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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.
| 7801. |
How to add and subtract integers without a number line? |
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Answer» Integers can be added and subtracted without a number line in different ways depending upon the sign of the numbers. A number line is a visual representation of numbers on a straight line. |
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| 7802. |
How many kilograms of tea worth ₹300/kg should be mixed with 10kg of tea worth ₹240/kg to produce a mixture to cost ₹260/kg? |
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Answer» 5kgof tea worth ₹300/kg was mixed. We'll form the equation to compare the total price of each variety with the total price of the mixture. |
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| 7803. |
What is 8.5 as aFraction? |
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Answer» 8.5 as a fraction would be written as 17/2. Let's convert 8.5 into a fraction. |
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| 7804. |
What substitution should be used to rewrite x8 - 3x4 + 2 = 0 as a quadratic equation?u = x2u = x4u = x8u = x16 |
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Answer» What substitution should be used to rewrite x8 - 3x4 + 2 = 0 as a quadratic equation?u = x2u = x4u = x8u = x16 Solution: |
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| 7805. |
What is 28 as aFraction? |
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Answer» 28 as a fraction would be written as 56/2. A fraction with a numerator with the number 1 is called a unit fraction. |
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| 7806. |
What is the Value of b2 - 4ac for the following Equation? x2 + 5x + 4 = 0 |
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Answer» What is the Value Of b2 - 4ac for the following Equation? x2 + 5x + 4 = 0 Solution: |
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| 7807. |
Where are the asymptotes of f(x) = tan(4x -π) from x = 0 to x = 2 ? |
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Answer» Where are the asymptotes of f(x) = tan(4x -π) from x = 0 to x = 2 ? Solution: |
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| 7808. |
What is the difference between the polynomials? (8r6s3 - 9r5s4 + 3r4s5) - (2r4s5 - 5r3s6 - 4r5s4) |
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Answer» What is the difference between the polynomials? (8r6s3 - 9r5s4 + 3r4s5) - (2r4s5 - 5r3s6 - 4r5s4) Solution: |
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| 7809. |
Find the first partial derivatives of the function. z = x sin(xy)? |
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Answer» Thefirst partial derivatives of the function. z = x sin(xy) aresin(xy) + xy cos(xy) andx2cos(xy). Differentiating with respect to a single variable while keeping other variables as constants in the expression is known as Partial differentiation. |
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| 7810. |
The outside diameter of a pipe is 5 and 7/32 inches. The walls of the pipe are 5/32 inches thick. What is the inside diameter? |
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Answer» The outside diameter of a pipe is 5 and 7/32 inches. The walls of the pipe are 5/32 inches thick. What is the inside diameter? Solution: |
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| 7811. |
What do you understand by the term vector space? |
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Answer» Avector space is a set of vectors that can be added together and multiplied by a scalar. Vector space can be imagined as a 3D space with a set of objects known as vectors, that can perform certain properties. |
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| 7812. |
What is .44 as a Fraction? |
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Answer» .44 as a fraction would be written as 11/25. A fraction is expressed as a/b, where a is the numerator and b is the denominator. |
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| 7813. |
Find the exact length of the polar curve. r = e2θ, 0 ≤ θ ≤ 2π |
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Answer» Find the exact length of the polar curve. r = e2θ, 0 ≤ θ ≤ 2π Solution: |
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| 7814. |
What is 3 7/8 as a decimal? |
