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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.
| 4301. |
How do you factor x2- y2? |
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Answer» x2− y2can be factorised as( x − y ) ( x + y ) In algebra, there is an identity for the difference of squares. |
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| 4302. |
If the HCF of 85 and 153 is expressible in the form of 85m -153; then find the value of m. |
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Answer» If the HCF of 85 and 153 is expressible in the form of 85m -153, the value of m is 2. HCF (Highest Common Factor) of twonumbers is the largest possible number which divides the two numbers exactly without leaving any remainder. |
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| 4303. |
The 0 and 1 in the binary numbering system are called binary digits or ____ |
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Answer» The 0 and 1 in the binary numbering system are called binary digits or ____ Solution: |
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| 4304. |
Two sides of a triangle are4m and5m in length and the angle between them is increasing at a rate of0.06rad/sec. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed lengths is π/3. |
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Answer» Two sides of a triangle are4m and5m in length and the angle between them is increasing at a rate of0.06rad/sec. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed lengths is π/3. Solution: |
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| 4305. |
What is the derivative of f (x) = tan-1(x)? |
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Answer» The derivative off (x) = tan-1(x) is1/ (1 + x2) In mathematics, the inverse trigonometricfunction is also known as 'arc functions'. To find the derivative off (x) = tan-1(x) we will use inverse identity. |
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| 4306. |
What is the radius of a circle whose equation is (x - 7)2 + (y - 10)2 = 4? |
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Answer» What is the radius of a circle whose equation is (x - 7)2+ (y - 10)2= 4? Solution: |
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| 4307. |
Choose the pair of numbers that is not a solution to the given equation. y = 5 - 2x (1, 3),(2, 1),(0, 3) |
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Answer» Choose the pair of numbers that is not a solution to the given equation. y = 5 - 2x Solution: |
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| 4308. |
Write the equation of the sphere in standard form 2x2 + 2y2 + 2z2 = 4x -16z + 1, Find its center and radius? |
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Answer» Write the equation of the sphere in standard form 2x2 + 2y2 + 2z2 = 4x -16z + 1, Find its center and radius? Solution: |
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| 4309. |
A pair of fair dice is rolled until a sum of either 5 or 7 is obtained. Then, the probability that 5 comes before 7 is .… |
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Answer» A pair of fair dice is rolled until a sum of either 5 or 7 is obtained. Then, the probability that 5 comes before 7 is .… Solution: |
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| 4310. |
Find the linearization L(x) of the function at a. f(x) = sin(x), a = π/6 |
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Answer» Find the linearization L(x) of the function at a. f(x) = sin(x), a = π/6 Solution: |
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| 4311. |
How do you define Ratio? |
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Answer» The term ratio means the quantitative relation between the two numbers showing how many times one value contains or is contained within the other. Let us see what does the term ratio mean. |
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| 4312. |
Use this equation to find dy/dx:3y cos (x) = x2 + y2 |
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Answer» Use this equation to find dy/dx:3y cos (x) = x2 + y2 Solution: |
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| 4313. |
What is the equation of a line that is perpendicular to y = 4x + 5 and passes through point (8, 3)? |
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Answer» What is the equation of a line that is perpendicular to y = 4x + 5 and passes through point (8, 3)? Solution: |
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| 4314. |
Explain the Term Numbers? |
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Answer» Numbers are used in mathematics to quantify a thing and provides a way to compare different quantities. Numbers are all maths is about. Let us see what numbers are. |
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| 4315. |
Prove that sin (π - x) = sin (x). |
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Answer» Hence proved that sin (π - x) = sin (x) Sine is one of the primary functions of trigonometry. To prove this, we will use trigonometric identity. |
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| 4316. |
What is the area of a triangle with vertices at (-2, 1), (2, 1), and (3, 4)? |
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Answer» What is the area of a triangle with vertices at (-2, 1), (2, 1), and (3, 4)? Solution: |
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| 4317. |
What is the integral of sec (x)? |
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Answer» The integral of sec (x) is In |secx + tanx| + c To integrate this we will multiply and dividesec x with sec x + tan x / sec x + tan x |
