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- 16. The total number of maps f : {1, 2, 3, 4, 5} → {1, 2, 3, 4, 5} such that f(6 − i) = f(i) for i = 1, 2, 3, 4, 5 is
  - 100
  - 125
  - 25
  - 115
- 17. If P and Q two matrices such that PQ = Q and QP = P, then P^3 + Q^3 =
  - 3P Q
  - 3QP
  - P + Q
  - P^3Q^3
- 18. If f(x) = sin(log10x) and h(x) = cos(log10x), then 1/2 (h(x/y ) + h(x/y)) − f(x)f(y) =
  - cos(log10(xy))
  - sin(log10(xy))
  - cos(log10(x/y))
  - sin(log10(x/y) )
- 19. The system of linear equations x + y + z = 2 x + 2y + z = −2 x + y + (λ − 5)z = λ has a unique solution, where λ ∈ R. Then
  - λ = 6
  - λ ̸= 6
  - λ = 2
  - λ ̸= 3
- 20. For 1 ≤ i ≤ n, 1 ≤ j ≤ n, aij =
  - 0
  - (−1) n^2
  - (−1)^n
  - (−1)^n(n+1)/2
- 21. Let A be 19 × 19 matrix whose entries in both the diagonals are all equal to 1 and all other entries are equal to 0. Then the rank(A) =
  - 9
  - 10
  - 11
  - 19
- 22. The highest power of 7 that divides 2022! is
  - 337
  - 334
  - 323
  - 345
- 23. Let a1, a2 ∈ R be such that |a1 − a2| = 10. Consider f(x) And Then the largest value of f(x) is
  - 15
  - 20
  - 25
  - 30
- 24. The letters of the word COVAXIN are permuted and all the permutations so formed are arranged in alphabetical order as in dictionary. Then the number of permutations which come before the word COVAXIN is
  - 916
  - 934
  - 892
  - 924
- 25. In how many ways can the 26 letters of the English alphabet be arranged such that no two vowels are next to each other in the arrangement?
  - A
  - B
  - C
  - D
- 26. What is the output of the following program?
  - Infinte loop
  - 13 10 7 4 1
  - 14 11 8 5 2
  - 15 12 8 5 2
- 27. Consider the code fragment written in C below :
  - Both P1 and P2.
  - P1 only.
  - P2 only.
  - neither P1 nor P2.
- 28. Consider the following C function:
  - 5
  - 6
  - 7
  - 8
- 29. What is the output of the following program?
  - 8,4,0,2,14
  - 8,4,0,2,0
  - 2,0,4,8,14
  - 2,0,4,8,0
- 30. Consider a Boolean function of n variables. The order of an algorithm that determines whether the Boolean function produces a output 1 is
  - logarithmic
  - linear
  - quadratic
  - exponentia
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