Date: March 2020

Duration: 2h

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

For simultaneous equations in variables x and y, D_{x }= 49, D_{y} = –63, D = 7 then what is x ?

7

-7

`1/7`

`(-1)/7`

Chapter: [3] Linear equations in two variables

Choose the correct alternative answer for the following question .

In an A.P. 1^{st} term is 1 and the last term is 20. The sum of all terms is = 399 then n = ....

42

38

21

19

Chapter: [1] Arithmetic Progression

Write the correct alternative for the following.

When a registered dealer sells goods to another registered dealer under GST, then this trading is termed as ...

BB

B2B

BC

B2C

Chapter: [6] Financial Planning

Choose the correct alternative answer for the following question.

There are 40 cards in a bag. Each bears a number from 1 to 40. One card is drawn at random. What is the probability that the card bears a number which is a multiple of 5 ?

`1/5 `

`3/5 `

`4/5`

`1/3`

Chapter: [4] Probability [4] Probability

**Find the value of discriminant of the following equation.**

\[2 y^2 - y + 2 = 0\]

Chapter: [2] Quadratic Equations

A card is drawn at random from a pack of well shuffled 52 playing cards. Find the probability that the card drawn is – a spade.

Chapter: [4] Probability

Find the values of following determinant.

Chapter: [3] Linear equations in two variables

Complete the following activity to solve the simultaneous equations.

5x + 3y = 9 -----(I)

2x + 3y = 12 ----- (II)

Chapter: [3] Linear equations in two variables

In an A.P. the first term is –5 and the last term is 45. If the sum of all numbers in the A.P. is 120, then how many terms are there? What is the common difference?

Chapter: [1] Arithmetic Progression

Anna Patil (Thane, Maharashtra) supplied vacuum cleaner to a shopkeeper in Vasai (Mumbai) for the taxable value of Rs 14,000, and GST rate of 28%. Shopkeeper sold it to the customer at the same GST rate for Rs16,800 (taxable value) Find the following –

Amount of CGST and SGST charged by the shopkeeper in Vasai.

Chapter: [6] Financial Planning

**Solve using formula.**

5m^{2} – 4m – 2 = 0

Chapter: [2] Quadratic Equations

On 1st Jan 2016, Sanika decides to save Rs 10, Rs 11 on second day, Rs 12 on third day. If she decides to save like this, then on 31^{st} Dec 2016 what would be her total saving ?

Chapter: [1] Arithmetic Progression

A ready-made garment shopkeeper gives 5% discount on the dress of Rs 1000 and charges 5% GST on the remaining amount, then what is the purchase price of the dress for the customer

Chapter: [6] Financial Planning

Joseph kept 26 cards in a cap, bearing one English alphabet on each card. One card is drawn at random. What is the probability that the card drawn is a vowel card ?

Chapter: [4] Probability [4] Probability

**Form the quadratic equation from the roots given below.**

0 and 4

Chapter: [2] Quadratic Equations

The following table shows the classification of number of vehicles and their speeds on Mumbai-Pune express way. Find the median of the data.

Average Speed of
Vehicles(Km/hr) |
60 - 64 | 64 - 69 | 70 - 74 | 75 - 79 | 79 - 84 | 84 - 89 |

No. of vehicles | 10 | 34 | 55 | 85 | 10 | 6 |

Chapter: [5] Statistics

Solve the following simultaneous equations.

\[\frac{1}{3x + y} + \frac{1}{3x - y} = \frac{3}{4}; \frac{1}{2\left( 3x + y \right)} - \frac{1}{2\left( 3x - y \right)} = - \frac{1}{8}\]

Chapter: [3] Linear equations in two variables

**Solve the following quadratic equation by completing the square method.**

2y^{2} + 9y +10 = 0

Chapter: [2] Quadratic Equations

Decide whether following sequence is an A.P., if so find the 20^{th} term of the progression.

–12, –5, 2, 9, 16, 23, 30,...

Chapter: [1] Arithmetic Progression

Shri. Aditya Sanghavi invested Rs 50,118 in shares of FV Rs 100, when the market value is Rs 50. Rate of brokerage is 0.2% and Rate of GST on brokerage is 18%, then How many shares were purchased for Rs 50,118 ?

Chapter: [6] Financial Planning

The table below shows the yield of jowar per acre. Show the data by histogram.

Yield per acre (quintal) | 2 - 3 | 4 - 5 | 6 - 7 | 8 - 9 | 10 - 11 |

No. of farmers | 30 | 50 | 55 | 40 | 20 |

Chapter: [5] Statistics [5] Statistics

Solve the following equations by Cramer’s method.

3*x* – 2*y *= \[\frac{5}{2}\] ; \[\frac{1}{3}x + 3y = - \frac{4}{3}\]

Chapter: [3] Linear equations in two variables

In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

Number of mangoe |
50 − 52 | 53 − 55 | 56 − 58 | 59 − 61 | 62 − 64 |

Number of boxes |
15 | 110 | 135 | 115 | 25 |

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

Chapter: [5] Statistics

Two water taps together can fill a tank in `9 3/8`hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Chapter: [2] Quadratic Equations

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag

Chapter: [4] Probability

A milk centre sold milk to 50 customers. The table below gives the number of customers and the milk they purchased. Find the mean of the milk sold by direct method.

Milk Sold (Litre) | 1 - 2 | 2 - 3 | 3 - 4 | 4 - 5 | 5 - 6 |

No. of Customers | 17 | 13 | 10 | 7 | 3 |

Chapter: [5] Statistics

Solve the following simultaneous equation graphically.

5x – 6y + 30 = 0 ; 5x + 4y – 20 = 0

Chapter: [3] Linear equations in two variables

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