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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.
| 3001. |
Find the antiderivative of tan2(x) dx? |
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Answer» The integral ofa function is an antiderivative of that function. |
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| 3002. |
Two water taps together can fill a tank in 9⅜hours.The tap of larger diameter takes 10 hrs less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank. |
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Answer» The tap of smaller diameter can separately fill the tank in 25 hours whereas the larger tap can separately fill the tank in 15 hours. The question is a real-life application of linear equations in two variables. |
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| 3003. |
What is the area of a rectangle with a width of 12 feet and a length of 10 feet? |
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Answer» What is the area of a rectangle with a width of 12 feet and a length of 10 feet? Solution: |
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| 3004. |
An angle measures radians. what is the degree measure of the angle? |
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Answer» The degree measure of the angle = Radian× (180/π) We will use the concept of the relationship between degree and angle to find the answer. |
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| 3005. |
8 is what percent of 20? |
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Answer» 8 is 40 percent of 20 Percentage is a fraction or a ratio in which the value of whole is always 100. |
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| 3006. |
Solve the differential equation. du/dt = 9 + 9u + t + tu. |
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Answer» Solve the differential equation. du/dt = 9 + 9u + t + tu. Solution: |
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| 3007. |
What is the measure of angle C, to the nearest degree? (Image Attached) |
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Answer» What is the measure of angle C, to the nearest degree?
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| 3008. |
What is the quotient when 2x3+ x + 3 is divided by x + 1? |
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Answer» What is the quotient when 2x3+ x + 3 is divided by x + 1? Solution: |
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| 3009. |
Find a polar equation for the curve represented by the given Cartesian equation. x2 + y2 = 6cx |
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Answer» Find a polar equation for the curve represented by the given Cartesian equation. x2 + y2 = 6cx Solution: |
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| 3010. |
What is 8% as a decimal? |
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Answer» 8% as a decimal is 0.08 Adecimalnumber can bedefinedas a number whose whole number part and the fractional part is separated by adecimalpoint. |
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| 3011. |
How do you verify (sec θ + csc θ)(cos θ - sin θ) = cot θ - tan θ? |
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Answer» How do you verify (sec θ + csc θ)(cos θ - sin θ) = cot θ - tan θ? Solution: |
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| 3012. |
Which of the following represents the zeros of f(x) = x3 - 4x2 - 5x + 20? -4, -square root of 5, -square root of 5 4, square root of 5, -square root of 5 4, -square root of 5, -square root of 5 -4, square root of 5, square root of 5 |
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Answer» Which of the following represents the zeros of f(x) = x3 - 4x2 - 5x + 20? Solution: |
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| 3013. |
Find the first six terms of the sequence. a1= 4, an = 2. an - 1 |
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Answer» Find the first six terms of the sequence. a1= 4, an = 2. an - 1 Solution: |
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| 3014. |
Which statement best describes the graph of x3 - 3x2 - x + 3? It starts down on the left and goes up on the right and intersects the x-axis at x = -1, 2, and 3. It starts down on the left and goes up on the right and intersects the x-axis at x = -1, 1, and 3. It starts up on the left and goes down on the right and intersects the x-axis at x = -1, 2, and 3. It starts up on the left and goes down on the right and intersects the x-axis at x = -1, 1, and 3. |
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Answer» Which statement best describes the graph of x3 - 3x2 - x + 3? Solution: |
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| 3015. |
Find the first six terms of the sequence. a1 = -1, an= 4.an - 1 |
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Answer» Find the first six terms of the sequence. a1 = -1, an= 4.an - 1 Solution: |
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| 3016. |
If a theatre holds 1,200 people, and sells 2/3 of its seats, how many tickets does it sell? |
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Answer» If a theatre holds 1,200 people, and sells 2/3 of its seats, how many tickets does it sell? Solution: |
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| 3017. |
What is0.5625 as a fraction? |
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Answer» 0.5625 as a fraction is 9/16. We use fractions to write a part of a whole. |
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| 3018. |
Circle F is congruent to circle J, and ∠EFD ≅ ∠GJH. m∠DFE = 80°. What is the measure of Arc GH? |
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Answer» Circle F is congruent to circle J, and ∠EFD ≅ ∠GJH. m∠DFE = 80°. What is the measure of Arc GH?
