Date & Time: 12th March 2020, 11:00 am

Duration: 2h

- All questions are compulsory.
- Use of calculator is not allowed.
- The numbers to the right of the questions indicate full marks.
- In case of MCQ’s Q. No. 1(A) only the first attempt will be evaluated and will be given credit.
- For every MCQ, the correct alternative (A), (B), (C) or (D) of answers with subquestion number is to be written as an answer.

Write the correct alternative for the following.

In the format of GSTIN there are ____________ alpha-numerals.

15

10

16

9

Chapter: [0.04] Financial Planning

From the following equations, which one is the quadratic equation?

`5/"x" = 3 = "x"^2`

x(x + 5) = 4

n – 1 = 2n

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

Chapter: [0.02] Quadratic Equations

**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: [0.01] Linear equations in two variables

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: [0.05] Probability [0.05] Probability

Find second and third terms of an A.P. whose first term is – 2 and the common difference is – 2.

Chapter: [0.03] Arithmetic Progression

‘Pawan Medical’ supplies medicines. On some medicines the rate of GST is 12%, then what is the rate of CGST and SGST?

Chapter: [0.04] Financial Planning

Find the values of a and b from the quadratic equation 2x^{2} – 5x + 7 = 0.

Chapter: [0.02] Quadratic Equations

If 15x + 17y = 21 and 17x + 15y = 11, then find the value of x + y.

Chapter: [0.01] Linear equations in two variables

**Complete the following table to draw the graph of 2x – 6y = 3:**

x | −5 | `square` |

y | `square` | 0 |

(x, y) | `square` | `square` |

Chapter: [0.01] Linear equations in two variables

**Solution:**

_{27}= ?

_{n}= \[\frac n2 [\Box + (n-1) d ]\]

_{27}= `27/2` [12 + (27 - 1)\[\Box ]\]

Chapter: [0.03] Arithmetic Progression

A card is drawn from a well-shuffled pack of 52 playing cards. Find the probability of the event, the card drawn is a red card.

**Solution:**

Suppose ‘S’ is sample space.

∴ n(S) = 52

**Event A:** Card drawn is a red card.

∴ Total red cards = `square` hearts + 13 diamonds

∴ n(A) = `square`

∴ p(A) = `square/("n"("s"))` ....formula

∴ p(A) = `26/52`

∴ p(A) = `square`

Chapter: [0.05] Probability

Find the value of the determinant:

`[(7/3,5/3),(3/2,1/2)]`

Chapter: [0.01] Linear equations in two variables

Solve the quadratic equation by factorisation method:

x^{2} - 15x + 54 = 0

Chapter: [0.02] 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: [0.03] Arithmetic Progression

A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is an odd number ?

Chapter: [0.05] Probability

Find the mode from the following information:

L = 10, h = 2, f_{0} = 58, f_{1} = 70, f_{2} = 42.

Chapter: [0.06] Statistics

Age group (in years) |
No. of Persons |
Measure of central angle |

20 - 25 | 80 | `square/200 xx 300 = square` |

25 - 30 | 60 | `60/200 xx 360 = square` |

30 - 35 | 35 | `35/200 xx square = 63^circ` |

35 - 40 | 25 | `25/200 xx 360 = square` |

Total | 200 | `square` |

Chapter: [0.06] Statistics [0.06] Statistics

Shri Shantilal has purchased 150 shares of FV ₹ 100, for MV of ₹ 120, Company has paid dividend at 7%, then to find the rate of return on his investment, complete the following activity:

**Solution:** FV = ₹ 100; Number of shares = 150

Market value = ₹ 120

1. Sum investment = MV × No. of Shares

= `square xx square`

∴ Sum investment = ₹ 18,000

2. Dividend per share = FV × Rate of dividend

= `square xx square/100`

= ₹ 7

∴ Total dividend received = 150 × 7

= `square`

3. Rate of return = `"Dividend income"/"Sum inve ted" xx 100`

= `1050/18000 xx 100`

= `square`

Chapter: [0.04] Financial Planning

A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets, a red balloon

Chapter: [0.05] Probability [0.05] Probability

A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets, a blue balloon

Chapter: [0.05] Probability [0.05] Probability

The denominator of a fraction is 4 more than twice its numerator. Denominator becomes 12 times the numerator, if both the numerator and the denominator are reduced by 6. Find the fraction.

Chapter: [0.01] Linear equations in two variables

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: [0.06] Statistics

In an A.P. sum of three consecutive terms is 27 and their products is 504. Find the terms.

(Assume that three consecutive terms in an A.P. are a – d, a, a + d.)

Chapter: [0.03] Arithmetic Progression

**Represent the following data by histogram:**

Price of Sugar (per kg in ₹) |
Number of Weeks |

18 – 20 | 4 |

20 – 22 | 8 |

22 – 24 | 22 |

24 – 26 | 12 |

26 – 28 | 6 |

28 – 30 | 8 |

Chapter: [0.06] Statistics [0.06] Statistics

One person borrows ₹ 4,000 and agrees to repay with a total interest of ₹ 500 in 10 instalments. Each instalment being less than the preceding instalment by ₹ 10. What should be the first and the last instalments?

Chapter: [0.03] Arithmetic Progression

The sum of the areas of two squares is 400 sq.m. If the difference between their perimeters is 16 m, find the sides of two squares.

Chapter: [0.02] Quadratic Equations

**Convert the following equations into simultaneous equations and solve:**

`sqrt("x"/"y") = 4, 1/"x" + 1/"y" = 1/"xy"`

Chapter: [0.02] Quadratic Equations

A dealer sells a toy for ₹ 24 and gains as much percent as the cost price of the toy. Find the cost price of the toy.

Chapter: [0.02] Quadratic Equations

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