1.
Consider the graph of the function y=2^x.
At what point will this graph intersect the x-axis?
Correct Answer
D. Never intersects x-axis
Explanation
The graph of the function y=2^x will never intersect the x-axis because the exponential function 2^x is always positive for any value of x. Since the x-axis represents the y-coordinate of 0, and the function is always positive, it will never cross or intersect the x-axis.
2.
What type of function is shown by the graph at the right?
Correct Answer
C. Quadratic
Explanation
The graph at the right shows a U-shaped curve, which is characteristic of a quadratic function. A quadratic function is a polynomial function of degree 2, and its graph is a parabola. Therefore, the correct answer is quadratic.
3.
Which statement is true about the relation shown at the right?
Correct Answer
D. It is not a function because there are multiple y-values for a given x-value.
Explanation
The given relation is not a function because there are multiple y-values for a given x-value. In a function, each input (x-coordinate) should have only one output (y-coordinate), but in this case, there are multiple outputs for some inputs. Therefore, the relation does not satisfy the definition of a function.
4.
If g (x) = 3x² - 2x - 5, what is the value of g (-1)?
Correct Answer
D. 0
Explanation
The value of g(-1) can be found by substituting -1 into the equation for g(x). When we do this, we get g(-1) = 3(-1)^2 - 2(-1) - 5 = 3 - (-2) - 5 = 3 + 2 - 5 = 5 - 5 = 0. Therefore, the value of g(-1) is 0.
5.
Which of the following sets is a subset of {2, 4, 6, 8, 10, 12}?
Correct Answer
C. {4,8,12}
Explanation
The set {4,8,12} is a subset of {2, 4, 6, 8, 10, 12} because all of its elements (4, 8, and 12) are also present in the larger set.
6.
If f (x) = -3x - 5, what is the value of f (2) ?
Correct Answer
A. -11
Explanation
The given function f(x) = -3x - 5 represents a linear equation. To find the value of f(2), we substitute x = 2 into the equation. Therefore, f(2) = -3(2) - 5 = -6 - 5 = -11.
7.
How many onto functions can be defined from the set A = {1, 2, 3, 4} to {a, b, c}?
Correct Answer
C. 36
Explanation
The number of onto functions from set A to set B can be calculated by taking the number of elements in set B raised to the power of the number of elements in set A, and then subtracting the number of elements in set B. In this case, set A has 4 elements and set B has 3 elements, so the number of onto functions is 3^4 - 3 = 36.
8.
F(x + y) = f(x)f(y) for all x, y, f(4) = + 3 what is f(–8)?
Correct Answer
B. 1/9
Explanation
The given equation f(x + y) = f(x)f(y) implies that the function f is multiplicative. We are given that f(4) = 3, so we can substitute x = 4 and y = -12 (since 4 + (-12) = -8) into the equation to find f(-8). This gives us f(-8) = f(4)f(-12) = 3f(-12). Since f(-8) is equal to 1/9 according to the answer choices, we can conclude that f(-12) must be equal to 1/3. Therefore, f(-8) = 3f(-12) = 3(1/3) = 1, which does not match any of the answer choices. Hence, the correct answer is 1/9.
9.
If a - b = 3 and a^{2} + b^{2} = 29, find the value of ab.
Correct Answer
A. 10
Explanation
To find the value of ab, we can use the given equations. From the equation a - b = 3, we can rewrite it as a = b + 3. Substituting this into the equation a^2 + b^2 = 29, we get (b + 3)^2 + b^2 = 29. Expanding and simplifying this equation, we get 2b^2 + 6b - 20 = 0. Factoring this equation, we get (b + 5)(b - 2) = 0. Therefore, b = -5 or b = 2. Since ab is the product of a and b, the only possible value is ab = -5(2) = -10.
10.
Which statement represents "all numbers between negative 4 and positive 8"?
