Welcome to your Maths 2009
2.
A team of 10 researchers consist 4 biologists and 6 chemists. If 3 persons are chosen randomly from the team, what is the probability that at least one is a biologist?
3.
The probability that an electronic device produced by a company does not function properly is equal to 0.1. If 2 devices are bought, then what is the probability that at least one device function properly? Not Answered
4.
Two machines A and B produce respectively 60% and 40% of the total number of items of a factory. The percentages of defective output of these machines are 2% and 5%, respectively. If an item is selected at random, then what is the probability that the item is defective?
5.
In how many ways can a committee of 3 members be formed from 7 candidates?
6.
The following is a frequency distribution table of a grouped data with variable X.
7.
The expenditure of 100 families is given below.
8.
The first group of 10 children has a mean weight of 15.6kg, the second group of another 10 children has a mean weight of 16kg, and the third group of children has a mean weight of 20kg. If the mean weight of all the children is 17kg, what is the total number of children in all of the three group?
9.
Which of the following is a valid argument?
10.
Consider the following open propositions: P(x) =x is a prime number, C(x) =x is a composite number, and E(x) =x is an even number, which one of the following has a truth value of True in the set of positive integers?
11.
Which of the following functions is a one to one correspondence?
12.
If f(x)=√x3 and (f ∘ g)(x)= ∜x, then what is the value of g(8)?
13.
Which one of the following is the inverse of f(x) = 8x3 + 2?
16.
What is the equation of a line that passes through point (a, a) in xy-plane if it is parallel to a line that passes through points (a, b) and (b, a) where a ≠ b?
17.
What are the values of the center (C) and radius (r) of a circle x2 + y2 - 4x + 6y = 5?
18.
What is the radius of the largest possible circle that can be inscribed in the ellipse given by 5(x - 1)2 + 3y2 = 15?
20.
Let p and q stands for the statements "Nejat is intelligent" and "Almaze is hardworking". Respectively, which of the following represent the statement "Almaze is hardworking if Nejat is intelligent"?
21.
Let f be differentiable function with f(1) = -1 and f '(1)= 1.
22.
If f(x) = ln(x2 + 2), then what is the value of f ''(1)?
24.
What is the equation of the tangent line to the graph of f(x) =3x2 + 4x - 5 at (1, 2)?
25.
If f(x) = π2 + 1, then what is the value of f'(x)?
26.
Suppose f is continuous on [2, 6] and the only solutions of the equation f(x) = 7 are x = 2 and x = 5. If f(3) = 9, then one of the following Can Not be the value of f(4)?
36.
Which of the following relations holds for the sequence: -10, -3, 4, 11,...?
39.
Suppose a radioactive material loses one third of its mass per year. If its current mass is 81g, then how much will its mass be just after 7 years?
40.
Which one of the following is a convergent sequence?
41.
What is the value of the area of the region enclosed by the graph of f(x) = ex and g(x) = x between the lines x = -1 and x = 1?
44.
A particle moves along the x-axis with velocity given by v(t) = 3t2 + 6t for time t = 0. If the particle is at position x = 2 at a time t = 0, what is the position of the particle at t = 1?
47.
Suppose f:(-∞, ∞) ⟶ R is differentiable and the graph of its derivative y = f '(x), is as shown in the figure below. Which one of the following is true about f?
48.
If 2 ≤ f'(x) ≤ 4 for all values of x, then the value of f(8) - f(2) is between which of the following numbers?
50.
A tin can of volume 54πcm3 is to be made in the form of a right circular cylinder that has both flat top and flat bottom. What is the base radius of the tin if it is to be made of the least amount of metal?
51.
Air is being pumped into a spherical balloon so that its volume increase at a rate of 50 cm3/s. How fast is the radius of the balloon increasing when the diameter is 5 cm?
52.
Which one of the following is a valid assertion that can be proved by principle of mathematical induction?
53.
Consider the assertion: "The sum of positive irrational numbers is positive irrational number". Which one of the following is correct about the assertion?
54.
Suppose "If x ∈ A, then y ∈ B" is a True statement. Then, which one of the following is necessarily true?
56.
If P(2, √5, 1) and Q(3, 0, 9) are points on a sphere whose center is on z-axis, then which one of the following point is outside of the sphere?
57.
If A(x, 0, 2), B(3, 0, 2) and C(2, √3, 2) are vertices of an equilateral triangle in space, then what is the value of x?
58.
A patrol boat on a sea sailed from its station 7km to the North; and changed its course and sailed 4√2 km in the direction of 450 South-East. What is the shortest (straight) distance the boat should travel in order to return to its station?
61.
A line given by the vector equation (x, y)=(-t, 6+2t), t ∈ ℜ, is tangent to a circle at a point (1, 4). What is the radius of the circle if its center is on the y-axis?
62.
What is the translation vector u=(h, k) so that the equation x2 + 2y2 + 6x - 8y + 15 = 0 is transformed to an equation of the form x2 + 2y2 + d = 0, where d is constant?
63.
If cotθ = √8 and θ is first quadrant angle, then what is the value of cscθ?
64.
If θ = arctan(2), then what is the value of sin(2θ)?
65.
Which one of the following is true?
