# CBSE Class 12 Mathematics Term 1 Sample Paper Set E

See below CBSE Class 12 Mathematics Term 1 Sample Paper Set E with solutions. We have provided CBSE Sample Papers for Class 12 Mathematics as per the latest paper pattern issued by CBSE for the current academic year. All sample papers provided by our Class 12 Mathematics teachers are with answers. You can see the sample paper given below and use them for more practice for Class 12 Mathematics examination.

## CBSE Sample Paper for Class 12 Mathematics Term 1 Set E

Section A

1. Find (482 X 813)mod7.
(a) 6
(b) 0
(c) 3
(d) 4

A

2. The least positive integer x satisfying 28 ≡ x(mod6) is
(a) 2
(b) 4
(c) 3
(d) 1

B

A

(a) 3 X 2
(b) 3 X 3
(c) 2 X 3
(d) 2 X 2

B

5. The least value of f(x) = ex+e -x is
(a) 0
(b) 1
(c) 2
(d) – 2

C

6. The interval on which f (x) = ex2 is decreasing, is
(a) (- ∞,1)
(b) (1, ∞)
(c) (- ∞, ∞)
(d) None of these

D

7. If the tangent line at a point (x, y) on the curve y = f (x) is parallel to X-axis, then the value of dy/dx is
(a) 0
(b) ∞
(c) 1
(d) None of these

A

8. Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. Then, the possible values of X are
(a) 0, 1, 3 and 5
(b) 0, 1, 2 and 3
(c) 0, 1, 2 and 4
(d) 0, 2, 4 and 6

D

9. The probability distribution of a random variable X is given below

The value of P(X < 2) is
(a) 14/16
(b) 1/15
(c) 13/16
(d) 14/15

D

10. Let X is a normal variable with mean 60 and standard deviation 5. If P(X > a) = 0.7881, then the value of a is
(a) 56
(b) 69
(c) 72
(d) 53

A

11. If a box has 100 pens of which 10 are defective, then what is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?

D

12. If all the values are not of equal importance the index is called
(a) simple
(b) unweight
(c) weighted
(d) None of these

C

13. Consumer price index numbers are obtained by
(a) Paasche’s index
(b) Fisher’s idea index
(c) Laspeyre’s index
(d) Marshall-Edgeworth’s

C

B

(a) 10
(b) 8
(c) 14
(d) 4

B

(a) 3
(b) 2
(c) 1
(d) 0

A

17. In 1 km, P beats T by 48 m in 6 s. The P’s time over the course is
(a) 118 s
(b) 138 s
(c) 119 s
(d) 117 s

C

18. The solution set of 5x – 3 < 3x + 1 is
(a) (2, ∞)
(b) (- ∞,2)
(c) (- ∞, ∞)
(d) None of these

B

19. A boat running downstream covers a distance of 20 km in 2 h while it covers the same distance upstream in 5 h. The speed of the boat in still water is
(a) 7 km/h
(b) 8 km/h
(c) 9 km/h
(d) 10 km/h

A

((a) A2 = I
(b) A2 = – I
(c) A2 = 2I
(d) None of these

B

Section B

21. The remainder when 561 is divided by 7 is
(a) 1
(b) 2
(c) 4
(d) 5

D

22. The unit digit in 1337 is
(a) 1
(b) 3
(c) 7
(d) 9

B

23. The least non-negative remainder, when 64 X 65 X 66 is divided by 67 is
(a) 1
(b) 5
(c) 13
(d) 61

D

(a) 10
(b) 16
(c) 32
(d) 8

D

25. A monopolistic demand function is P = 300 – 50x, then the price at which marginal revenue is zero, is
(a) 1
(b) 2
(c) 3
(d) 4

C

26. The normal at point (1, 1) of the curve y2 = x3  is parallel to the line
(a) 3x – y -2 = 0
(b) 2x +3y -7 = 0
(c) 2x -3y +1 = 0
(d) 2y -3x +1 = 0

B

27. Three cards are drawn successively with replacement from a well-shuffled pack of 52 cards. The variance of the number of red cards is
(a) 1/4
(b) 1/2
(c) 3/4
(d) 1

