MID TERM EXAMINATION 2018 - 19
CLASS: X
SUBJECT – MATHEMATICS
TIME: 3HRS. M.M. 80
General Instructions :
1. All questions are compulsory.
2. The question paper consist of 30 questions divided into four sections A, B, C and D.
3. Section A contains 6 questions 1 mark each question.
4. Section B contains 6 questions 2 mark each question.
5. Section C contains 10 questions 3 mark each question.
6. Section D contains 8 questions 4 mark each question.
7. There is no overall choice. However, an internal choice has been provided in 4 questions of 3 marks each and 3 questions of 4 marks each. You have to attempt only on the alternatives in all such questions.
8. Use of calculator is not permitted.
SECTION – A
1. The decimal expansion of rational number 49/40 will terminate after how many places of decimal? 2. Check whether (x + 3)3 = x3 – 8 is a quadratic equation ?
3. Find the next term of the A.P. √8, √18, √32,…….
4. If ∆ABC ~ ∆DEF such that ∠A = 45 and ∠E = 56, then find the value of ∠C.
5. The ordinate of a point A on the y-axis is 5 and B has coordinates (-3, 1), then find the length of AB.
6. Two players, Rajiv and Raju play a badminton match. If the probability of Raju’s winning the match is 0.62, then find the probability of Rajiv’s winning.
SECTION - B
7. Show that any positive odd integer is of the for 4q + 1 or 4q + 3, where q is some positive integer.
8. Find a quadratic polynomial, the sum and product of whose zeroes are 5 and -2 respectively.
9. The ladder is placed against a wall such that its foot is at distance of 5m from the wall and its top reaches a window 5√3m above the ground. Find the length of ladder.
10. If the point (m,3) lies on the line segment joining the points
A(- 2 5 ,6) and B(2,8), find the value of m.
11. The following table shows the cumulative frequency distribution of marks of 800 students in an examination. Marks No. of Students Marks No. of Students Below 10 Below 20 Below 30 Below 40 Below 50 10 50 130 270 440 Below 60 Below 70 Below 80 Below 90 Below 100 570 670 740 780 800 Construct a frequency distribution table for the above data.
12. A card is drawn at random from a well-shuffled deck of 52 playing cards. Find the probability of getting neither a red colour card nor a queen.
SECTION - C
13. The traffic lights at three different road crossing change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 9:00 AM, at what time will they change simultaneously again ? 3
OR Find the HCF and LCM of 78, 52, 91 using the prime factorisation method.
14. Solve : 43x + 67y = -24 67 x + 43y = 24
OR Draw the graph of 2x + y = 6 and 2x – y + 2 = 0/ Shade the region bounded by these lines and x-axis. Find the area of the shaded region.
15. The cost of 5 oranges and 3 apples is Rs 30 and the cost of 2 oranges and 4 apples is Rs 26. Find the cost of an orange and an apple.
16. A two digit number is such that the product of its digit is 18. When 63 is subtracted from the numbers, the digits interchange their places. Find the number.
17. If the sum of first n terms of an A.P. is given by Sn = 3n2 +5n, find the nth term of the A.P.
OR If the sum of first 9 terms of an A.P. is 81 and that of first 17 terms is 289, find the sum of first n terms.
18. In figure, the line segment ST is parallel to side PR of ∆PQR and it divides the triangle into two parts of equal area. Find the ratio PS PQ . 3 * *
OR In the given figure, ABIIPQIICD, AB = x, CD = y and PQ = z, then prove that 1 x + 1 y = 1 z
19. Find the ratio in which the line x – y = 2 divides the line segment joining the points A(3,1) and B(8,9).
20. If the median of the distribution given below is 28.5, find the values of x and y : 3 Class interval 0-10 10-20 20-30 30-40 40-50 50-60 Total Frequency 5 x 20 15 y 5 60
21. Find the mean and mode age in years for the following frequency distribution : 3 Age (in years) 10-19 20-29 30-39 40-49 50-59 60-69 No. of persons 8 8 10 14 28 12
22. Two coins are tosses simultaneously. Find the probability of getting : 3 (i) Two heads (ii) No head
SECTION – D
23. Prove that √5 is an irrational number. 4
24. Find the values of a and b so that x4 + x3 + 8x2 +ax +b is divisible by x2 + 1.
25. Solve for x and y : 4
44 x+y + 30 x−y = 10
55 x+y + 40 x−y = 13
26. If -5, 2x2 + px -15 = 0 and roots of p(x2 +x) + k = 0 are equal, then find the value of p and k. OR Using quadratic formula, solve the following equation : abx2 + (b2 – ac)x –bc = 0
27. Find the value of the middle term of the A.P. 7, 13, 19..., 247.
28. State and prove the Basic Proportionality Theorem. 4 29. Show that points (1,7), (4,2), (-1,-1) and (-4,4) are the vertices of a square.
