# Class 12 Mathematics Sample Paper Term 1 Set E

Please refer to Class 12 Mathematics Sample Paper Term 1 Set E with solutions below. The following CBSE Sample Paper for Class 12 Mathematics has been prepared as per the latest pattern and examination guidelines issued by CBSE. By practicing the Mathematics Sample Paper for Class 12 students will be able to improve their understanding of the subject and get more marks.

## CBSE Class 12 Mathematics Sample Paper for Term 1

Section A

1. The value of 612 (mod 7) is
(a) 0
(b) 3
(c) 5
(d) 1

D

2. (9 X 8)mod 5 is equal to
(a) 0
(b) 1
(c) 2
(d) 3

C

3. The unit digit in 3300 is
(a) 1
(b) 2
(c) 3
(d) 6

A

A

A

6. The cost function C(x) of a firm is given by C(x) = 2x2 – 4x + 5. Then, value of average cost when 10 units are produced is (in ₹)
(a) 14.5
(b) 15.5
(c) 16.5
(d) 17.5

C

7. The minimum value of f (x) = xex is
(a) e
(b) – e
(c) 1/e
(d) – (1/e)

D

8. The interval in which f (x) = 1 – (1/x) is strictly increasing is
(a) (- ∞, 0)
(b) (0,∞)
(c) (- ∞, ∞)
(d) None of these

D

9. If the probability that a person is not a swimmer is 0.3, then the probability that out of 5 persons 4 are swimmers is
(a) 5C4(0.7)4 (0.3)4
(b) 5C1(0.7) (0.3)4
(c) 5C4(0.7) (0.3)4
(d) (0.7)4 (0.3)

A

10. A die is thrown thrice getting a even number is considered a success. The mean of the Binomial distribution is
(a) 1/2
(b) 1
(c) 3/2
(d) 2

C

11. Out of 1000 balls, 50 are red and the rest white. If 60 balls are picked at random, then the probability of picking up 3 red balls is
(a) 0.3214
(b) 0.2341
(c) 0.3241
(d) 0.2241

D

12. The problems which frequently occur in the construction of index number is
(a) selection of number of items
(b) selection of an appropriate method
(c) selection of base period
(d) All of these

D

13. If along with base prices and current prices of a number of items, the weights of each item are given, then the index number based on weighted aggregates is given by

B

A

(a) 1
(b) ± √2
(c) ± √3
(d) 0

C

16. If the points (0, 2), (1, x) and (3, 1) are collinear, then the value of x is
(a) 3/5
(b) 5/3
(c) 1
(d) 0

B

17. In a 1000 m Race. A beat B by 80 m or 20 s. The time taken by A to complete the race
(a) 230 m
(b) 240 m
(c) 210 m
(d) 200 m

A

18. A cistern is normally filled in 8 h but takes 2 h more to fill because of a leak in its bottom. If the cistern is full, then the leak will make it empty in
(a) 16 h
(b) 20 h
(c) 32 h
(d) 40 h

D

19. The speed of boat in still water is 500% more than the speed of current. The respective ratio between the speed of the boat downstream and speed of the boat upstream is
(a) 9 : 2
(b) 7 : 3
(c) 7 : 5
(d) 9 : 4

C

20. Ramesh started a business by investing ₹ 30000. Six months later, Yogesh joined the same business by investing ₹15000. If they make a profit of ₹10000 at the end of the year. Ramesh share will be
(a) ₹8000
(b) ₹7500
(c) ₹6000
(d) ₹2000

A

Section B

21. The least non-negative remainder when 175 X 375 X 69 is divided by 17 is
(a) 1
(b) 5
(c) 7
(d) 11

B

22. The value of x in the set {0, 1, 2, …, 10} satisfying 3 – x ≡ 5 (mod 11) is
(a) 10
(b) 9
(c) 8
(d) 2

B

C

24. If y = x(x – 3) 2 decreases for the value of x given by
(a) 1 < x < 3
(b) x < 0
(c) x > 0
(d) 0 < x < 3/2

A

25. The points at which the tangents to the curve y = x3 – 12x + 18 are parallel to X-axis are
(a) (2, – 2) and (-2, – 34)
(b) (2, 34) and (- 2, 0)
(c) (0,34) and (- 2,0)
(d) (2, 2) and (- 2, 34)