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Answer» The mixed fraction, 3 7/8 written as adecimal is equal to 3.875 Decimalshavea whole numberand the fractional part separated by a decimal point. The decimalpresent between the whole number and fractions part is called the decimal point. For example, 3.5 is a decimal number. |
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| 7815. |
If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(A|B) will be 0.0325, 0.8, 0.65, 0.05 |
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Answer» If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(A|B) will be 0.0325, 0.8, 0.65, 0.05 Solution: |
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| 7816. |
What is 11/7as a Mixed Number? |
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Answer» 11/7as a mixed number can be written as 1 4/7 We can see that 11/7is an improper fraction that can be written as a mixed number consisting of a whole and fractional part. |
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| 7817. |
D) f(k) = 0 |
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Answer» Option Cf(–k) = 0 is correct. On dividing two numbers,if we are getting remainder equal to zero then the smaller numberwill be thefactorof the larger number. |
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| 7818. |
C) f(–k) = 0 |
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Answer» Option Cf(–k) = 0 is correct. On dividing two numbers,if we are getting remainder equal to zero then the smaller numberwill be thefactorof the larger number. |
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| 7819. |
B) Neither x = –k nor x = kis a root of f(x). |
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Answer» Option Cf(–k) = 0 is correct. On dividing two numbers,if we are getting remainder equal to zero then the smaller numberwill be thefactorof the larger number. |
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| 7820. |
A) x = –kand x = kare roots of f(x) |
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Answer» Option Cf(–k) = 0 is correct. On dividing two numbers,if we are getting remainder equal to zero then the smaller numberwill be thefactorof the larger number. |
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| 7821. |
If (x + k) is a factor of f(x), which of the following must be true? |
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Answer» Option Cf(–k) = 0 is correct. On dividing two numbers,if we are getting remainder equal to zero then the smaller numberwill be thefactorof the larger number. |
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| 7822. |
What is 7/12 as a decimal? |
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Answer» 7/12as a decimal is equivalentto 0.583. Bothfractionsanddecimalsare just two ways to represent the same numbers. |
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| 7823. |
One year ago, you invested $1,800. Today it is worth $1,924.62. What rate of interest did you earn? |
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Answer» One year ago, you invested $1,800. Today it is worth $1,924.62. What rate of interest did you earn? Solution: |
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| 7824. |
Simplify completely the quantity of x squared minus 15 x plus 36 all over 5 x minus 60? |
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Answer» x minus 3 over 5 or (x-3)/5 is the completely simplified quantity of x squared minus 15 x plus 36 all over 5 x minus 60 We will use the concept of factorization of quadratic equations in order to find the required answer. |
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| 7825. |
What is the rule for subtracting integers? |
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Answer» What is the rule for subtracting integers? Solution: |
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| 7826. |
Find a.b if a = 4i + 8j, b = -2i + 3j |
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Answer» Find a.b if a = 4i + 8j, b = -2i + 3j Solution: |
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| 7827. |
Express 3 divided by 2 as a fraction. |
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Answer» The value of 3 divided by 2as a fraction is 3/2 =1½. To writea fraction in its simplest form meansthe numeratorand denominator can no longer be divided by the same whole number exactly or evenly. |
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| 7828. |
In which diagram do angles 1 and 2 form a linear pair? |
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Answer» angle1 and 2 in option b forms a linear pair.
