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This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 5051. |
What are the sine, cosine, and tangent of 5π over 4 radians? |
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Answer» What are the sine, cosine, and tangent of 5π over 4 radians? Solution: |
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| 5052. |
The sum of three numbers is 123. If the ratio between the first and second number is 2 : 5 and that of between the second and third is 3 : 4,then find the difference between the second and third number. |
| Answer» The required numbers are 18, 45, 60 which add up to 123, with the ratio between the first and second number as2 : 5 and the ratio of second and thirdas3 : 4. | |
| 5053. |
The sum of the measures of angle A and angle Y is 90. If the measure of angle X is 30 less than twice the measure of angle Y, what is the measure of angle X? |
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Answer» The sum of the measures of angle A and angle Y is 90. If the measure of angle X is 30 less than twice the measure of angle Y, what is the measure of angle X? Solution: |
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| 5054. |
What is the derivative of y = (1 - x)(2 - x)....(n - x) at x = 1? |
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Answer» The value ofy = (1 - x)(2 - x)....(n - x) at x = 1 is - 1(n - 1)! To find the derivative ofy = (1-x)(2-x)....(n-x) at x=1 we will differentiate y with respect to 'x'. |
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| 5055. |
What is 20% of 40? |
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Answer» 20% of 40is 8. A percentis a ratio of a number expressed out of100. |
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| 5056. |
Find the point on the line y = 2x + 4 that is closest to the origin. |
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Answer» Find the point on the line y = 2x + 4 that is closest to the origin. Solution: |
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| 5057. |
What is 40%of 25? |
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Answer» 40%of 25is 10. A percentis a ratio of a number expressed out of100. |
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| 5058. |
Use basic identities to simplify the expression. cot θ sec θ sin θ |
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Answer» Use basic identities to simplify the expression. cot θ sec θ sin θ Solution: |
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| 5059. |
Which expressions are equivalent to 16x4 - 64? Check all that apply. 16x4 + 16x - 16x - 64 16x4 - 8x - 8x - 64 (4x2 + 8)(4x2 - 8) 16(x2 + 2)(x2 - 2) 4(4x4 - 8) |
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Answer» Which expressions are equivalent to 16x4 - 64? Check all that apply. Solution: |
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| 5060. |
Integrate [x - sin x]/ [1 - cos x]. |
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Answer» Afterintegrating [x- sin x]/ [1 - cos x], we get-x cot (x/2) + C The methodof calculatingthe antiderivative of a function is called integration. |
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| 5061. |
How many ways are there to choose a committee of 3 people from a group of 5 people? |
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Answer» How many ways are there to choose a committee of 3 people from a group of 5 people? Solution: |
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| 5062. |
Evaluate the limit lim h → 0 √(4 + h) - 2 / h |
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Answer» Evaluate the limit lim h → 0 √(4 + h) - 2 / h Solution: |
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| 5063. |
How to tell if a function is even odd or neither? |
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Answer» For an even function, f(-x) = f(x), for all x, for an odd function f(-x) = -f(x), for all x. Iff(x) ≠ f(−x) and−f(x) ≠ f(−x) for some values of x, then f is neither even nor odd. A functionis defined as the change in the output value with respect to input where the output variableis dependent upon the input variable. |
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| 5064. |
What is the equation in point-slope form of the line passing through (-2, 0) and (2, 8)? y= 2(x + 2) y= 2(x - 2) y= -2(x - 2) y= -2(x + 2) |
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Answer» What is the equation in point-slope form of the line passing through (-2, 0) and (2, 8)? Solution: |
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| 5065. |
Read the numbers and decide what the next number should be. 20, 30, 40, 50, 60, 70,…? |
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Answer» Read the numbers and decide what the next number should be. 20, 30, 40, 50, 60, 70,…? Solution: |
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| 5066. |
The figure below shows a regular hexagon with sides of length a and a square with sides of length a. If the area of the hexagon is 384√3 square inches, what is the area, in square inches, of the square? |
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Answer» For a regular hexagon with sides of length a and a square with sides of length a, given area of the hexagon as 384√3 square inches, the area of the square is 256 square inches.