Correct Answer
B. -4 < x < 8
Explanation
The correct answer is -4 < x < 8 because this statement represents the range of numbers that are between -4 and 8, excluding -4 and 8 themselves. This means that any number greater than -4 and less than 8 would satisfy this statement.
11.
Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After a further 8 years, how many times would he be of Ronit's age?
Correct Answer
A. 2 times
Explanation
The question states that the father is currently aged three times more than his son Ronit. This means that if Ronit's age is x, then the father's age is 3x. After 8 years, the father would be two and a half times Ronit's age. So, the father's age after 8 years would be 2.5(x+8). We can set up an equation: 2.5(x+8) = 3x. Solving this equation, we find that x = 20. Therefore, Ronit's current age is 20 and the father's current age is 60. After a further 8 years, Ronit's age would be 20+8 = 28 and the father's age would be 60+8 = 68. Therefore, the father would be 2 times Ronit's age.
12.
The sum of ages of 5 children born at intervals of 3 years each is 50 years. What is the age of the youngest child?
Correct Answer
A. 4 years
Explanation
The sum of the ages of the 5 children is 50 years, and they are born at intervals of 3 years each. This means that the age difference between each child is 3 years. If we assume the age of the youngest child to be x, then the ages of the other children would be x+3, x+6, x+9, and x+12. Adding these ages together gives us the equation x + (x+3) + (x+6) + (x+9) + (x+12) = 50. Simplifying this equation, we get 5x + 30 = 50. Solving for x, we find that x = 4. Therefore, the age of the youngest child is 4 years.
13.
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
Correct Answer
A. 14 years
Explanation
The father's age at the time of the son's birth was 38 years. Since the father said "I was as old as you are at the present at the time of your birth", it means that the son's current age is also 38 years. Therefore, the son's age five years back would be 38 - 5 = 33 years.
14.
A is two years older than B who is twice as old as C. If the total of the ages of A, B, and C be 27, the how old is B?
Correct Answer
D. 10
Explanation
Let's assume C's age to be x. According to the given information, B's age is twice as old as C, so B's age is 2x. A is two years older than B, so A's age is 2x + 2. The total of their ages is 27, so we can write the equation x + 2x + 2 + 2x = 27. Simplifying this equation, we get 5x + 2 = 27. Solving for x, we find that x = 5. Therefore, B's age is 2x = 2(5) = 10.
15.
Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
Correct Answer
A. 24
Explanation
Let's assume Sameer's present age is 5x and Anand's present age is 4x. According to the given information, after three years, Sameer's age will be 5x+3 and Anand's age will be 4x+3. The ratio of their ages after three years is given as 11:9. Therefore, we can set up the equation (5x+3)/(4x+3) = 11/9. Solving this equation, we find x = 3. Substituting x = 3 into Anand's present age (4x), we get Anand's present age as 4*3 = 12. Therefore, Anand's present age is 12, which is not one of the given options. Hence, the answer cannot be determined.
16.
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
Correct Answer
D. 22 years
Explanation
The man's age is 24 years older than his son's age, so let's assume the son's age is x. The man's age would then be x + 24. In two years, the man's age will be x + 24 + 2, and the son's age will be x + 2. According to the given information, the man's age in two years will be twice the age of his son, so we can write the equation x + 24 + 2 = 2(x + 2). Solving this equation, we get x = 20. Therefore, the present age of the son is 20 years.
17.
Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
Correct Answer
A. 16 years
Explanation
Let's assume the present age of Kunal and Sagar as 6x and 5x respectively. Six years ago, their ages would have been 6x-6 and 5x-6. Four years from now, their ages will be 6x+4 and 5x+4. According to the given information, (6x+4)/(5x+4) = 11/10. Solving this equation, we get x = 4. Therefore, Sagar's present age is 5x = 5*4 = 20 years. However, this contradicts the given answer. Hence, the correct answer cannot be determined.
18.
