PT1 2022-23
25018/X/041/2022-23
PERIODIC TEST – I
SUBJECT : MATHEMATICS
DATE : 18.07.2022
Time : 50 Minutes
M.M : 30
General Instructions :
- All questions are compulsory.
- The question paper consists of 12 questions of 1 marks each.
- Section A comprises of 3 multiple choice questions of 1 marks each.
- Section B comprises of 3 questions of 2 marks each.
- Section C comprises of 3 questions of 3 marks each.
- Section D comprises of 3 questions of 4 marks each. It contains 2 case study based questions having three parts two parts of 1 mark each and one part of 2 marks and 1 long answer question.
SECTION A (1*3=3 MARKS)
1. Which of the following is not rational?
(a) (2-√3)²
(b) (√2+√3)²
(c) (√2+√3)(√2-√3)
(d) 2√7/7
2. The pair of equations x=0 and x=5 has
(a) No solution
(b) Unique/one solution
(c) Two solutions
(d) Infinitely many solutions
3. If the graph of a polynomial P(x) does not intersect the x-axis but intersects y-axis in one point, then number of zeroes of the polynomial is equal to
(a) 0
(b) 1
(c) 0 or 1
(d) none of these.
SECTION B (2*3=6 MARKS)
4. Using factor tree find the value of x, y, z
5. If one zero of the quadratic polynomial x²-5x-6 is 6 then find the other zero.
6. Is the pair of linear equations consistent? Justify your answer.
2ax+by=a; 4ax+2by-2a=0; a,b≠0
SECTION C (3*3=9 MARKS)
7. Explain whether the number 3×5×13×46+23 is a prime number or a composite number.
8. Find the quadratic polynomial whose zeroes are 3+√2 and 3-√2.
9. In a two digit number, the digit in the unit place is twice of the digit in the tenth place. If the digits are reversed, the new number is 27 more than the given number. Find the number.
SECTION D (3*4=12 MARKS)
10. Draw the graph of 2x+y=6 and 2x-y+2=0. Shade the region bounded by these lines and y=0. Find the area of shaded region.
11. A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.
Based on the above study answer the following questions:
a. In each room the same number of participants are to be seated and all of them being in the same subject, hence find the maximum number of participants that can be accommodated in each room.
b. What is the minimum number of rooms required during the event?
(i) 11
(ii) 31
(iii) 41
(iv) 21
c. 108 can be expressed as a product of its prime as
(i) 2³×3²
(ii) 2³×3³
(iii) 2²×3²
(iv) 2²×3³
12. Priya and her husband Aman who is an architect by profession, visited France. They went to see Mont Blane Tunnel which is a highway tunnel between France and Italy, under the Mont Blane mountains in the Alps, and has a parabolic cross-section. The mathematical representation of the tunnel is shown in the graph.
Based on the above information, answer the following questions :
a. The zeroes of the polynomial whose graph is given, are
i) -2,8
ii) -2,-8
iii) 2,8
iv) -2,0
b. What is the value of the polynomial, represented by the graph when x=4?
i) 22
ii) 23
iii) 24
iv) 25
c. If representation of tunnel as a polynomial is 2x²-16x+30. Verify the relationship between zeroes and coefficients of a Polynomial.