MATHS I
BOARD SAMPLE PAPER
IMPORTANT PAPER TO PRACTICE
SSC MAHARASHTRA BOARD
WITH SOLUTION
Q. 1. (A) Solve the following questions. (Any four) [ 4 Marks]
(1) If x + y = 14 and 2x - y = 16, then x = ?
(2) Find the value of
(3) If then find a and b.
(4) From one footwear shop, 12 pairs of chappals were sold. The sizes of these chappals are given below. 7, 8, 6, 7, 7, 5, 9, 7, 6, 7, 8, 7. Find their mode.
(5) In the given figure, the path from school to Meera's home is given in the form of a direction map. The unit of measurement is 1 cm = 50 metre. Find out how much total distance she will cover from school to home?
(6) Mr. Dubey's payable amount of income tax is Rs. 7,000. He needs to pay education cess at 3 % on income tax. Hence how much total income tax will he bas to pay?
Q. 1. B. Solve the following questions. (Any Two) [4 Marks]
(1) The length and breadth of a rectangular field are (2x + 3y) units and (3x - y) units, respectively. Find the perimeter of the field in the form of an algebraic expression.
(2) Determine whether (x - 3) is a factor of polynomial x3 - 19x + 30.
(3) An information was gathered about 40 families, about the newspaper they subscribe to. The following observations are made: 9 families subscribe to English newspaper, 20 families subscribe to Marathi newspaper, 7 families subscribe to newspapers of both the languages, Represent this information using venn diagram. Find the number of familite not subscribing to any of the newspapers.
Q. 2. A. Choose the correct alternative. [ 4 Marks]
(1) For an A.P., if a = 7 and d = 2.5, then find t12 = ?
(A) 37.5 (B) 34.5 (C) 28.2 (D) 44.5
(2) 28% GST was charged on the scooter having cost Rs. 50,000 then find the amount of CGST charged.
(A) Rs. 8000 (B) Rs. 7500 (C) Rs. 14000 (D) Rs. 7000
(3) If α and β are the roots of the equation 3x2 + x - 10 = 0, then the value of is ......
(A) 10 (B) (C) (D)
(4) Two coins are tossed simultaneously. Then the probability of getting at the most one head is .....
(A) (B) (C) (D)
Q. 2. (B) Solve the following questions. (Any Two) [ 4 marks]
(1) If and from the given information form the two simultaneous equations in x and y and solve them.
(2) Find the sum of all odd numbers between 351 and 373.
(3) Solve: 7x2 - 30x - 25 = 0.
Q. 3. A. Complete the following activities. (Any two ) [4 Marks]
(1) In the adjoining figure, the arrow rests on any number, after the rotation of the disc. The probability that it will rest on any of the numbers on the disc is equal. Let A be any random event. To find the probability of A, fill in the boxes.
(2) Complete the following table.
Face Value
|
The share is at
|
Market Value
| |
(i)
|
Rs. 100
|
discount of Rs. 15
|
----------------
|
(ii)
|
Rs. 25
|
----------------
|
Rs. 360
|
(3) In the pie - diagram, the data of 720 students who opted for their favourite literature type is shown. The data is expressed in percentages. Using this diagram complete the following table.
Type of Literature
|
Angular measure
|
Number of students.
|
Comics
|
720
|
144
|
Mystery
|
900
|
----------
|
Fiction
|
_________
|
216
|
Drama
|
__________
|
__________
|
Science Fiction
|
720
|
144
|
Q. 3. B. Solve the following questions. (Any Two) [ 4 Marks]
(1) Solve : 4m + 6n = 54; 3m + 2n = 28
(2) Compare the quadratic equation to ax2 + bx + c = 0 and find the value of discriminant, and hence write the nature of the roots.
(3) Mukta had Rs. 12 on 4th Jan 2018, she saved Rs. 15 after this day, every day she saved 2 more rupees than the earlier day. Then including the savings upto on 30th of Jan 2018, how much total amount did she have?
Q. 4. Solve the following questions. (Any three) [9 Marks]
(1) Using the digits 0, 2, 3, 5 the two digit numbers are constructed without repetition of digits. Find the probability of the following events:
Condition for event A: The number formed is an even number.
Condition for event B: The number formed is a prime number.
(2) Solve the given simultaneous equations using graphical method. 3x + 2y = 6; 5x + y = 10.
(3) A businessman supplied CCTV camera sets for police control room, worth Rs. 1, 77, 000. The rate of GST is 18%. Then find the amount of SGST and CGST. Also find the taxable price of CCTV sets.
(4) For arithmetic progression, first term is - 8 and last term is 55. If sum of all these terms is 235, find the number of terms and common difference.
Q. 5. Solve the following questions. (Any two) [ 4 Marks ]
(1) The difference between two numbers is 2 and the product is 1443. Find the numbers.
(2) An electric company producing electric bulb, has packed 100 bulbs is each box. Some bulbs from 16 such boxes are tested for defective. The information of number of defective bulbs in 16 boxes is given below.
No. of defective bulb
|
No. of boxes
|
0 - 2
|
3
|
2 - 4
|
4
|
4 - 6
|
5
|
6 - 8
|
3
|
8 - 10
|
1
|
(i) How many boxes contain maximum number of defective bulbs?
(ii) Find the mean of the defective bulbs.
(ii) If the box is selected at random, then what is the probability that it will contain average 2 to 4 defective bulbs?
(3) Find the probability of getting highest number of defective bulbs?
Q. 6. Solve the following questions. (Any one) [3 Marks]
(1) The following determinants are obtained from the simultaneous equations in the variables x and y.
If Dx = Dy = D =
and the solutions for this equations are x = 5 and y = -1, then find the values of 'a' and 'b'. Also form the original simultaneous equations having this solution.
(2) An analysis of particular information is given in the following table.
Age group
|
Frequency
|
0 - 10
|
2
|
10 - 20
|
5
|
20 - 30
|
6
|
30 - 40
|
5
|
40 - 50
|
2
|
For this data, mode = median = 25. Calculate the mean. Observing the given frequency distribution and values of the central tendency, interpret your observation.
Solution:
