Explore topic-wise InterviewSolutions in .

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.

6451.

Evaluate the limit by first recognizing the sum as the Riemann sum for a function defined on the interval [0,1]: lim as n approaches infinity (1/n)((sqrt(1/n)+(sqrt(2/n)+(sqrt(3/n)+...............+(sqrt(n/n))

Answer» Evaluate the limit by first recognizing the sum as the Riemann sum for a function defined on the interval [0,1]: lim as n approaches infinity (1/n)((sqrt(1/n)+(sqrt(2/n)+(sqrt(3/n)+...............+(sqrt(n/n))

Solution:

6452.

What is an example of the commutative property of multiplication?

Answer» 5 × 7 = 7 × 5 = 35 is an example of the commutative property of multiplication.

The Commutative Property of Multiplication says that the order in which we multiply the numbers does not change the final product.

6453.

What is the reciprocal of 3/5?

Answer» What is the reciprocal of 3/5?

Solution:

6454.

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.4.6 + 5.7 + 6.8 + ... + 4n( 4n + 2)

Answer» Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.4.6 + 5.7 + 6.8 + ... + 4n( 4n + 2)

Solution:

6455.

Can you find the sum of the summation of 3 i minus 15, from i equals 2 to 7?

Answer» -9 is the sum ofthe summationof 3 i minus 15, from i equals 2 to 7.

The summationis the sum of consecutive terms of a sequence.The summation brings consecutive terms together to make a new total.

6456.

Data is in ____ sequence if it is in order from lowest to highest.

Answer» Data is in ascending sequence if it is in the order of the lowest to the highest.

A sequence can be of two types when it is sorted in order from either lowest to highest orhighest to lowest.

6457.

There are 6 diagonals that can be drawn from one vertex of an octagon. True or false?

Answer» The given statement is false, only 5 diagonals can be drawn from one vertex of an octagon.

Octagons are polygons that have 8 sides.

6458.

A segment of a circle has a 120 arc and a chord of 8 √3 in. Find the area of the segment.

Answer» A segment of a circle has a 120 arc and a chord of 8 √3 in. Find the area of the segment.

finding the area of the segment

6459.

What is 2 to the 3rd power?

Answer» 2raised to the thirdpower is equal to 23= 8.

Theexponentof a number shows how many times the number ismultipliedby itself.

6460.

What is the range for the following set of scores? scores: 5, 7, 9, 15.

Answer» What is the range for the following set of scores? scores: 5, 7, 9, 15.

Solution:

6461.

What is the perimeter of the polygon in the diagram?

Answer» What is the perimeter of the polygon in the diagram?

6462.

What is .32 as a fraction?

Answer» 0.32 as a fraction is represented as 32/100 and can be reduced to 8/25.

Fractions are represented as a numerical value and are defined as a part of a whole. A fraction consists of a numerator and a denominator.

6463.

Find the cosine and sine of 180°. round your answers to the nearest hundredth if necessary.

Answer» Find the cosine and sine of 180°. round your answers to the nearest hundredth if necessary.

Solution:

6464.

Eliminate theta between a=cos(theta-alpha) and b=sin(theta-beta)?

Answer» We getcos-1a - sin-1b=beta - alpha after eliminatingtheta between a = cos(theta-alpha) and b = sin(theta-beta).

We will be solving this question by using the concept of inverse trigonometric functions.

6465.

If sin θ = 15 over 17, use the Pythagorean identity to find cos θ.

Answer» If sin θ = 15 over 17, use the Pythagorean identity to find cos θ.

Solution:

6466.

What is the simplified form of the quantity 4 x squared minus 25 over the quantity 4x minus 5?

Answer» What is the simplified form of the quantity 4 x squared minus 25 over the quantity 4x minus 5?

Solution:

6467.

If the roots of the quadratic equation kx2+ (a + b)x+ ab are (-1,- b),What is the value of k?

Answer» If the roots of the quadratic equation kx2+ (a + b)x + ab are (-1) and (-b) then the value of k is 1.

Aquadratic equationis in the form ax2+ bx + c = 0, where a ≠ 0.

6468.

How do you differentiate the function sin2x.cos x?

