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

1, 4, 7, 10, ………………..

Concept: Arithmetic Progression

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

Concept: Sample Space

If 12x +13y =29 and 13x +12y=21, find x + y.

Concept: Linear Equations in Two Variables Applications

For a sequence if n `S_n=n/(n+1)` then find the value of S_{10}.

Concept: Introduction to Sequence

Verify whether 1 is the root of the quadratic equation : `x^2+3x-4=0`

Concept: Quadratic Equations

If x + y = 5 and x = 3, then find the value of y.

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method

Solve the following quadratic equation by factorization method : `x^2-5x+6=0`

Concept: Solutions of Quadratic Equations by Factorization

Find the term t15 of an A.P. : 4, 9, 14, …………..

Concept: General Term of an Arithmetic Progression

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

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method

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.

Concept: Sample Space

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

Concept: Median of Grouped Data

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

Concept: Quadratic Equations

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 |

Concept: Pie Diagram

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

Concept: Probability Examples and Solutions

Solve the following simultaneous equations by using graphical method : x + y = 6; x – y = 4.

Concept: Graphical Method of Solution of a Pair of Linear Equations

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.

Concept: Arithmetic Progression

Solve the following quadratic equation by completing square method : x^{2} + 10x + 21 = 0.

Concept: Solutions of Quadratic Equations by Completing the Square

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.

Concept: Probability Examples and Solutions

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.

Concept: Median of Grouped Data

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

Concept: Quadratic Equations

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?

Concept: Arithmetic Progression

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.

Concept: Simple Situational Problems

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.

Concept: Histograms, Frequency Polygon and Frequency Curve