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

Concept: Arithmetic Progression

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

Concept: Quadratic Equations

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

Concept: Quadratic Equations

Find the value of determinant: `|[4,-2],[3,1]|`

Concept: Determinant of Order Two

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

Concept: Sample Space

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

Concept: Probability Examples and Solutions

Write the first three terms of the A.P. whose common difference is ‒3 and first term is 4.

Concept: Arithmetic Progression

Solve the following quadratic equation by Factorisation method: x^{2} + 7x + 10 = 0

Concept: Solutions of Quadratic Equations by Factorization

If the value of determinant `|[m,2],[-5,7]|`is 31, find the value of m

Concept: Determinant of Order Two

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

A is an Event: getting an odd number on the top upper surface of the die.

B is an Event: getting a perfect square on the upper surface of the die.

Concept: Probability Examples and Solutions

Below is the given frequency distribution of words in an essay

Number of Words | Number of Candidates |

600 – 800 | 8 |

800 – 1000 | 22 |

1000 – 1200 | 40 |

1200 – 1400 | 18 |

1400 - 1600 | 12 |

Find the mean number of words written.

Concept: Median of Grouped Data

Subjectwise marks obtained by a student in an examination are given below

Subject | Marks |

Marathi | 85 |

Hindi | 85 |

Science | 90 |

Mathematics | 100 |

Total | 360 |

Draw pie diagram

Concept: Pie Diagram

Solve the following quadratic equation by using formula method: 5m^{2} + 5m – 1 = 0

Concept: Nature of Roots

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

Concept: Probability Examples and Solutions

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

Diameter (in mm) | No. of Screws |

33 — 35 | 10 |

36 — 38 | 19 |

39 — 41 | 23 |

42 — 44 | 21 |

45 — 47 | 27 |

Calculate mean diameter of head of a screw by ‘Assumed Mean Method’.

Concept: Mean of Grouped Data

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

Marks Scored | Number of Students |

0 — 20 | 3 |

20 — 40 | 8 |

40 — 60 | 19 |

60 — 80 | 18 |

80 — 100 | 6 |

Draw histogram for the above data.

Concept: Histograms, Frequency Polygon and Frequency Curve

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 |

Concept: Histograms, Frequency Polygon and Frequency Curve

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

Concept: Arithmetic Progression

Solve the following simultaneous equations: `7/(2X+1)+13/(Y+2)=27,13/(2X+1)+7/(Y+2)=33`

Concept: Equations Reducible to a Pair of 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.

Concept: Probability Examples and Solutions

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

Concept: Quadratic Equations Examples and Solutions

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.

Concept: Sum of First n Terms of an AP

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.

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