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| 4318. |
Suppose f(x) is a function such that if p < q, f(p) < f(q). Which statement best describes f(x)? -f(x) can be odd or even. -f(x) can be odd but cannot be even. -f(x) can be even but cannot be odd. -f(x) cannot be odd or even. |
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Answer» Suppose f(x) is a function such that if p < q, f(p) < f(q). Which statement best describes f(x)? -f(x) can be odd or even. -f(x) can be odd but cannot be even. -f(x) can be even but cannot be odd. -f(x) cannot be odd or even. Solution: |
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| 4319. |
Is the logarithmic function inverse of an exponential function? |
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Answer» Is the logarithmic function inverse of an exponential function? Solution: |
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| 4320. |
Which equation is y = 3(x - 2)2 - (x - 5)2 rewritten in vertex form? y = 3(x minus seven-halves) squared minus Start Fraction 27 Over 4 End Fraction y = 2(x minus 1) squared minus 11 y = 2(x minus one-half) squared minus Start Fraction 53 Over 4 End Fraction y = 2(x minus one-half) squared minus Start Fraction 27 Over 2 End Fraction |
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Answer» Which equation is y = 3(x - 2)2 - (x - 5)2 rewritten in vertex form? Solution: |
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| 4321. |
What is the volume of a square pyramid with a base length of 4 cm and a height of 9 cm? |
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Answer» What is the volume of a square pyramid with a base length of 4 cm and a height of 9 cm? Solution: |
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| 4322. |
A model is made of a car. The car is 9 feet long and the model is 6 inches long. What is the ratio of the length of the car to the length of the model? |
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Answer» A model is made of a car. The car is 9 feet long and the model is 6 inches long. What is the ratio of the length of the car to the length of the model? Solution: |
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| 4323. |
What is the antiderivative of 1 / (x2)? |
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Answer» The antiderivative of 1 / (x2) is −1 / (x) + c. To findtheantiderivative, we will use the power rulefor antiderivatives/integrals. |
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| 4324. |
According to the rational root theorem, the following are potential roots of f(x) = 2x2 + 2x - 24. -4, -3, 2, 3, 4 Which are the actual roots of f(x)? 4 and 3; 4, 2 and 3; 3 and -4; 3, 2, and 4 |
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Answer» According to the rational root theorem, the following are potential roots of f(x) = 2x2+ 2x - 24. -4, -3, 2, 3, 4 Which are the actual roots of f(x)? Solution: |
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| 4325. |
How Do You Solve For y For The Equation 2x–3y = 6? |
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Answer» To solve for y for the equation 2x – 3y = 6, we will need to shift y to one side of the equation. Let us find the value of the variable y in the given equation 2x - 3y = 6 |
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| 4326. |
What is the rate of change between the interval x = π and x = three pi over two? |
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Answer» What is the rate of change between the interval x = π and x = three pi over two? Solution: |
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| 4327. |
What is the next number? 2, 3, 5, 7, 11, 13, 17, ... |
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Answer» What is the next number? 2, 3, 5, 7, 11, 13, 17, ... Solution: |
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| 4328. |
Which of the following is the solution set of the given equation?14 + 8m = 14 - 3m - 5m ∅,{0},{all reals} |
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Answer» Which of the following is the solution set of the given equation?14 + 8m = 14 - 3m - 5m Solution: |
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| 4329. |
If p(x) = x3- x2+ 3x + 4, then find the value of p (1) and p (- 2) |
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Answer» If p(x) = x3- x2+ 3x + 4, then, the value of p (1) = 7and p (- 2 ) = - 14. To solve this equation, we will substitutethe values of x and simplify. |
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| 4330. |
If one of the factors of x2 + x -20 is (x + 5), then the other factor is? |
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Answer» If one of the factors of x2+ x -20 is (x + 5), then the other factor is? Solution: |
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| 4331. |
Choose the correct simplification of the expression (-2x + 10y)(4x - 6y). |
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Answer» Choose the correct simplification of the expression (-2x + 10y)(4x - 6y). Solution: |
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| 4332. |
Write the expression as the sine, cosine, or tangent of an angle. sin9x cosx - cos9x sinx |
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Answer» Write the expression as the sine, cosine, or tangent of an angle. sin9x cosx - cos9x sinx Solution: |
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| 4333. |
Explain the Term Equation |
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Answer» In Mathematics, an equation is formed when two expressions are equated to each other using the "equal to" sign. An equation is a mathematical statement with an 'equal to' symbol between two algebraic expressions that have equal values. |
