# Class 12 Mathematics Sample Paper Term 1 With Solutions Set E

Please refer to Class 12 Mathematics Sample Paper Term 1 With Solutions Set E below. These Class 12 Mathematics Sample Papers will help you to get more understanding of the type of questions expected in the upcoming exams. All sample guess papers for Mathematics Class 12 have been designed as per the latest examination pattern issued by CBSE. Please practice all Term 1 CBSE Sample Papers for Mathematics in Standard 12.

## Sample Paper Term 1 Class 12 Mathematics With Solutions Set E

Section A

1. The value of x in the set {0, 1, 2, 3, 4, 5} such that 73583 ≡ x (mod6) is
(a) 3
(b) 5
(c) 4
(d) 2

B

2. The value of 43 mod 6 is
(a) 0
(b) 1
(c) 2
(d) 3

B

3. The unit’s digit of 7100 is
(a) 1
(b) 7
(c) 2
(d) 4

A

4. If A is a matrix having 3 rows and 5 columns, then number of elements in matrix A is
(a) 15
(b) 10
(c) 8
(d) 16

A

B

6. If the cost function of a certain commodity is C(x) = 2000 + 50x – (1/5)x2, then the average cost of producing 5 units is
(a) ₹ 451
(b) ₹ 450
(c) ₹ 449
(d) ₹ 2245

C

7. The interval in which f (x) = (x + 2)e-x is decreasing is
(a) (- ∞, – 1)
(b) (- 1, ∞)
(c) (-1,1)
(d) R

B

8. The maximum value of the function f (x) = – (x – 1)2 + 2 , x ∈ R, is
(a) 1
(b) 2
(c) – 1
(d) – 2

B

9. In a meeting, 70% of the members favour of certain proposal, 30% being opposite. A member is selected at random and let X = 0 , if he opposed and X = 1, if he is in favour.
Then, E(X) is
(a) 3/10
(b) 5/10
(c) 7/10
(d) 9/10

C

10. Ten eggs are drawn successively with replacement from a lot containing 10% defective eggs. Then, the probability that there is atleast one defective egg is

D

11. As a result of tests on 20000 electric fans manufactured by a company, it was found that lifetime of the fans was normally distributed with an average life of 2040 h and standard deviation of 60 h. On the basis of the above information, the number of fans that is expected to run for more than 2150 h are
(a) 672
(b) 536
(c) 622
(d) 414

A

12. Suppose 2% of the bolts manufactured by the factory are defective. The probability of 5 defective bolts from a sample of 200 bolts is (use e-4 = 0.0183)
(a) 0.169
(b) 0.144
(c) 0.156
(d) 0.256

C

13. Most widely used weighted index is
(a) Paasche’s index
(b) Marshall-Edgeworth’s index
(c) Fisher’s ideal index
(d) Laspeyre’s index

D

14. Purchasing power of money is
(a) unequal to price index number
(b) equal to price index number
(c) reciprocal of price index number
(d) None of the above

C

15. The ratio of sum of products of the price relative with weights to sum of weights is called
(a) consumer price index
(b) whole sale price index
(c) rate of inflation
(d) None of these

A

16. If A and B are two square matrices of order 2 with |A|= 2 and |B|= 3, then the value of |7AB|is
(a) 294
(b) 290
(c) 221
(d) 42

A

A

18. Sourav purchased 30 kg of rice at the rate of ₹ 10 per kg and 35 kg at the rate of ₹ 11 per kg. He mixed these two varieties. He sell the mixture to make a 30% profit in the transaction at the price of
(a) ₹ 12.5
(b) ₹ 13
(c) ₹ 13.7
(d) ₹ 14.25

C

19. The solution set of the linear inequalities
(a) (- 23,2]
(b) (- 20, 4)
(c) [- 23,2)
(d) None of these

A

20. A, B and C started a business by investing ₹ 55000, ₹65000 and ₹ 75000 respectively. A is an active partner and gets 20% of the profit as working allowance and remaining is distributed in the proportion of their investment. If the money received by C is ₹ 27000.
The total profit is
(a) ₹ 87750
(b) ₹ 85500
(c) ₹ 76850
(d) ₹ 70200

A

Section B

21. The least non-negative remainder, when 89 X 111 X 135 is divided by 11 is
(a) 1
(b) 2
(c) 3
(d) 4

C

22. It is 7:00 pm currently. What time (in am or pm) will be in next 1500 h?
(a) 4:00 pm
(b) 4:00 am
(c) 7:00 pm
(d) 7:00 am

D

23. If A and B are symmetric matrices of same order, then (BA – AB) is a
(a) symmetric matrix
(b) skew-symmetric matrix
(c) zero matrix
(d) identity matrix

B

24. The tangent to the curve y = e2x at the point (0, 1) meets X-axis at

B

25. A right circular cylinder which is open at the top and has a given surface area, will have the greatest volume, if its height h and radius r are related by
(a) 2h = r
(b) h = 4r
(c) h = 2r
(d) h = r

