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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.
| 2451. |
Find the length of the curve. r(t) = cos(8t) i + sin(8t) j + 8 ln(cos(t)) k, 0, 0 £ t £ |
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Answer» Find the length of the curve. r(t) = cos(8t) i + sin(8t) j + 8 ln(cos(t)) k, 0, 0 £ t £ Solution: |
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| 2452. |
What number should be added to both sides of the equation to complete the square? x2-10x = 7 |
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Answer» What number should be added to both sides of the equation to complete the square?x2-10x = 7 Solution: |
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| 2453. |
Rewrite the quadratic equation x2 - 8x + 13 = 0 to the form (x - a)2 = b, where a and b are integers, to determine the a and b values. |
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Answer» Rewrite the quadratic equation x2 - 8x + 13 = 0 to the form (x - a)2 = b, where a and b are integers, to determine the a and b values. Solution: |
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| 2454. |
Find the length of the curve. r(t) = cos(3t) i + sin(3t) j + 3ln(cos(t)) k, 0 ≤ t ≤ π/4. |
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Answer» Find the length of the curve. r(t) = cos(3t) i + sin(3t) j + 3ln(cos(t)) k, 0 ≤ t ≤ π/4. Solution: |
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| 2455. |
Which of the following equations has only one solution? x2 + 4x + 4 = 0,x2 + x = 0,x2 - 1 = 0 |
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Answer» Which of the following equations has only one solution? Solution: |
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| 2456. |
Find the length of the curve. r(t) = cos(6t) i + sin(6t) j + 6 ln(cos(t)) k, 0 ≤ t ≤ π/4. |
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Answer» Find the length of the curve. r(t) = cos(6t) i + sin(6t) j + 6 ln(cos(t)) k, 0 ≤ t ≤ π/4. Solution: |
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| 2457. |
Find the points on the cone z2 = x2 + y2 that are closest to the point (2, 2, 0)? |
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Answer» Find the points on the cone z2= x2+ y2that are closest to the point (2, 2, 0)? Solution: |
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| 2458. |
Is the sequence arithmetic? If so, identify the common difference. 13, 20 ,17 ,34… |
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Answer» Is the sequence arithmetic? If so, identify the common difference. 13, 20 ,17 ,34… Solution: |
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| 2459. |
Simplify using the horizontal method. (2n2 + 4n + 3)(2n - 3) |
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Answer» Simplify using the horizontal method. (2n2 + 4n + 3)(2n - 3) Solution: |
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| 2460. |
Angle K measures 67º and angle L measures 119°. Circle O is inscribed by quadrilateral LMNK. What are the measures of angles M and N? |
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Answer» Angle K measures 67º and angle L measures 119°. Circle O is inscribed by quadrilateral LMNK. What are the measures of angles M and N? Solution: |
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| 2461. |
Kate paid $27 for a dress that was on sale at 10% off. What was the original price for this dress? |
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Answer» Kate paid $27 for a dress that was on sale at 10% off. What was the original price for this dress? Solution: |
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| 2462. |
Factor completely 3x2+ 5x + 1. (3x + 1)(x + 1), (3x + 5)(x + 1), (3x - 5)(x + 1), Prime |
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Answer» Factor completely 3x² + 5x + 1. (3x + 1)(x + 1), (3x + 5)(x + 1), (3x - 5)(x + 1), Prime Solution: |
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| 2463. |
If you roll two fair six-sided dice, what is the probability that the sum is 9 or higher? |
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Answer» If you roll two fair six-sided dice, what is the probability that the sum is 9 or higher? Solution: |
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| 2464. |
Find the volume of the largest right circular cone that can be inscribed in a sphere of radius R. |
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Answer» Find the volume of the largest right circular cone that can be inscribed in a sphere of radius R. Solution: |
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| 2465. |
Write the equation of the sphere in standard form. 2x2 + 2y2 + 2z2 = 12x - 24z + 1 |
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Answer» Write the equation of the sphere in standard form. 2x2+ 2y2+ 2z2= 12x − 24z + 1 Solution: |
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| 2466. |
Given the parent functions f(x) = log3(5x - 5) and g(x) = log3(x - 1), what is f(x) - g(x)? |
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Answer» Given the parent functions f(x) = log3 (5x - 5) and g(x) = log3 (x - 1), what is f(x) - g(x)? Solution: |
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| 2467. |
The prism has a volume of 70 mm3. Find the volume of a scaled image with a scale factor of 3. |
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Answer» The prism has a volume of 70 mm3. Find the volume of a scaled image with a scale factor of 3. Solution: |
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| 2468. |
Which of the following is the correct factored form of the given equation x2+ 3x - 4 = 0? (x +4) (x - 1) = 0, (x - 4) (x - 1) = 0, (x - 4) (x +1)= 0 |
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Answer» Which of the following is the correct factored form of the given equation x2+ 3x - 4 = 0? Solution: |
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| 2469. |
Write an equation in slope-intercept form of the line through point (6, -1) with slope m = 4. |
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Answer» Write an equation in slope-intercept form of the line through point (6, -1) with slope m = 4. Solution: |
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| 2470. |