Answer» When we differentiatesin2x.cos x, we get (2 sin x cos2x - sin3x).

Differentiation or derivatives areone of the most important concepts in calculus. It is the reverse of integration. The slopes of various curves at different points can be found out using differentiation.

6469.

What is the Area of an Equilateral Triangle with a height of 9 inches?

Answer» The area of an equilateral triangle with a height of 9 inches is equal to27√3 square inches.

A triangle that has all three equal sides along with equal angles is known as an equilateral triangle.

6470.

How do you write a polynomial with roots: −square root of 3, square root of 3, and 2?

Answer» The polynomial is written as y = x3 - 2x2 - 3x + 6.

A polynomial with three roots is a three-degree polynomial also known as a cubic polynomial.

6471.

What value(s) of x make the equation x2 - 18x + 81 = 0 true?

Answer» What value(s) of x make the equation x2- 18x + 81 = 0 true?

Solution:

6472.

What are the values of a, b, and c in the quadratic equation y=5x-4x2-2?

Answer» What are the values of a, b, and c in the quadratic equation y=5x-4x2-2?

Solution:

6473.

What is the approximate value of a local maximum for the polynomial?

Answer» f ''(x0) < 0 is the condition for all values of x = x0, where the polynomial will have a local maximum.

We need to calculate at least the second derivative of a polynomial, to know about the maxima or minima of the function.

6474.

What is the largest 2-digit multiple of 17?

Answer» The largest 2-digit multiple of 17 is 85.

A multiple is a product that we get when one number is multiplied by another number.

6475.

Which functions have an axis of symmetry of x = -2? Check all that apply. f(x) = x2 + 4x + 3 f(x) = x2 - 4x - 5 f(x) = x2 + 6x + 2 f(x) = -2x2 - 8x + 1 f(x) = -2x2 + 8x - 2

Answer» Which functions have an axis of symmetry of x = -2? Check all that apply.

Solution:

6476.

What is the difference between a rhombus and a parallelogram?

Answer» The difference between a parallelogram and a rhombus is that aparallelogram has opposite sides equal, while in a rhombus all four sides are equal in measurement.

Parallelogram and Rhombus are four-sided polygons also known as quadrilaterals having four sides and four angles.

6477.

Find the derivative of the function: f(x) = (2x − 3)4(x2 + x + 1)5.

Answer» The derivative of the function: f(x) = (2x − 3)4(x2 + x + 1)5is(2x -3)3(x2 + x + 1)4(28x2- 12x - 7).

We will use the product rule to find the derivative of the given function.

6478.

How to differentiate? y = e2x

Answer» On differentiation we get dy / dx = 2e2x .

We will use the concept of differentiation to find the value of the derivative dy / dx.

6479.

The average rate of change of g(x) between x = 4 and x = 7 is 5/6. Which statement must be true a) g(7) - g(4) = 5/6 b) bg(7 - 4)/(7 - 4) = 5/6 c) g(7) - g(4)/(7 - 4)=5/6 d) g(7)/g(4)= 5/6

Answer» The average rate of change of g(x) between x = 4 and x = 7 is 5/6. Which statement must be true
a) g(7) - g(4) = 5/6
b) bg(7 - 4)/(7 - 4) = 5/6
c) g(7) - g(4)/(7 - 4)=5/6
d) g(7)/g(4)= 5/6

Solution:

6480.

Starting from (-1) × 5, write various products showing some pattern to show (-1) × (-1) = 1.

Answer» The pattern shown by the numbers starting with the product (-1) × 5 to(-1) × (-1) = 1is that thenumbers increase by 1 as we move further.

Integers are both negative and positive. The operations perfomed on different integers depend on the properties of integers.

6481.

What is 50degrees Fahrenheit in Celsius?

Answer» 50 degrees Fahrenheit is equal to 10 degrees Celsius.

CelsiusandFahrenheit are the two different types of units used formeasuringtemperature.

6482.

Write the equation of the circle with center (2, -3) and a radius of 4.

Answer» Write the equation of the circle with center (2, -3) and a radius of 4.

Solution:

6483.

Using the fraction 4/6, which number is the denominator?