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| 3019. |
Solve the system of linear equations by Cramer’s rule 3x + y = 19 3x - y = 23 |
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Answer» Solve the system of linear equations by Cramer’s rule 3x + y = 19 3x - y = 23 Solution: |
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| 3020. |
What is the value of r in the equation 2(2r + 8) = 3r + 16? |
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Answer» What is the value of r in the equation 2(2r + 8) = 3r + 16? Solution: |
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| 3021. |
One factor of f(x) = 4x3 - 4x2 - 16x + 16 is (x - 2). What are all the roots of the function? Use the Remainder Theorem. |
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Answer» One factor of f(x) = 4x3 - 4x2 - 16x + 16 is (x - 2). What are all the roots of the function? Use the Remainder Theorem. Solution: |
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| 3022. |
Choose the correct simplification of the expression -6x2(4x - 7x2 - 2) 42x4 + 24x3 - 12x2 -42x4 + 24x3 - 12x2 -13x4 - 2x3 - 8x2 42x4 - 24x3 + 12x2 |
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Answer» Choose the correct simplification of the expression -6x2(4x - 7x2 - 2) Solution: |
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| 3023. |
A cyclist travels a distance of 1 km in the first hour, 0.5 km in the second hour and 0.3 km in the third hour. What is the average speed in km/hr and m/sec? |
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Answer» Answers: The average speed of the cyclist who travels a distance of1 km in the first hour, 0.5 km in the second hour and 0.3 km in the third hour is 0.6 km/hr or 1/6 m/s. Time, speed, and distance are related using the equation: Distance = Speed× Time. |
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| 3024. |
A kite is a parallelogram only when it is a rhombus. Is this statement true or false? |
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Answer» A kite is a parallelogram only when it is a rhombus. The given statement is true. Aparallelogramis defined as a quadrilateral in whichboth pairs of opposite sides are parallel and equal. |
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| 3025. |
Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5, find the numbers. |
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Answer» The two numbers are 40 and 48, which arein the ratio 5 : 6. The question is based on the conceptsof linear equations in two variablesand ratios. |
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| 3026. |
A hat that costs $25 is on sale for 30% off. What is the sale price? |
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Answer» A hat that costs $25 is on sale for 30% off. What is the sale price? Solution: |
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| 3027. |
Find the exact length of the curve. y = (1 − x2 ), 0 ≤ x ≤ 1/4. |
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Answer» Find the exact length of the curve. y = (1 − x2 ), 0 ≤ x ≤ 1/4. Solution: |
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| 3028. |
If two events are mutually exclusive,then show that they have no outcomes in common. |
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Answer» Proved that if two events are mutually exclusive, they cannot have any common outcomes. The definition of the mutually exclusive event itself states, that two events are mutually exclusive if they cannot occur at the same time. |
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| 3029. |
Ten times the sum of half a number and 6 is 8. Find the number. |
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Answer» The number is -10.4. We can simplify the equation after writing it mathematically to obtain the answer. |
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| 3030. |
How to turn a mixed fraction into a whole number? |
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Answer» We cannot turn a mixed fraction into a whole number. Amixedfraction is the combination of a whole number and a properfractionrepresented together. |
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| 3031. |
What is 4 to the 4th power? |
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Answer» The value of 4 to the 4th power i.e., 44is 256. The exponentor power of a number shows how many times the number is multiplied by itself. |
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| 3032. |
Given the exponential equation 3x = 27, what is the logarithmic form of the equation in base 10? |
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Answer» Given the exponential equation 3x = 27, what is the logarithmic form of the equation in base 10? Solution: |
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| 3033. |
Identify the vertex for the graph of y = 3x2 + 12x + 5. |
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Answer» Identify the vertex for the graph of y = 3x2 + 12x + 5. Solution |
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| 3034. |
What is the antiderivative of sin2(x)? |
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Answer» Theantiderivative ofsin2x isx/ 2 - (sinx cosx) / 2. The antiderivative of a function is the integral of the function. |
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| 3035. |
