There is an auditorium with 35 rows of seats. There are 20 seats in the first row, 22 seats in the second row, 24 seats in the third row and so on. Find the number of seats in the twenty-fifth row.

Solve the following quadratic equation by completing square method :

x^{2} + 10x + 21 = 0.

Two digit numbers are formed using the digits 0, 1, 2, 3, 4, 5 where digits are not repeated.

P is the event that the number so formed is even.

Q is the event that the number so formed is greater than 50.

R is the event that the number so formed is divisible by 3.

Then write the sample space S and events P, Q, R using set notation.

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.

If α + β = 5 and α^{3} +β^{3} = 35, find the quadratic equation whose roots are α and β.

Babubhai borrows Rs. 4,000 and agrees to repay with a total interest of Rs. 500 in 10 instlments, each instalment being less than the preceding instalment by Rs. 10.

What should be the first and the last instalments?

On the first day of the sale of tickets of a drama, in all 35 tickets were sold. If the rates tickets were Rs. 20 and Rs. 40 per ticket and the total collection was Rs, 900,

find the number of tickets sold of each rate.

Given below is the frequency distribution of driving speeds (in km/hour) of the vehicles of 400 college students:

Speed (in km/hr) | No. of Students |

20-30 | 6 |

30-40 | 80 |

40-50 | 156 |

50-60 | 98 |

60-70 | 60 |

Draw Histogram and hence the frequency polygon for the above data.