Answer» For the fraction 4/6, the denominator is 6.

The denominator can be defined as the bottom number in a fraction that shows the number of equal parts an item is divided into.

6484.

Is a square prism the same as a cube? Explain.

Answer» Asquare prism may or may not be the same as a cube

A square prism is a 3-D hexagonal solid figure with all its sides as polygons with square bases. A cube is a 3-D hexagonal solid figure with all its sides as squares.

6485.

Find the exact length of the curve:y = 4 + 4x3/2, 0 ≤ x ≤ 1?

Answer» The exactlength of the curvey = 4 + 4x3/2, 0 ≤ x ≤ 1, is 4.149 units.

We will be using the formula of the exact length of the curve to solve this.

6486.

The number system that has 16 numerals is known as _____.

Answer» The number system that has 16 symbols is known as the hexadecimal number system.

A number system is defined as therepresentation ofnumbers by using digits or other symbols in a consistent manner.

6487.

How do you subtract a fraction from a whole number?

Answer» To subtract a fraction from a whole number, convert thewhole numberinto afraction, then take the lcm to make the denominator the same and subtract.

Whole numbersare all natural numbers including 0.

6488.

How to integrate sin x?

Answer» The final integral ofsin xis− cos x + C

We will useintegration by substitution to integrate sin x.

6489.

If the exterior sides of two adjacent angles are opposite rays, then the angles are _____ angles.

Answer» If the exterior sides of two adjacent angles are opposite rays, then the angles are supplementary angles.

If the sum of two adjacent angles is 180°, then the non-common arms of the angles form a straightline.If a ray stands on a line, the sum of the pair of adjacent angles is 180°.

6490.

What are the vertex focus and directrix of the parabola with the given equation y = 1/28(x - 4)2 - 5

Answer» What are the vertex focus and directrix of the parabola with the given equation y = 1/28(x - 4)2- 5

Solution:

6491.

Find the general solution of the given differential equation. dy/dx +y = e2x

Answer» Find the general solution of the given differential equation. dy/dx +y = e2x

Solution:

6492.

What is the first term of the quotient of the following division problem (x3-1) ÷ (x+2)?

Answer» What is the first term of the quotient of the following division problem (x3-1) ÷ (x+2)?

Solution:

6493.

How do you find the prime factor of a number?

Answer» The prime factors of a number can be found with the help of the division method or the factor tree method.

The process of writing a number as the product of prime numbers is prime factorization.

6494.

What is the slope of the line whose equation is 2x - 4y = 10?

Answer» What is the slope of the line whose equation is 2x - 4y = 10?

Solution:

6495.

The sumof the two-digit number is 9. When we interchange the digits the new number is 27 greater than the earlier number. Find the number.

Answer» The number whosesum of the digits is 9, and when we interchange the digits the new number is 27 greater than the earlier number,is 36.

A two-digit number 'ab' can be represented as a sum of its respectiveplace valuesi.e., ab = 10a + b

6496.

Find the general solution of the given differential equation. dy/dx +2y = e3x

Answer» Find the general solution of the given differential equation. dy/dx +2y = e3x

Solution:

6497.

What is the equation of a line, in general form, that passes through points (-1, 2) and (5, 2)?

Answer» What is the equation of a line, in general form, that passes through points (-1, 2) and (5, 2)?

Solution:

6498.

Find the slope of the curve y = 2x3-8x2 +1at the point (2,-15)

Answer» The slope of the curve y = 2x3-8x2 +1at the point (2,-15) is equal to -8.

We will use the concept of differentiation in order to find the slope of the curve at the given point.

6499.

A cylinder has a height h that is 2 times as large as its radius r. Find its volume V in terms of its radius.

Answer» The volume of acylinder that has a height 2 times as large as its radius r, is 2πr3cubic units.

Volumes are important quantities that have an immense number of applications in various fieldswhich include medical, engineering as well as science. Different solids have different formulae for volumes. Let's solve a problem related to the volume of a cylinder.

6500.

Find all polar coordinates of point p where p = ordered pair 5 comma negative pi divided by 6.

Answer» Find all polar coordinates of point p where p = ordered pair 5 comma negative pi divided by 6.

Solution: