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3/22/2019

Linear Algebra Test

Linear Algebra Test Published By - SB TechMath

Editor - Sunil Bansal

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Single Correct Questions 20x2=40 2. Q.1

Mark only one oval. 75 80 60 5 3. Q.2

Mark only one oval. A and B are correct. B and C are correct. C and D are correct. A and D are correct 4. Q.3 Let A be a matrix of size mxn, then Mark only one oval. Rank(A) = n Null (A) = n Rank(A) + Null(A) = n Rank(A) + Null(A) = m

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5. Q.4 Consider the matrix P of size mxn and Q be of the of size nxm such that PQ=I, then Mark only one oval. Rank (P) = n Rank (Q) = n Rank (P) = m Rank (Q) < m 6. Q.5 For which set of the values of “a”, Ax=0 has nontrivial solution, where A equals to

Mark only one oval. {1} {-1} {-1, 0} {-1, 1}

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7. Q.6

Mark only one oval.

Option 1

Option 2

Option 3

Option 4

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8. Q.7

Mark only one oval.

Option 1

Option 2

Option 3

Option 4

9. Q.8

Mark only one oval. All are positive definite Only A, B and D Only A and B Only B and D

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10. Q.9

Mark only one oval. 45/3 46/3 46/5 23/3 11. Q.10

Mark only one oval. 38 76 39 0 12. Q.11

Mark only one oval. 0 6 -6 -9 13. Q.12

Mark only one oval. Less than n Less than or equal to n Exactly n None of these https://docs.google.com/forms/d/1SJaBGWDBfpvE08cTPJ9kifp9fZ7vlA3QlNqKhJ9O3ik/edit

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14. Q.13

Mark only one oval.

Option 1

Option 2

Option 3

Option 4

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15. Q.14

Mark only one oval.

Option 1

Option 2

Option 3

Option 4

16. Q.15

Mark only one oval. 1 2 3 4

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17. Q.16

Mark only one oval.

Option 1

Option 2

Option 3

Option 4

18. Q.17

Mark only one oval. 0 1 1/sqrt3 1/3

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19. Q.18

Mark only one oval. if n=1, then system has infinite solution. if rank(A:b)
Mark only one oval. 13 16 82 81 21. Q.20 Find the rank of B.

Mark only one oval. 2n-4 3n 3n-3 2

Multiple Correct Answer Type 5x4=20

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22. Q.21 Multiple correct answer type

Check all that apply.

Option 1

Option 2

Option 3

Option 4

23. Q.22 Multiple correct answer type

Check all that apply. Rank(T) + Null(T) = 7 Rank(T) - Null(T) = 7 Null(T) = 7 Dim (Ker T) = 0

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24. Q.23 Multiple correct answer type

Check all that apply. m[F]= [2 1 -7 -1]' m[F]= [2 1 -7 -1] dim(kerF) = 3 F is onto transformation 25. Q.24 Multiple correct answer type

Check all that apply.

Option 1

Option 2

Option 3

Option 4

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26. Q.25 Multiple correct answer type

Check all that apply. T is one one T is onto T is singular det(T)= {-1, 1}

Aptitude Section 5x2=10 27. Q.1- A and B together can complete a job in 16 days. Both B and C, working alone can finish the same job in 12 days, A and B commence work on the job, and work for 4 days, where upon A leaves, B continues for 2 more days, and then he leaves too, C now starts working, and finishes the job. How many days will C require? Mark only one oval. 5 8 3 7 28. Q.2- 10 5 5 10 40 ? Mark only one oval. 350 320 360 370 29. Q.3- If the average marks of 1/5th of class is 70% and 2/5th class is 45% and the average mark of remaining class is 60%, then the average % of the whole class is Mark only one oval. 73% 45% 62% 56%

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30. Q.4- An alloy contains Brass, Iron and Zinc in the ratio 2:3:1 and another contains Iron, zinc and lead in the ratio 5:4:3.If equal weights of both alloys are melted together to form a third alloy, then what will be the weight of lead per kg in new alloy? Mark only one oval. 46/9 1/4 29/7 1/8 31. Q.5- The present age of a boy is obtained by 2 times his age after 2 years, subtracted by 2 times his age before 2 years. Find his present age Mark only one oval. 12 8 9 10 32. ∑

33. ∑

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