Duration: 2h

**Choose correct alternative for the following question.**

To draw graph of 4x + 5y = 19, Find y when x = 1.

4

3

2

-3

Chapter: [3] Linear equations in two variables

**Choose the correct answer for the following question.**

Which one is the quadratic equation?

\[\frac{5}{x} - 3 = x^2\]

x ( x+5 ) = 2

n - 1 = 2n

`1/x^2(x+2)=x`

Chapter: [2] Quadratic Equations

Choose the correct alternative answer for the following question.

If n(A) = 2, P(A) =`1/5` , then n(S) = ?

10

` 5/2`

`2/5`

`1/3`

Chapter: [4] Probability

No. of trees planted by each student | 1 - 3 | 4 - 6 | 7 - 9 | 10 - 12 |

No. of students | 7 | 8 | 6 | 4 |

The above data is to be shown by a frequency polygon. The coordinates of the points to show number of students in the class 4-6 are . . . .

(A) (4, 8) | (B) (3, 5) | (C) (5, 8) | (D) (8, 4) |

Chapter: [5] Statistics

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

Chapter: [1] Arithmetic Progression

State whether the given equation is quadratic or not. Give reason.

`5/4m^2 - 7 = 0`

Chapter: [2] Quadratic Equations

Factorise : m^{2} + 5m + 6.

Chapter: [2] Quadratic Equations

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

Chapter: [4] Probability

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

Chapter: [3] Linear equations in two variables

Represent the following data by Histogram:

Price of Sugar per kg (in Rs.) |
Number of Weeks |

18-20 | 4 |

20-22 | 8 |

22-24 | 22 |

24-26 | 12 |

26-28 | 8 |

28-30 | 6 |

Chapter: [5] Statistics

Find n if the nth term of the following A.P. is 68

5, 8, 11, 14, ..........

Chapter: [1] Arithmetic Progression

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: [3] Linear equations in two variables

If one of the roots of the quadratic equation x^{2} - 11x + k = 0 is 9, then find the value of k

Chapter: [2] Quadratic Equations

The first term of an A. P. is 5 and the common difference is 4. Complete the following activity and find the sum of the first 12 terms of the A. P.

a = 5, d = 4, s12 = ?

`s_n = n/2 [ square ]`

`s_12 = 12/2 [10 +square]`

`= 6 × square `

` =square`

Chapter: [1] Arithmetic Progression

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

Chapter: [5] Statistics

The market price of share is Rs. 200 and the rate of brokerage is 0.3%.

Find the cost of one such share.

Chapter: [6] Financial Planning

A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

Chapter: [3] Linear equations in two variables

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

Chapter: [2] Quadratic Equations

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

Chapter: [1] Arithmetic Progression

Prasad purchased a share of face value Rs. 100 when its market price was Rs. 150. Company declared a dividend of 12% on the share. What was the rate of return on the investment Prasad made ?

Chapter: [6] Financial Planning

Two coins are tossed simultaneously. Write the sample space ‘S’ and the number of sample points n(S). Write the following events using set notation and mention the number of elements in each of them:-

(a) A is the event of getting at least one head.

(b) B is the event of getting exactly one head

Chapter: [4] Probability

The sales of salesmen in a week are given in the pie diagram. Study the diagram and answer the following questions. If the total sale due to salesmen A is Rs. 18,000, then

a) Find the total sale.

b) Find the sale of each salesman.

c) Find the salesman with the highest sale.

d) Find the difference between the highest sale and the lowest sale.

Chapter: [5] Statistics

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.

Chapter: [3] Linear equations in two variables

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

Chapter: [2] Quadratic Equations

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.

Chapter: [5] Statistics

Market value of shares and dividend declared by the two companies is given below. Face Value is same and it is Rs 100 for both the shares. Investment in which company is more profitable ?

(1) Company A - Rs 132 , 12%

(2) Company B - Rs 144 , 16%

Chapter: [6] Financial Planning

Two dice are thrown. Find the probability of getting :

1) The sum of the numbers on their upper faces is at least 9.

2) The sum of the numbers on their upper faces is 15.

3) The number on the upper face of the second die is greater than the number on the upper face of the first die.

Chapter: [4] Probability

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