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### Maths I, SSC New Syllabus, Sample Paper for Board Exam 2019. Maharashtra state board.

Mathematics – I      Paper No. 3
Time : 2Hrs.            Marks: 40
Q. 1. A. Solve the following questions. (Any 4)             [4 Marks]
1. Write the following set in the set builder form: F = {5, 10, 15, 20}
2. Find the rationalizing factor of : √8
3. Write the degree of the following polynomial. ab2cd – 3a2bcd3 +2ac4

4. 15 chocolates were distributed between Raju and Sanju in the ratio 2 : 3. How many chocolates did Raju receive?
5. Write three solutions of the equation x – y = 9.
6. Find the median of : 18, 14, 22, 23, 14, 18, 17, 18, 28, 28, 14, 25, 14.
B. Solve the following questions. (Any 2) [4]
1. If the class mark of a class is 25 and the class width is 10. Find the class.
2. What is the investment, if there is a loss of Rs. 600 at 20% loss?

3. 2x +y = 5.   ∴ y = _________________
Q. 2. A. Choose the correct alternative: [4 marks]
1. One card is drawn from well shuffled pack of 52 cards, then probability of getting red face card is
A) 3/13      B) 3/4        C) 3/26         D) 1/13
2. √5 m2 - √5 m + √5 = 0 which of the following statement is true for this given equation?
A) Real and Unequal roots    B) Real and equal roots C) Roots are not real D) Three roots.
3. The equations 3x – 4y = 7  and 9x – 12y = 12 will have
A) Unique solution    B) Infinitely many solutions.    C) No Solution D) Cannot be determined.
4. 28% GST was charged on a scooter having cost of Rs. 50,000 find the amount of CGST charged.

A) Rs. 8000    B) Rs. 7500 C) Rs. 14,000   D) Rs. 7000

B. Solve the following questions. (Any 2) [4 Marks]
1) Find the 25th term of A.P. 12, 16, 20, 24, ….
2) Obtain the quadratic equation if roots are – 3 , - 7.
3. The record of a weather station shows that out of the past 250 consecutive days. If weather forecasts were correct 175 times. What is the probability that on a given day it was correct?

Q. 3. (A) Complete the following activities. (Any 2) [4 Marks]
1) If x = 5 is the root of a equation kx2 – 14x – 5 = 0, then find the value of k by completing the following activity.
2) Form a Road Safety committee of two from 2 boys (B1, B2) and 2 girls (G1, G2) complete the following activity to write the sample space.

(a) Committee of 2 boys = ___________________
(b) Committee of 2 girls = ____________________
(c) Committee of one boy and one girl = _____________________
∴ Sample Space = { _______________________________ }
3) Complete the following table.
 Face Value The Share is at Market Value (i) Rs. 100 Discount of Rs. 15 _______________ (ii) Rs. 25 ________________ Rs. 360
B) Solve the following questions (Any 2)
1) The sum of two roots of a quadratic equation is 5 and sum of their cubes is 35. Find the equation.
2) Prashant bought 50 shares of FV of Rs. 100 having MV Rs. 180. Company gave 40% dividend on the shares. Find the rate of return on Investments.
3) Medical check-up of 180 women was conducted in a health centre in a village. 50 of them were short of hemoglobin, 10 suffered from cataract and 25 had respiratory disorders. The remaining women were healthy. Show the information in a pie chart.

Q. 4. Solve the following questions (Ans 3) [9 Marks]

1. Solve 5x – 6y + 30 = 0 and 5x + 4y – 20 = 0 graphically.

2. A trader from Surat, Gujarat sold cotton clothes to a trader in Rajkot, Gujarat. The taxable value of cotton clothes is Rs. 2.5 lacs. What is the amount of GST at 5% paid by the trader in Rajkot.

3. Find the sum of all odd numbers from 1 to 150.

4. Najima saves in a ‘Mahila Bachat Gat’ Rs. 2 on the first day, Rs. 4 on the second day, Rs. 6 on the third day and so on. What will be her saving in the month of February 2010?
Q. 5. Solve the following questions. (Any 1)  [ 4 Marks]

1. Mukund possesses Rs. 50 more than what Sagar possesses. The product of the amount they have is Rs. 15,000. Find the amount each one has.

2. The sum of two number is 45 and the greater number is twice the smaller number. Find the numbers.

Q. 6. Solve the following questions. (Any 1) (3 Marks)

1. 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?

2) Find how many three-digit natural numbers are divisible by 5.