Solve the given initial-value problem (x + y)2 dx + (2xy + x2 - 5) dy = 0, y(1) = 1 |
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Answer» Solve the given initial-value problem (x + y)2 dx + (2xy + x2 - 5) dy = 0, y(1) = 1 Solution: |
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| 2471. |
Find a function whose maclaurin expansion is 1 + x3 + x6 /2! + x9 /3! + x12 /4! +... |
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Answer» Find a function whose maclaurin expansion is 1 + x3 + x6 /2! + x9 /3! + x12 /4! +... Solution: |
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| 2472. |
What magnitude is not possible when a vector of magnitude 3 is added to a vector of magnitude 4? 7, 0, 1 , 5 |
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Answer» What magnitude is not possible when a vector of magnitude 3 is added to a vector of magnitude 4? Solution: |
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| 2473. |
Which of the following is the conjugate of 6 + 7i? 6 + 7i, 6 - 7i, 7 + 6i, 7 - 6i |
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Answer» Which of the following is the conjugate of 6 + 7i? 6 + 7i, 6 - 7i, 7 + 6i, 7 - 6i Solution: |
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| 2474. |
Triangle ABC is shown below. What is the length of line segment AC? 7, 9, 14, 18 |
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Answer» Triangle ABC is shown below. What is the length of line segment AC?
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| 2475. |
Given the function f(x) = 4(x+3) - 5, solve for the inverse function when x = 3? -21, -16, -10, -1 |
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Answer» Given the function f(x) = 4(x+3) - 5, solve for the inverse function when x = 3? Solution: |
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| 2476. |
Circle L is inscribed with triangle G J K. Line segment G J is a diameter. Line segments G K and K J are secants. Angle K has a measure of (4x + 6) degrees. What is the value of x? 21, 24, 32,44 |
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Answer» Circle L is inscribed with triangle G J K. Line segment G J is a diameter. Line segments G K and K J are secants. Angle K has a measure of (4x + 6) degrees. What is the value of x? Solution: |
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| 2477. |
Find the height of a triangle that has an area of 30 square units and a base measuring 12 units? |
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Answer» Find the height of a triangle that has an area of 30 square units and a base measuring 12 units? Solution: |
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| 2478. |
Find the value of x in 4000(1.5x) = 25,000. Show your work. |
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Answer» Find the value of x in 4000(1.5x) = 25,000. Show your work. Solution: |
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| 2479. |
If r(x) = 3x – 1 and s(x) = 2x + 1, which expression is equivalent to r/s (6)? |
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Answer» If r(x) = 3x – 1 and s(x) = 2x + 1, r/s (6) is equivalent to 17/13. Functionsare the backbone of calculus and algebra.Let's see how usingin this problem. |
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| 2480. |
Solve the given differential equation. x2y'' + xy' + 4y = 0 |
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Answer» Solve the given differential equation. x2y'' + xy' + 4y = 0 Solution: |
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| 2481. |
How many degrees would the hour hand movein 4 hours? |
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Answer» The hour hand moves 120 degrees in 4 hours We will use the concept of complete angle and the unitary method to find the required angle. |
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| 2482. |
A solid cylinder with a radius of 4.0 cm has the same mass as a solid sphere of radius R. If the cylinder and sphere have the same moment of inertia about their centers, what is the sphere's radius? |
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Answer» A solid cylinder with a radius of 4.0 cm has the same mass as a solid sphere of radius R. If the cylinder and sphere have the same moment of inertia about their centers, what is the sphere's radius? Solution: |
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| 2483. |
What is the slope of the line represented by the equation y = 4/5 x - 3? |
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Answer» What is the slope of the line represented by the equation y = 4/5 x - 3? Solution: |
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| 2484. |
A is elder to B by 2 years. A’s father F is twice as old as A and B is twice as old as his sister S. If the age of the father and sister differ by 40 years, find the age of A. |
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Answer» The age of A is 26 years. We can solve such problems using methods to solve linear equations. |
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| 2485. |
The slope of a line that is perpendicular to a line whose slope is -2/7 is |
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Answer» The slope of a line that is perpendicular to a line whose slope is -2/7 is Solution: |
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| 2486. |
What is the slope of a line that is perpendicular to the line whose equation is 2y = 3x - 1? |
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Answer» What is the slope of a line that is perpendicular to the line whose equation is 2y = 3x - 1? Solution: |
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| 2487. |
What is the solution to this system of linear equations? 3x -2y = 14 and5x + y = 32 |
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Answer» What is the solution to this system of linear equations? 3x -2y = 14 and5x + y = 32 Solution: |
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| 2488. |
What is the volume of a square pyramid with a base length of 5 cm and a height of 6 cm? |
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Answer» What is the volume of a square pyramid with a base length of 5 cm and a height of 6 cm?