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| 4334. |
Evaluate the expression. r = , v = , w = v ⋅ w |
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Answer» Evaluate the expression. r = <5, 9, -4>, v = <3, 3, -8>, w = <9, -6, -1> v ⋅ w Solution: |
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| 4335. |
Given f(x) = the quantity of x minus 5, divided by 3, solve for f-1(3). |
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Answer» Given f(x) = the quantity of x minus 5, divided by 3, solve for f-1(3). Solution: |
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| 4336. |
How do you write 140 as the product of its prime factors? |
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Answer» 140 as the product of its prime factors is written as 2 × 2 ×5 × 7 Prime factorizationis a way of expressing a number as a product of its prime factors. |
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| 4337. |
Given f(x) = the quantity of x minus 7, divided by 3, solve for f-1(4). |
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Answer» Given f(x) = the quantity of x minus 7, divided by 3, solve for f-1(4). Solution: |
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| 4338. |
How can you write 15 as a fraction in the lowest terms? |
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Answer» 15 as a fraction in the lowest termscan be written as 15/1. In mathematics, afractionis used to represent the portion of the whole quantity. Also, we know that every integer is a rational number and any whole numbercan be written in theform of n/1, where n is any whole number. |
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| 4339. |
If the ratio of the length to the breadth of a rectangle be 5 : 3and its perimeter is 144 m, find the length of the rectangle. |
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Answer» The length of the rectangle is 45 m. A rectangle is a four-sided polygon whose perimeter is the sum of all its sides. |
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| 4340. |
A circle has its center at (-2, 5) and a radius of 4 units. What is the equation of the circle? (x + 2)2 + (y - 5)2 = 16 (x + 2)2 + (y + 5)2 = 16 (x + 2)2 + (y - 5)2 = 4 (x - 2)2 + (y + 5)2 = 4 |
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Answer» A circle has its center at (-2, 5) and a radius of 4 units. What is the equation of the circle? Solution: |
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| 4341. |
Write the sum or difference in the standard form a + bi. (3 + 3i) -(-6 + i) |
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Answer» Write the sum or difference in the standard form a + bi. (3 + 3i) -(-6 + i) Solution: |
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| 4342. |
These three points are collinear. (3, 6), (-2, -9), (0, -4). True or False |
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Answer» These three points are collinear. (3, 6), (-2, -9), (0, -4). True or False Solution: |
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| 4343. |
Given a(n) = a + d(n - 1), find the value of a and d for the arithmetic sequence 3, 5, 7, 9, …? |
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Answer» Given a(n) = a + d(n - 1), find the value of a and d for the arithmetic sequence 3, 5, 7, 9, …? Solution: |
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| 4344. |
For the given statement 2 < x |
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Answer» x can have 7 different values which are 3, 4, 5, 6, 7, 8, 9. Whole numbers are the set of natural numbers along with zero. |
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| 4345. |
A circle has its center at (-2, 3) and a radius of 3 units. What is the equation of the circle? |
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Answer» A circle has its center at (-2, 3) and a radius of 3 units. What is the equation of the circle? Solution: |
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| 4346. |
What is half of 1/8? |
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Answer» Half of 1/8 is 1/16 Themultiplication of fractionsstarts with the multiplication of the given numerators, followed by the multiplication of the denominators. |
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| 4347. |
A circle has its center at (-1, 2) and a radius of 3 units. What is the equation of the circle? |
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Answer» A circle has its center at (-1, 2) and a radius of 3 units. What is the equation of the circle? Solution: |
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| 4348. |
Is the diagonal of a square the same length as the side? |
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Answer» No,the diagonal of a square is not the same length as the side. The length of the diagonal of the squareis equal to √2 times of its side. |
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| 4349. |
What is a cubic polynomial function in standard form with zeros 1, -2, and 2? x3 + x2 - 3x + 4 x3 + x2 - 4x - 2 x3 + x2 + 4x + 4 x3 - x2 - 4x + 4 |
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Answer» What is a cubic polynomial function in standard form with zeros 1, -2, and 2? Solution: |
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| 4350. |
If (x - 2k) is a factor of f(x), which of the following must be true? f(2k) = 0 f(-2k) = 0 A root of f(x) is x = -2k. Any intercept of f(x) is x = 2k. |
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Answer» If (x - 2k) is a factor of f(x), which of the following must be true? Solution: |
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