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| 5067. |
Which of the following is an even function? f(x) = |x|,f(x) = x3 - 1,f(x) = -3x |
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Answer» Which of the following is an even function? f(x) = |x|,f(x) = x3- 1,f(x) = -3x Solution: |
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| 5068. |
The variance of a binomial distribution for which n = 100 and p = 0.20 is: |
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Answer» The variance of a binomial distribution for which n = 100 and p = 0.20 is: Solution: |
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| 5069. |
What are the formulae of (1) 1 + cos2x (2) 1 - cos2x |
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Answer» (1) 1 + cos2x = 2cos2x , (2) 1 - cos2x = 2sin2x Trigonometric identities are equations that relate different trigonometric functions and are true for all the values that are lies in their domain. |
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| 5070. |
An open box with a square base is required to have a volume of 10 cubic feet. What is the surface area as a function of x? |
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Answer» An open box with a square base is required to have a volume of 10 cubic feet. What is the surface area as a function of x? Solution: |
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| 5071. |
What is the length of a side of a JKLM rhombus? 4 units,8 units,12 units,16 units |
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Answer» What is the length of a side of a JKLM rhombus?
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| 5072. |
Find the area of a regular hexagon with a 48-inch perimeter. |
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Answer» Find the area of a regular hexagon with a 48-inch perimeter. Solution: |
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| 5073. |
What is the sum of any two? (a) Odd numbers (b) Even numbers |
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Answer» What is the sum of any two? (a) Odd numbers (b) Even numbers Solution: |
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| 5074. |
What is the area of an equilateral triangle that has sides of 2 yards and a height of 4.25 feet? |
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Answer» What is the area of an equilateral triangle that has sides of 2 yards and a height of 4.25 feet? Solution: |
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| 5075. |
The circumference of a circle is 6.28. What is the area of the circle? |
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Answer» The area of the circle whosecircumferenceis 6.28, is 3.14 square units Thecircumference of a circle =2πr(where r denotes the radius of the circle) |
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| 5076. |
Find remainder and quotient of the polynomialx4- 9x2+ 9 when divided by x2- 3x. |
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Answer» The remainder and quotient of the polynomialx4- 9x2+ 9 when divided by x2- 3xare9 and x² + 3x respectively. A polynomial is an algebraic expression with coefficients, variable and constants. |
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| 5077. |
Represent 25% as a fraction and decimal. |
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Answer» 25% can be represented as 1/4in fraction form, and 0.25 in decimal form. Fractions are numbers that have two parts: a numerator and a denominator. They have many applications and are very useful in calculations. Decimals are those numbers that liebetween two whole numbers. |
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| 5078. |
Which factors can be multiplied together to make the trinomial 5x2 + 8x - 4? Check all that apply. (x + 1),(2x + 1),(x + 2),(5x + 1),(5x - 2) |
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Answer» Which factors can be multiplied together to make the trinomial 5x2+ 8x - 4? Check all that apply. Solution: |
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| 5079. |
Express the number in the form a/b, where a and b are integers. |
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Answer» Below are the steps to convert a number in the form of a/b We have to convert a given number in the form of a/b which is a rational number. |
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| 5080. |
What if there is no mode in a set of numbers? |
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Answer» It is possible for a data set to have no mode. In that case, we cannot use mode as a measure of central tendency. Mode means a value or a number that appears most frequently in a data set. |
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| 5081. |
What is the angle between the hour hand and minute hand at 4'o clock in an analog clock? |
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Answer» The angle between the hour hand and minute hand at 4'o clock in an analog clock is 120 degrees. Ananalog clockis a tool for reading the time of day. The shortest hand indicates the hour, a longer hand indicates the minutes, and the longest arm indicates the seconds. |
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| 5082. |
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 8 cos3θ |
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Answer» Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 8 cos3θ Solution: |
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| 5083. |
Express 2/3 ×2/3 × 2/3 as a fraction. |
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Answer» The product of2/3 × 2/3 × 2/3 as a fraction in its lowest form is 8/27. A fraction is a part of the whole. It is in the form of a/b where a represents the part and b represents the whole. |
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| 5084. |
Derive the expression 1 + tan2x. |
