Mathematics Test 28

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Mathematics Test 28

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Weekly Quiz Competition

Question 1
4 / -1

Let f : R+ → R and f(x) = log_ex, R being the set of real numbers then which of the following is not correct?

A
f is onto

B
f is one-one

C
f is invertible

D
f is into

Solution

f(x) = log_ex is same as ln x defined over real positive numbers.
f(x) is onto because for every element in the codomain of f has at least one element in the domain of f. Thus, a function which is onto cannot be an into function.
f(x) is one-one and invertible too.
Question 2
4 / -1

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is

A
220

B
219

C
211

D
256

Solution

A × B will have 8 elements.
2⁸ − ⁸C₀ − ⁸C₁ − ⁸C₂= 256 − 1 − 8 − 28 = 219
Hence option B is correct.
Question 3
4 / -1

The number of 3 × 3 non–singular matrices, with four entries as 1 and all other entries as 0, is

A
less than 4

B
5

C
6

D
at least 7

Solution

Let's say that the first row has only one 0 and two 1s. We can have 6 such non-singular matrices. Let's say the first row has 2 zeros, which will give us 12 more cases. Hence the count will be more than 7