D

26. The variance of the following distribution is

(a) 663/324
(b) 664/324
(c) 610/324
(d) 665/324

D

27. Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Then, P (only 3 cards are spades) is
(a) 45/512
(b) 45/256
(c) 49/512
(d) 56/512

A

28. If P(y < z < 1.5) = 0.4531, then the value of y is
(a) 0.5
(b) – 0.5
(c) 0.05
(d) – 0.05

D

29. If X has a Poisson distribution such that P(X = 3) = P(X = 4) , then the value P(X > 1) is
(a) 1 – 5e4
(b) 1 + 4e-4
(c) 1 – 5e-4
(d) None of these

C

30. For data regarding ∑p0 q0 = 500, ∑p1q0 = 510, ∑p0 q1 = 505 and ∑p1q1 = 550, where subscript 0 and 1 are used for base year and current year respectively. The Laspeyre’s price index is
(a) 115
(b) 110
(c) 112
(d) 118

B

31. The prices indexes for some commodities using Laspeyre’s and Passche’s method are 212.1 and 211.6 respectively. The Fisher’s prices index for the data is
(a) 211.8
(b) 212.5
(c) 214.4
(d) 216.2

A

32. The price relative of a goods in 2016 compared to 2014 is 125. If the cost of goods was ₹ 20 per kg in 2014, the cost of goods is 2016 is
(a) ₹ 35
(b) ₹ 30
(c) ₹ 25
(d) ₹ 22

C

33. The price and quantities of certain commodities are shown in the following table

If ratio of Laspeyre’s (L) and Paasche’s (P) index number i.e. L:P = 17 :18, then the value of x is
(a) 4
(b) 2
(c) 3
(d) 1

C

34. The index number which measures the average change in prices paid by the specific class of consumers for goods and services consumed by them in the current year in comparison with base year is called
(a) cost of living index
(b) Paasche’s index
(c) Fisher’s index
(d) Bowley’s index

A

(a) (1 – x3)
(b) (1 – x3)2
(c) (1 + x3)
(d) (1 + x3)2

B

36. As an active partner, A receives 1/10 of the total profit of a business and the remaining profit is shared by A and B in the ratio of 4 : 5. If the total profit received by A is ₹ 325, then B receive
(a) ₹ 325
(b) ₹ 425
(c) ₹ 350
(d) ₹ 375

A

37. A sailor sails a distance of 72 km along with the flow of a river in 6 h. If it takes 18 h to return at the same point, then the speed of the flow of the river is
(a) 3 km/h
(b) 2 km/h
(c) 4 km/h
(d) 5 km/h

C

38. Two pipes can fill a tank in 10 h and 16 h, respectively. A third pipe can empty the tank in 32 h. If all the three pipes function simultaneously, then the tank will be filled in

B

B

(a) 3I
(b) 5I
(c) 7I
(d) None of these

C

Section C

41. The probability that a man age 60 yr will die within year is 0.01245. The probability that out of 16 such men atleast 15 will reach their sixty first birthday is ( use e-0 1992 = 0 819 )
(a) 0.365
(b) 0.982
(c) 0.695
(d) 0.692

B

42. There are 4 cards numbered 1, 3, 5 and 7, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two drawn cards. Then, the mean of X is
(a) 8
(b) 6
(c) 4
(d) 2

A

43. The values of ‘a’ for which the function f (x) = (a + 2)x3 – 3ax2 + 9ax – 1 decreases for all real values of x, is
(a) (- ∞, – 3)
(b) (- 3, ∞)
(c) (- ∞, 3)
(d) (3, ∞)

A

44. A container contains 10 L mixture in which there is 10% sulphuric acid. The quantity of sulphuric acid that has to be added to make the solution containing 25% sulphuric acid is
(a) 2 L
(b) 1 L
(c) 4 L
(d) None of these

A

45. A boat covers 24 km upstream and 36 km downstream in 6 h while it covers 36 km upstream and 24 km downstream in 6(1/2)h. The speed of the current is
(a) 10 km/h
(b) 1 km/h
(c) 3 km/h
(d) 2 km/h

A

Case Study
Suppose two parametric functions, say y = f (t) and x = g(t), are given to us and we have to find their second order derivative, i.e. d2y/dx2 then we use the following steps

I. First, write the given functions and differentiate them w.r.t. parameters.
i.e. Let y = f (t) and x = f (t), then find

II. Divide derivative of first function by derivative of second function, i.e. put the values of

III. Now, differentiate Eq. (i) w.r.t. x to get required second order derivative,

Now, we have, x = 4at2 and y = 6at
On the basis of above information, answer the following questions.

46. dx/dt is equal to
(a) 4at
(b) 8at
(c) 4a
(d) 8a

B

47. dy/dt is equal to
(a) 6a
(b) 4a
(c) 2a
(d) a

A

48. dy/dx is equal to
(a) 3/4t
(b) 4t/3
(c) 0
(d) None of these

A

49. d2y/dx2 is equal to
(a) 32/3at3
(b) 3/32at3
(c) -32/3at3
(d) -3/32at3