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Answer» The expression 1 + tan2x can be expressed as 1 + tan2x= sec2x In a right-angled triangle, the tangent of an angle is defined as 'The ratio of the length of the side opposite the angle to the length of the adjacent side'. |
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| 5085. |
A merchant had Rs 78,592 with her. She placed an order for purchasing 40 radio sets at Rs 1,200 each. How much money will remain with her after the purchase? |
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Answer» The merchant after placing an order of purchasing 40 radio sets at Rs 1200 each will remain with Rs 30,592 after her purchase. The total cost of 40 radio sets can be calculated by multiplying Rs 1,200 and 40. |
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| 5086. |
If a coin is tossed three times, the likelihood of obtaining three heads in a row is? |
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Answer» If a coin is tossed three times, the likelihood of obtaining three heads in a row is 1/8. Probability is defined as how likely an event is to occur. |
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| 5087. |
Which are factors of x2- 4x - 5? Check all that apply. (x - 5), (x - 4),(x - 2), (x + 1),(x + 5) |
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Answer» Which are factors of x2- 4x - 5? Check all that apply. (x - 5), (x - 4),(x - 2), (x + 1),(x + 5) Solution: |
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| 5088. |
Derive the equation of the parabola with a focus at (-7, 5) and a directrix of y = -11 |
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Answer» Derive the equation of the parabola with a focus at (-7, 5) and a directrix of y = -11 Solution: |
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| 5089. |
What is 55% as a Fraction in Simplest Form? |
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Answer» 55% can be represented as 11/20in fractional form. Fractions are numbers that have two parts- a numerator and a denominator. They have many applications and are very useful in calculations. |
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| 5090. |
How to find the nthterm of an arithmetic sequence? |
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Answer» The expression to calculatethe nthterm of an arithmetic sequence isan= a + (n - 1) d. An arithmetic progression is a sequence where the differences between every two consecutive termsare the same. |
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| 5091. |
How to find the area and perimeter of a square |
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Answer» The area of a square is equal tothe square of the length of its sideand the perimeter of the square is 4 times the length of its side. A square has 4 sides of similar length which are at right angles to each other. |
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| 5092. |
Find the general solution of the given second-order differential equation. y'' - 6y' +10y = 0 |
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Answer» Find the general solution of the given second-order differential equation. y'' - 6y' +10y = 0 Solution: |
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| 5093. |
What is 2% as a Fraction in Simplest Form? |
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Answer» 2% can be represented as 1/50in fractional form. Fractions are numbers that have two parts- a numerator and a denominator. They have many applications and are very useful in calculations. |
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| 5094. |
What is the solution of log3x + 4125 = 3? |
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Answer» What is the solution of log3x + 4125 = 3? Solution: |
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| 5095. |
For what value of x is the rational expression given equal to zero: (2 - x) / (2 + x)? |
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Answer» The value of x for which the given expression(2 - x) / (2 + x) is zero is x = 2. (2 - x) / (2 + x)is an exampleof rational expression. Such types ofequations can have more than one variable, and can also have infinite, one or no solutions. These equations are used extensively in many fields of engineering and mathematics. Let's solve a question on this concept. |
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| 5096. |
Find the exact value of cos 180° - sin 180°? |
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Answer» The value ofcos 180° - sin 180° is -1 We will use the values ofcosπ and sinπ from the trigonometric ratio table to determine the value. |
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| 5097. |
What is 10% of 200? |
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Answer» 10% of 200 is 20. A percentis a ratio of a number expressed out of100. |
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| 5098. |
Given that f(x) = 5x − 10 and g(x) = x + 3, Solve for f(g(x)) when x = −1. |
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Answer» Iff(x) = 5x − 10 and g(x) = x + 3, then the value of f(g(-1))is 0. We will use the concept of functions to solve the given problem. |
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| 5099. |
What is the quotient of (x3 - 3x2 + 3x - 2) ÷ (x2 - x + 1)? |
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Answer» What is the quotient of (x3 - 3x2 + 3x - 2) ÷ (x2 - x + 1)? Solution: |
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| 5100. |
Use completing the square to solve for in the equation (x - 12) (x + 4) = 9. |
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Answer» By using completing the square method, equation (x - 12) (x + 4) = 9 can be solved asx = (4+ √ 73) or (4-√ 73) A quadratic equation is in the form of ax2+ bx + c = 0. To find the roots of the quadratic equation we can use completing the square method. |
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