State whether the following sequence is an Arithmetic Progression or not:

3, 6, 12, 24,......

Concept: Arithmetic Progression

If one root of the quadratic equation is `3 – 2sqrt5` , then write another root of the equation.

Concept: Nature of Roots

There are 15 tickets bearing the numbers from 1 to 15 in a bag and one ticket is drawn from this bag at random. Write the sample space (S) and n(S).

Concept: Sample Space

Find the class mark of the class 35 - 39.

Concept: Probability Examples and Solutions

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

Concept: Arithmetic Progression

Find the values of a, b, c for the quadratic equation 2x_{2} = x + 3 by comparing with standard form ax^{2} + bx + c = 0.

Concept: Quadratic Equations

Find the first two terms of the sequence for which S_{n} is given below: `S_n=n^2(n+1)`

Concept: Introduction to Sequence

Find the value of discriminant (Δ) for the quadratic equation: `x^2+7x+6=0`

Concept: Quadratic Equations

Write the equation of X-axis. Hence, find the point of intersection of the graph of the equation x + y = 5 with the X-axis.

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

For a certain frequency distribution, the values of Assumed mean (A) = 1300, `sumf_id_i` = 900 and `sumfi` = 100. Find the value of mean (`barx`) .

Concept: Median of Grouped Data

Two coins are tossed simultaneously. Write the sample space (S), n(S), the following event A

using set notation and n(A), where ‘A is the event of getting at least one head.’

Concept: Probability Examples and Solutions

Find the value of k for which the given simultaneous equations have infinitely many solutions:

kx + 4y = 10;

3x + 2y = 5.

Concept: Linear Equations in Two Variables Applications

How many three digit natural numbers are divisible by 5?

Concept: Introduction to Sequence

Solve the following quadratic equation by factorization method : `3x^2-29x+40=0`

Concept: Solutions of Quadratic Equations by Factorization

Solve the following simultaneous equations by using Cramers’s rule: 3x-y =7, x +4y =11

Concept: Cramer'S Rule

Two dice are thrown. Find the probability of the event that the product of numbers on their upper faces is 12.

Concept: Probability Examples and Solutions

The following is the frequency distribution of waiting time at ATM centre; draw histogram to

represent the data:

Waiting time (in seconds) |
Number of Customers |

0 -30 | 15 |

30 - 60 | 23 |

60 - 90 | 64 |

90 - 120 | 50 |

120 - 150 | 5 |

Concept: Histograms, Frequency Polygon and Frequency Curve

Three horses A, B and C are in a race, A is twice as likely to win as B and B is twice as likely to win as C. What are their probabilities of winning?

Concept: Probability - A Theoretical Approach

The following is the distribution of the size of certain farms from a taluka (tehasil):

Size of Farms (in acres) |
Number of Farms |

5 – 15 | 7 |

15 – 25 | 12 |

25 – 35 | 17 |

35 – 45 | 25 |

45 – 55 | 31 |

55 – 65 | 5 |

65 – 75 | 3 |

Find median size of farms.

Concept: Median of Grouped Data

The following pie diagram represents the sectorwise loan amount in crores of rupees distributed by a bank. From the information answer the following questions:

a. If the dairy sector receives `20 crores, then find the total loan disbursed.

b. Find the loan amount for agriculture sector and also for industrial sector.

c. How much additional amount did industrial sector receive than agriculture sector?

Concept: Pie Diagram

If the cost of bananas is increased by Rs. 10 per dozen, one can get 3 dozen less for Rs.600. Find the original cost of one dozen of bananas.

Concept: Simple Situational Problems

If the sum of first p terms of an A.P. is equal to the sum of first q terms, then show that the sum of its first (p + q) terms is zero where p ≠ q.

Concept: Sum of First n Terms of an AP

Solve the following simultaneous equations

`1/(3x)-1/(4y)+1=0`;

`1/(5x)+1/(2y)=4/15`

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