Logarithms

Question 1

Multiple choice

Which of the following functions will produce a value 10 if x = 9.7?

log
floor
abs
ceil
round

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Answer

$\Theta$ (n²logn)

Answer

f (n) = 0(g(n)) and g(n) $\ne$Y 0(f (n))

Answer

$\frac{(3^{k+1}-1)}{2}$

Answer

A = 957 B = 2055 C = 720

Answer

$\frac{343}{125}$

Answer

O(n log n)

Answer

O(lognloglogn)

Question 2

Multiple choice

If Log (P) = (1/2) Log (Q) = (1/3) Log (R), then which of the following options is TRUE?

P² = Q³R²
Q² = PR
Q² = R³P
R = P²Q²

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Question 3

Multiple choice

Consider the following function.

int unknown (int n) {
    int i, j, k 0;
    for i n / 2; i &lt;- n; i + +)
    for j = 2; j &lt;- n; j = j * 2
    k = k + n / 2;
    return (k);
}

$\Theta$ (n²)
$\Theta$ (n³)
$\Theta$ (n³logn)

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Question 4

Multiple choice

What does the following algorithm approximate? (Assume m>1,

log m
m²
m^1/2
m^1/3

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Question 5

Multiple choice

Let f (n) = n2 logn and g(n) = n(logn)10 be two positive functions of n. Which of the following statements is correct?

g (n) = 0(f (n)) and f (n) $\ne$Y 0(g(n))
f (n) $\ne$Y 0(g(n)) and g(n) $\ne$Y 0(f (n))
f (n) = 0(g(n)) and g(n) = 0(f (n))

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Question 6

Multiple choice

The solution to the recurrence equation $T(2^k) = 3T(2^{k-1})+1, T(1) =1$ is

$2^k$
$3^{\log_2 k}$
$2^{\log_3 k}$

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Question 7

Multiple choice

If the solution of the previous question was the log at the time of crash, then what will be the output of A, B and C after recovery?

A = 1050 B = 2055 C = 720
A = 957 B = 2055 C = 640
None of these

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Question 8

Multiple choice

If log ^{$x(\frac{5}{7}) = - \frac{1}{3}$}, then the value of x is

$\frac{125}{343}$
$\frac{-25}{49}$
$\frac{-49}{25}$

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Question 9

Multiple choice

log tan 1^o + log tan 2^o + ..... + log tan 89^o is

1
$\frac{1}{\sqrt{2}}$
0
– 1

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Question 10

Multiple choice

Directions: Find the time complexities of the following question.

T(n)=T(n-1)+logn

O(n²)
O(n)
O(log n)

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Question 11

Multiple choice

Directions: Find the time complexities of the following question.

T(n)=T(n-2)+2logn

O(n²)
O(n^log3)
O(n)
O(log n)

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Question 12

Multiple choice

Directions: Find the time complexities of the following question.

T(n)=2T(√n)+logn

O(n²)
O(n^log3)
O(log n)

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Question 13

Multiple choice

The value of log 256 to base 4 is

4
16
5
9
None of these

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Question 14

Multiple choice

The value of log 5 is (Given: log 2 = 0.3010)

0.6990
1.6990
0.3010
0.1555
None of these

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Question 15

Multiple choice

The value of log 0.00001 is

- 2
- 3
- 5
- 4
None of these

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Logarithms

Logarithms Questions