P(t) = P₀ e^{k t} ; P(0) = P₀ = 50 ; P(1) = 50 e^{k 1} = 250 ; e^k = 5 ; ln e^k = ln 5 ; k = ln 5 ; x = 50 e^{(ln5) 4} ; a = ln 5⁴ ; x = 50 e^a = 50 5⁴ = 10 5⁵ = 3.125. Correct answer is A.

Extend the given fractions to the common denominator 60.

Then we find that 7/12 =35/60, 3/5 = 36/60, 11/15 = 44/60, 14/20 = 42/60, and 23/30 = 46/60. The greatest number among these is, therefore, 23/30.  

4 x 25= 100

Correct answer is E.

f (x) = 7x - 3 and f ^–1(x)=(x+3)/7

Constant functions map every element from their domain to the same element of the range. We may therefore define a constant function for every element in the range. Since there are 9 different elements in the range we may write 9 different constant functions. 

x = ((7 . 5)^1/2 / 5^1/2) . (7 . 100)^1/2 = 70. Correct answer is E.

Let A = (-2, 5), B = (1, 6) be open intervals. Find A ? B, A ? B, and A \ B.  

A ? B = (–2, 6),      A ? B = (1, 5),      A \ B = (-2, 1]

As also understood from the information given, the correct answer is E. All of the statements in the options are correct.

6x-5=y›(y+5)/6=x›f^-1(x)=(x+5)/6

In order for the square root to make sense, the argument (the terms inside the square root) should not be negative. (2x - 12)^1/2 is the square root of 2x - 12. Therefore, the inequality 2x–12 ≥ 0 should be satisfied. This means that x ≥ 6 must be satisfied. Hence, the largest domain of definition of f is [6, ∞).  

5x+25≥0

5x ≥ -25

x ≥ - 5

The exponent of x must be 3 for a 3rd degree polynomial. So the answer is C.

if x=0 and x=2 are the roots of the equation then we can write x(x-2)=0, so x²-2x=0

The answer is E.

From the definition of the absolute value |b – a| = b – a since a < b and |a – c| = c - a since a < c. Therefore |b – a| + |a – c| = b – a + c – a  = -2a + b + c. 

Example

For given sets A and B assume that s(A) = 10, s(B) = 16 and s(A ? B) = 23. Find s(B \ A).

Solution

s(A ? B) = s(A) + s(B) – s(A ? B) = 10 + 16 – 23 = 3. Therefore s(A \ B) = 7 and  s(B \ A) = 13

As also understood form the solution given for the example, all of the statements in the options are correct, so the correct answer is E.

s(A ? B) = s(A) + s(B) – s(A ? B) = 20 + 26 – 33 = 13. Therefore s(A \ B) = 7 and  s(B \ A) = 13.

x² - 8x + 16 = 0

(x-4)² = 0

x-4 = 0

x = 4