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| 2489. |
In circle O, AE and FC are diameters. Arc ED measures 17°. What is the measure of EFC? |
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Answer» In circle O, AE and FC are diameters. Arc ED measures 17°. What is the measure of EFC?
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| 2490. |
How to find the altitude of a right triangle with only the hypotenuse? |
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Answer» Thealtitude can be easily found out with help of hypotenuse as per the mentioned formula in the explanation. The ratio in which the altitude divides the hypotenuse is always in geometric progression with the altitude. |
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| 2491. |
For what values of a and b is the line 2x + y = b tangent to the parabola y = ax² when x = 4? |
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Answer» For what values of a and b is the line 2x + y = b tangent to the parabola y = ax² when x = 4? Solution: |
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| 2492. |
Which of the following represents the zeros of f(x) = 5x3 - 6x2 - 59x + 12? 4, 3, 1/5 4, 3, -1/5 4, -3, 1/5 4, -3, -1/5 |
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Answer» Which of the following represents the zeros of f(x) = 5x3 - 6x2 - 59x + 12? Solution: |
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| 2493. |
What is the value of sinθ given that (-6, -8) is a point on the terminal side of θ? |
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Answer» What is the value of sinθ given that (-6, -8) is a point on the terminal side of θ? Solution: |
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| 2494. |
Choose the correct classification of 5x + 3x2 - 7x3 + 2. Third degree polynomial Fourth degree trinomial Sixth degree polynomial First degree binomial |
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Answer» Choose the correct classification of 5x + 3x2 - 7x3 + 2. Solution: |
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| 2495. |
Which of the following represents the zeros of f(x) = 4x3 - 13x2 - 37x + 10? 5, -2, -1/4 5, -2, 1/4 5, 2, -1/4 5, 2, 1/4 |
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Answer» Which of the following represents the zeros of f(x) = 4x3 - 13x2 - 37x + 10? Solution: |
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| 2496. |
If x varies directly as y, and x = 48 when y = 16, find x when y = 5. 5/3,153.6,15 |
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Answer» If x varies directly as y, and x = 48 when y = 16, find x when y = 5. Solution: |
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| 2497. |
What are the values of these sums, where S={1,3,5,7}? ∑(jϵS) j ∑(jϵS) j2 ∑(jϵS) (1/j) ∑(jϵS) 1 |
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Answer» What are the values of these sums, where S={1,3,5,7}? ∑(jϵS) j ∑(jϵS) j2 ∑(jϵS) (1/j) ∑(jϵS) 1 Solution: |
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| 2498. |
What is the sum of the arithmetic sequence 8, 14, 20 …, if there are 22 terms? |
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Answer» What is the sum of the arithmetic sequence 8, 14, 20 …, if there are 22 terms? Solution: |
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| 2499. |
To solve 493x = 3432x + 1, write each side of the equation in terms of base. |
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Answer» To solve 493x = 3432x + 1, write each side of the equation in terms of base. Solution: |
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| 2500. |
If c(x) = 4x - 2 and d(x) = x2 + 5x, what is (c*d)(x)? |
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Answer» If c(x) = 4x - 2 and d(x) = x2 + 5x, what is (c*d)(x)? Solution: |
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