D

26. The monthly mess bill of a student who is staying in a hostel follow a normal distribution with a mean of ₹ 2000 and a standard deviation of ₹ 200. The probability that in the next month his bill will go above ₹ 2400, is
(a) 0.141
(b) 0.143
(c) 0.0228
(d) 0.227

C

27. There are 500 items in a box. The probability that any one of them will be defective is 0.01. Assuming Poisson distribution, the probability that at least one of the items is defective is
(a) e5 – 1/e5
(b) 1 – e5
(c) e5 + 1/e5
(d) none of these

A

28. In an examination, 10% of the candidate score more than 75 marks and 30% of the candidate score less than 40 marks. If the distribution of marks is normal, then the standard deviation is
(a) 17.45
(b) 16.32
(c) 19.44
(d) 18.75

C

29. For data regarding, some commodities the price index using Laspeyre’s and Paasche’s method are 234.4 and 242.6, respectively. The Fisher’s price index for the data is
(a) 256.37
(b) 275.84
(c) 219.28
(d) 238.46

D

30. The index number are classified as
(a) price indexes
(b) quantity indexes
(c) value index
(d) All of these

D

31. For data regarding to ∑p0q0 = 160, ∑p0q1 = 180, ∑p1q0 = 185 and ∑p1q = 200, where subscript 0 and 1 are used for base year and current year respectively. The Laspeyre’s price index is
(a) 125
(b) 135
(c) 120
(d) 140

A

32. Given that, p0q0 = 468, ∑p1q0 = 478, ∑p0q1= 482 and ∑p1q1 = 512, where subscript 0 and 1 are used for base year and current year respectively. The Paasche’s index number is
(a) 108.54
(b) 106.22
(c) 112.63
(d) 110.79

B

D

(a) 73
(b) – 73
(c) 70
(d) – 70

B

(a) 4abc
(b) 4a2bc
(c) 4a2b2c2
(d) – 4a2b2c2

C

36. In a games of 100 points, A give C 28 points and B 20 points, then how many points B can give to C is
(a) 11
(b) 10
(c) 20
(d) 15

B

A

38. The speed of a boat in still water is 10 km/h. If it can travel 26 km downstream and 14 km upstream in the same time, the speed of the stream is
(a) 3 km/h
(b) 4 km/h
(c) 5 km/h
(d) None of these

A

39. A, B and C enter into a partnership and their shares are in the ratio

After 2 months, A withdraws half of his capital and after 10 months more, a profit of ₹ 378 is divided among them. Then, B’s share is
(a) ₹129
(b) ₹144
(c) ₹156
(d) ₹168

B

40. From a container, full of pure milk, 20% is replaced by water and this process is repeated three times. At the end of third operation, the quantity of pure milk reduces to
(a) 40.0%
(b) 50.0%
(c) 51.2%
(d) 58.8%

C

Section C

41. If a two sector economy, the input-output efficient matrix is

If the final demands of two sector’s are 20 and 30, then the gross output is given by

C

42. The price relative of a commodities in 2018 compared to 2016 is 168, if the cost of good was ₹ 24 per kg in 2016, the cost of goods in 2018 is
(a) ₹ 35.26
(b) ₹ 37.29
(c) ₹ 40.32
(d) ₹ 45.34

C

43. If the length of three sides of a trapezium other than base are equal to 10 cm, then the area of trapezium when it is maximum, is (in cm2 )
(a) 75√3
(b) 75√3/2
(c) 25√3
(d) 25√3/2

A

44. If a rectangle of maximum perimeter which can be inscribed in a circle of radius a, then rectangle is a square of side is
(a) 2a
(b) a
(c) 2a
(d) a/√2

D

45. If two pipes alone can fill a tank in 6 h and 7 h, respectively. If each pipe is opened one by one for 1 h, then time taken to fill the tank is

C

Case Study
A random variable X has following probability distribution.

Based on the above information, answer the following.

46. The value of k is
(a) 1/10
(b) 1/20
(c) – 1
(d) 1/18

A

47. P(X < 3) is equal to
(a) 1/10
(b) 2/10
(c) 3/10
(d) 4/10

C

48. P(X > 6) is equal to
(a) 13/100
(b) 15/100
(c) 17/100
(d) 19/100

C

49. P(0 < X < 3) is equal to
(a) 1/10
(b) 2/10
(c) 3/10
(d) 4/10