29. Show that points (1,7), (4,2), (-1,-1) and (-4,4) are the vertices of a square
30. Find the mean of the following distribution by step- deviation method : 4 Daily expenditure (in Rs) 100-150 150-200 200-250 250-300 300-350
No. of households 4 5 12 2 2
CLASS: X
SUBJECT – MATHEMATICS
TIME: 3HRS. M.M. 80
General Instructions :
1. All questions are compulsory.
2. The question paper consist of 30 questions divided into four sections A, B, C and D.
3. Section A contains 6 questions 1 mark each question.
4. Section B contains 6 questions 2 mark each question.
5. Section C contains 10 questions 3 mark each question.
6. Section D contains 8 questions 4 mark each question.
7. There is no overall choice. However, an internal choice has been provided in 4 questions of 3 marks each and 3 questions of 4 marks each. You have to attempt only on the alternatives in all such questions.
8. Use of calculator is not permitted.
SECTION – A
1. The decimal expansion of rational number 49/40 will terminate after how many places of decimal? 2. Check whether (x + 3)3 = x3 – 8 is a quadratic equation ?
3. Find the next term of the A.P. √8, √18, √32,…….
4. If ∆ABC ~ ∆DEF such that ∠A = 45 and ∠E = 56, then find the value of ∠C.
5. The ordinate of a point A on the y-axis is 5 and B has coordinates (-3, 1), then find the length of AB.
6. Two players, Rajiv and Raju play a badminton match. If the probability of Raju’s winning the match is 0.62, then find the probability of Rajiv’s winning.
SECTION - B
7. Show that any positive odd integer is of the for 4q + 1 or 4q + 3, where q is some positive integer.
8. Find a quadratic polynomial, the sum and product of whose zeroes are 5 and -2 respectively.
9. The ladder is placed against a wall such that its foot is at distance of 5m from the wall and its top reaches a window 5√3m above the ground. Find the length of ladder.
10. If the point (m,3) lies on the line segment joining the points
A(- 2 5 ,6) and B(2,8), find the value of m.
11. The following table shows the cumulative frequency distribution of marks of 800 students in an examination. Marks No. of Students Marks No. of Students Below 10 Below 20 Below 30 Below 40 Below 50 10 50 130 270 440 Below 60 Below 70 Below 80 Below 90 Below 100 570 670 740 780 800 Construct a frequency distribution table for the above data.
12. A card is drawn at random from a well-shuffled deck of 52 playing cards. Find the probability of getting neither a red colour card nor a queen.
SECTION - C
13. The traffic lights at three different road crossing change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 9:00 AM, at what time will they change simultaneously again ? 3
OR Find the HCF and LCM of 78, 52, 91 using the prime factorisation method.
14. Solve : 43x + 67y = -24 67 x + 43y = 24
OR Draw the graph of 2x + y = 6 and 2x – y + 2 = 0/ Shade the region bounded by these lines and x-axis. Find the area of the shaded region.
15. The cost of 5 oranges and 3 apples is Rs 30 and the cost of 2 oranges and 4 apples is Rs 26. Find the cost of an orange and an apple.
16. A two digit number is such that the product of its digit is 18. When 63 is subtracted from the numbers, the digits interchange their places. Find the number.
17. If the sum of first n terms of an A.P. is given by Sn = 3n2 +5n, find the nth term of the A.P.
OR If the sum of first 9 terms of an A.P. is 81 and that of first 17 terms is 289, find the sum of first n terms.
18. In figure, the line segment ST is parallel to side PR of ∆PQR and it divides the triangle into two parts of equal area. Find the ratio PS PQ . 3 * *
OR In the given figure, ABIIPQIICD, AB = x, CD = y and PQ = z, then prove that 1 x + 1 y = 1 z
19. Find the ratio in which the line x – y = 2 divides the line segment joining the points A(3,1) and B(8,9).
20. If the median of the distribution given below is 28.5, find the values of x and y : 3 Class interval 0-10 10-20 20-30 30-40 40-50 50-60 Total Frequency 5 x 20 15 y 5 60
21. Find the mean and mode age in years for the following frequency distribution : 3 Age (in years) 10-19 20-29 30-39 40-49 50-59 60-69 No. of persons 8 8 10 14 28 12
22. Two coins are tosses simultaneously. Find the probability of getting : 3 (i) Two heads (ii) No head
SECTION – D
23. Prove that √5 is an irrational number. 4
24. Find the values of a and b so that x4 + x3 + 8x2 +ax +b is divisible by x2 + 1.
25. Solve for x and y : 4
44 x+y + 30 x−y = 10
55 x+y + 40 x−y = 13
26. If -5, 2x2 + px -15 = 0 and roots of p(x2 +x) + k = 0 are equal, then find the value of p and k. OR Using quadratic formula, solve the following equation : abx2 + (b2 – ac)x –bc = 0
27. Find the value of the middle term of the A.P. 7, 13, 19..., 247.
28. State and prove the Basic Proportionality Theorem. 4 29. Show that points (1,7), (4,2), (-1,-1) and (-4,4) are the vertices of a square.
29. Show that points (1,7), (4,2), (-1,-1) and (-4,4) are the vertices of a square
30. Find the mean of the following distribution by step- deviation method : 4 Daily expenditure (in Rs) 100-150 150-200 200-250 250-300 300-350
No. of households 4 5 12 2 2
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