The sides of a rhombus with an angle of 60° are 6 inches. Find the area of the rhombus. |
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Answer» The sides of a rhombus with an angle of 60° are 6 inches. Find the area of the rhombus. Solution: |
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| 3036. |
The sum of the perimeters of an equilateral triangle and a square is 10. Find the dimensions of the triangle and the square that produce a minimum total area. |
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Answer» The sum of the perimeters of an equilateral triangle and a square is 10. Find the dimensions of the triangle and the square that produce a minimum total area. Solution: |
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| 3037. |
In simplest radical form, what are the solutions to the quadratic equation 6 = x2 - 10x? |
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Answer» In simplest radical form, what are the solutions to the quadratic equation 6 = x2 - 10x? Solution: |
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| 3038. |
Prove that if one angle of a triangle is 90°, then the other two add to 90°. |
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Answer» Hence proved that the sum of the other two angles of a right-angled triangle is90°. A right-angled triangle has one angle equal to90º and the other two angles are acute angles. |
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| 3039. |
How to divide a mixed number by a whole number? |
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Answer» The steps to divide a mixed number by a whole number are given below. Whole numbersare all natural numbers including zero. Amixedfraction is the combination of a whole number and a properfractionrepresented together. |
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| 3040. |
How to find the percentage of a number between two numbers? |
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Answer» To find the percentage of a number between two numbers, divide one number with the otherand then multiply the result by 100. The percentage is a fraction or a ratio in which the value of the whole is always 100. |
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| 3041. |
Find the points on the cone z2 = x2 + y2 that are closest to the point (4,2,0). |
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Answer» Find the points on the cone z2 = x2 + y2 that are closest to the point (4,2,0). Solution: |
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| 3042. |
How many squares make up the surface of a cube? |
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Answer» 6 squares make up the surface of a cube. A cube is a three-dimensional object in which all the faces are in the shape of a square. |
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| 3043. |
What is the next number in the sequence? 9….3….1….1/3… |
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Answer» What is the next number in the sequence? 9….3….1….1/3… Solution: |
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| 3044. |
What is the arc length if θ = 2 pi over 3 and the radius is 4 cm? |
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Answer» What is the arc length if θ = 2 pi over 3 and the radius is 4 cm? Solution: |
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| 3045. |
Solve x2+ 9x + 20. x = 2, x = 10, x = −2, x = −10 x = −5, x = −4, x = 5, x = 4 |
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Answer» The quadratic equation is satisfied when x = -5, and x = -4 The abovequadratic equation is in the form of ax2+ bx + c |
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| 3046. |
Find theroots of the function f(x) = x3+ x2+ 6x |
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Answer» The roots of the functionf(x) = x3+ x2+ 6x are 0 , -3 , -2 We will use the concept of factorization to find the roots of the above function. |
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| 3047. |
What is a number divided by 0? |
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Answer» Any number divided by 0is not defined. Divide means sharing equally. |
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| 3048. |
You roll a six-sided die. Find the probability of each of the following scenarios. (a) Rolling a 5 or a number greater than 3. (b) Rolling a number less than 5 or an even number. (c) Rolling a 6 or an odd number. |
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Answer» You roll a six-sided die. Find the probability of each of the following scenarios. (a) Rolling a 5 or a number greater than 3. (b) Rolling a number less than 5 or an even number. (c) Rolling a 6 or an odd number. Solution: |
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| 3049. |
Each leg of a 45° -45° -90° triangle measures 12 cm. What is the length of the hypotenuse? |
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Answer» Each leg of a 45°-45°-90° triangle measures 12 cm. What is the length of the hypotenuse? Solution: |
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| 3050. |
Given the sequence 2, 6, 18, 54, ..., which expression shown would give the fifteenth term? 215, 2·315, 2·314 |
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Answer» Given the sequence 2, 6, 18, 54, ..., which expression shown would give the fifteenth term? Solution: |
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