Date & Time: 13th March 2017, 1:00 pm

Duration: 2h

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

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

Chapter: [0.03] Arithmetic Progression

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

Chapter: [0.02] Quadratic Equations

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).

Chapter: [0.05] Probability

Find the class mark of the class 35 - 39.

Chapter: [0.05] Probability [0.05] Probability

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

Chapter: [0.03] 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.

Chapter: [0.02] Quadratic Equations

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

Chapter: [0.03] Arithmetic Progression

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

Chapter: [0.02] 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.

Chapter: [0.01] Linear equations in two variables

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`) .

Chapter: [0.06] Statistics

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.’

Chapter: [0.05] Probability [0.05] Probability

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

kx + 4y = 10;

3x + 2y = 5.

Chapter: [0.01] Linear equations in two variables

How many three digit natural numbers are divisible by 5?

Chapter: [0.03] Arithmetic Progression

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

Chapter: [0.02] Quadratic Equations

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

Chapter: [0.01] Linear equations in two variables

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

Chapter: [0.05] Probability [0.05] Probability

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

Waiting time(in seconds) |
Number ofCustomers |

0 -30 | 15 |

30 - 60 | 23 |

60 - 90 | 64 |

90 - 120 | 50 |

120 - 150 | 5 |

Chapter: [0.06] Statistics [0.06] Statistics

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?

Chapter: [0.05] Probability

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.

Chapter: [0.06] Statistics

**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?

Chapter: [0.06] Statistics [0.06] Statistics

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.

Chapter: [0.01] Linear equations in two variables

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.

Chapter: [0.03] Arithmetic Progression

Solve the following simultaneous equations

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

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

Chapter: [0.01] Linear equations in two variables

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