C

28. The probability of throwing at most 2 sixes in 6 throws of a single die is

A

29. If a random variable X follows Poisson’s distribution such that
P(X = 2) = 9 · P(X = 4) + 90 · P(X = 6)
The mean of X is
(a) 9
(b) 3
(c) 1
(d) 15

C

30. The mean weight of 800 items is 66 kg and 89 items has weight more than or equal to 72 kg. If the item are distributed normally, then the number of times having weight less than 55 kg is
(a) 10
(b) 7
(c) 9
(d) 8

A

(a) x/y
(b) – x/y
(c) y/x
(d) – y/x

C

(a) 1
(b) 0
(c) 2
(d) a + b + c

B

D

A

35. A, B and C are three participants in 1 km race. If A can give ‘B’ a start of 40 m and B can give ‘C’ a start of 25 m. Then, A can give ‘C’ a start of
(a) 64 m
(b) 74 m
(c) 936 m
(d) 975 m

A

36. An alloy contains copper, zinc and nickel in the ratio of 5 : 3 : 2. The quantity of nickel in kg that must be added to 100 kg of this alloy to have the new ratio 5 : 3 : 3 is
(a) 8 kg
(b) 10 kg
(c) 12 kg
(d) 15 kg

B

37. A boat goes 40 km upstream in 8 h and 36 km downstream in 6 h. The speed of the boat in still water is
(a) 6.5 km/h
(b) 5.5 km/h
(c) 6 km/h
(d) 5 km/h

B

38. Pipes A and B can fill a tank in 12 min and 16 min, respectively. Both pipes A and B are opened for 4 min and then A is closed. The extra time B will take to fill the tank completely is

A

39. Shiv Kumar started a business by investing ₹ 25000 in 2010. In 2011, he invested an additional amount of ₹ 10000 and Rakesh joined him with an amount of ₹ 35000. In 2012, Shiv Kumar again invested another additional amount of ₹ 10000 and Suresh joined them with an amount of ₹ 35000. Rakesh’s share in the profit of ₹ 150000 earned at the end of three years from the start of the business in 2010 is
(a) ₹ 70000
(b) ₹ 50000
(c) ₹ 45000
(d) ₹ 75000

B

40. The values of positive numbers x and y such that x + y = 60 and xy3 is maximum, is
(a) 45 and 15
(b) 30 and 30
(c) 15 and 45
(d) 40 and 20

A

Section C

41. The variance and standard deviation of the number of heads in three tosses of a coin are respectively

A

42. If X has a Poisson distribution such that P(X = 1) = 1/2, P(X = 0) + P(X = 2), then P(X = 4) is
(a) 1/24e
(b) 1/12e
(c) e/24
(d) e/12

A

43. If the total cost function is given by C(x) = a + bx + cx2 , then

B

44. There are three vessels of same volume containing milk and water in the ratio of 2 : 3, 3 : 2 and 5 : 4. The content of these three vessels is poured into an another vessel of large volume, then the ratio of milk and water in this vessel is
(a) 14 : 13
(b) 14 : 11
(c) 70 : 69
(d) 13 : 15

B

45. A, B and C are three taps connected to a tank. A and B together can fill the tank in 6 h, B and C together can fill it in 10 h and A and C together can fill it in 7(1/2)h. The time taken by C alone to fill the tank is
(a) 10 h
(b) 12 h
(c) 20 h
(d) 30 h

D

Case Study
Consider the following data that shows price and quantity for the year 2013 and 2015 respectively

Based on the above information, answer the following questions

46. Laspeyre’s index is
(a) 140.56
(b) 135.12
(c) 129.64
(d) 141.72

B

47. Paasche’s index is
(a) 128.19
(b) 145.42
(c) 136.40
(d) 154.78

C

48. Fisher’s index is
(a) 135.50
(b) 139.85
(c) 131.26
(d) 136.43

A

49. Bowley’s index is
(a) 146.54
(b) 128.46
(c) 131.4
(d) 135.5