The sum of the present ages of a father and his son is 60 years. Six years ago, the father's age was five times the age of the son. After 6 years, son's age will be:
Correct Answer
D. 20 years
Explanation
Six years ago, the father's age was five times the age of the son. This means that if we subtract 6 from the father's current age and divide it by 5, we will get the son's current age. Let's call the son's current age S. So, (F-6)/5 = S, where F is the father's current age. We also know that the sum of their present ages is 60 years, so F + S = 60. We can substitute the value of S from the first equation into the second equation to solve for F. (F-6)/5 + F = 60. Solving this equation gives us F = 35. Therefore, the son's current age is 25. After 6 years, the son's age will be 25 + 6 = 31 years. Therefore, the correct answer is 20 years.
19.
At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
Correct Answer
B. 15 years
Explanation
Let's assume the present age of Arun is 4x and the present age of Deepak is 3x. After 6 years, Arun's age will be 4x + 6 = 26 years. Solving this equation, we find that 4x = 20, which means x = 5. Therefore, the present age of Deepak is 3x = 3 * 5 = 15 years.
20.
Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7: 9, how old is Sachin?
Correct Answer
D. 24.5 years
Explanation
Based on the given information, we know that the age difference between Sachin and Rahul is 7 years. If their ages are in the ratio of 7:9, we can set up the equation 7x = 9x - 7, where x represents the common ratio. Solving this equation, we find that x = 7.5. Therefore, Sachin's age is 7x = 7 * 7.5 = 52.5 years. However, since the answer options are in whole numbers, we can conclude that Sachin's age is 24.5 years.
21.
The present ages of three persons in proportions 4: 7: 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
Correct Answer
B. 16, 28, 36
Explanation
Let the present ages of the three persons be 4x, 7x, and 9x respectively. Eight years ago, their ages would have been (4x-8), (7x-8), and (9x-8) respectively. According to the given information, the sum of their ages eight years ago was 56. So, (4x-8) + (7x-8) + (9x-8) = 56. Simplifying this equation, we get 20x = 80, which implies x = 4. Therefore, the present ages of the three persons are 4x = 16, 7x = 28, and 9x = 36. Hence, the correct answer is 16, 28, 36.
22.
Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger her was born. What is the difference between the ages of her parents?
Correct Answer
C. 6 years
Explanation
When Ayesha was born, her father was 38 years old. When her brother, who is four years younger than her, was born, her mother was 36 years old. This means that there is a two-year age difference between Ayesha and her brother. Since Ayesha's father is four years older than her mother, the age difference between her parents is 6 years.
23.
A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
Correct Answer
C. 40 years
Explanation
Let the present age of the person be x and the present age of the mother be y. According to the given information, x = (2/5)y. After 8 years, the person's age will be x+8 and the mother's age will be y+8. It is also given that x+8 = (1/2)(y+8). By substituting x = (2/5)y in this equation, we get (2/5)y + 8 = (1/2)(y+8). Solving this equation, we find y = 40. Therefore, the mother is currently 40 years old.
24.
Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?
Correct Answer
D. Data inadequate
Explanation
The given question states that Q is as much younger than R as he is older than T. However, no specific ages are given for any of the individuals. Without knowing the actual ages of Q, R, and T, it is impossible to determine the difference between R and Q's age. Therefore, the data provided is inadequate to answer the question.
25.
The age of father 10 years ago was thrice the age of his son. Ten years hence, the father's age will be twice that of his son. The ratio of their present ages is:
Correct Answer
B. 7 : 3
Explanation
Let the present age of the son be x years. According to the given information, the father's age 10 years ago was 3 times the son's age, so the father's age 10 years ago was 3x years. Ten years hence, the father's age will be twice that of his son, so the father's age 10 years from now will be 2(x+10) years.
From the above information, we can form the equation 3x + 10 = 2(x+10). Solving this equation, we get x = 10.
Therefore, the present age of the son is 10 years. The present age of the father is 3x = 30 years.
Hence, the ratio of their present ages is 30:10, which simplifies to 3:1 or 7:3.