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| 7829. |
What does it mean to be cancelled? |
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Answer» The term 'cancelled' in math means to remove or simply that particular value or expression by subtracting, or dividingwitha common term. The cancellation in math is defined as reducing the given expression by division. |
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| 7830. |
Suppose 2,1 = 9 4,2 = 18 5,3 = 18 6,3 = 27 then 9,4= ? |
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Answer» 2,1 = 9 4,2 = 18 5,3 = 18 6,3 = 27. Then,then 9,4 = 45 and the solution is 94 - 49 = 45. Math Patterns are sequences that repeat based on a rule, and a rule is a set way to calculate or solve a problem. |
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| 7831. |
What is the population variance of the following set of numbers: 3, 5, 8, 9, 10? |
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Answer» What is the population variance of the following set of numbers: 3, 5, 8, 9, 10? Solution: |
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| 7832. |
Find the First Partial Derivatives of the Function. u = 2xy/z |
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Answer» TheFirst Partial Derivatives of the Functionu = 2xy/z areux=2y/z,uy= 2x/z, anduz= -2xy/z2. We will be using the concept of differentiation to solve this. |
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| 7833. |
How to find the length of a line segment in a circle? |
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Answer» To find the length of a line segment in a circle, we can use the formula d = 2r sin(t/2), where r is the radius of the circle and t is the angle between the radii. Linesegmentsare a very important part of geometry. Line segments make polygons and can also be used to represent equations on graphs. They have interesting properties which are to be learned in order to do well in geometry exams! Let's learn how to find the length of a line segment in a circle, which can also be called chords. |
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| 7834. |
The ratio of the width to the length of a rectangle is 4:5. lf the area of the rectangle is 500 square centimeters, what is the length of the rectangle? |
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Answer» For the given rectangle with ratio of the width to the length as 4:5 and area 500 square centimeters, the length is 25 cm. Rectangles are types of quadrilaterals having two pairs of parallel sides and having four 90 degree angles. The area of a rectangle is given by the product of length and breadth. |
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| 7835. |
What are the exact solutions of x2 = 5x + 2? |
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Answer» What are the exact solutions of x2= 5x + 2? Solution: |
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| 7836. |
How to find the mean and standard deviation of a standard normal distribution? |
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Answer» The mean of a standard normal distribution is zero, and the standard deviation is one. Statistics is an important branch of mathematicsthat concerns the collection, organization, analysis, interpretation, and presentation of data. Various parameters like mean, median, and mode are used to analyze data and extract information from them. Here, we will see how to find the mean and standard deviation of standard normally distributed data. |
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| 7837. |
Let X= {a, b, c, d}. What is {A: A∈ P(X) and |A| = 2}? |
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Answer» {A: A∈ P(X) and |A| = 2} = {{a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}} A set is a collection of elements. A powerset is a collection of all the possible sets that can be formed of the given set. |
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| 7838. |
The organizers of an essay competition decide that a winner gets a prize of Rs.100 and who does notwin gets a prize of Rs.25. The total prize money distributed is 3000. Find the no. of winners if no. of participants is 63. |
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Answer» The number of winners who receiveda prize of Rs.100 is 19 where the total number of participants in the essay competition is 63. An equation is a mathematical statement that shows equality between two different algebraic expressions or constants. |
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| 7839. |
Find the lateral area of a cone with a radius of 7ft. and a slant height of 13ft. Use 3.14 for pi and round to the nearest tenth? |
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Answer» Find the lateral area of a cone with a radius of 7ft. and a slant height of 13ft. Use 3.14 for pi and round to the nearest tenth? Solution: |
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| 7840. |
If a function is odd its graph is symmetric with respect to the origin. Explain. |
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Answer» The graph of an odd function which is always symmetric with respect to the origin, satisfies the condition f(-x) = -f(x). Functions are very important concepts in mathematics. Every advanced topic in mathematics has to deal with functions at some point in time; be it trigonometry, linear algebra, or calculus. We can tell if a function is even or not by looking at its graph. Let's see how. |
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| 7841. |
What is 0.3as a percent? |
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Answer» 0.3as a percentis equal to 30% We have to convert a decimal number to percent. |
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| 7842. |
(a) A ⊂ B; (b) A ⊃ B; (c) A ⊆ B; (d) A⊇ B |
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Answer» IfA ={x|x is a polygon}, B ={x|x is a triangle} then A⊃ B. The given question is based on subsets and supersets and properties of geometric shapes. |
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| 7843. |
Consider the sets below. A ={x|x is a polygon}, B ={x|x is a triangle} which is true? |
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Answer» IfA ={x|x is a polygon}, B ={x|x is a triangle} then A⊃ B. The given question is based on subsets and supersets and properties of geometric shapes. |
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| 7844. |
Suppose that y varies directly with x and inversely with z, y = 18 when x = 15 and z = 5. How do you write the equation that models the relationship, then find y when x = 21 and z = 7? |
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Answer» Suppose that y varies directly with x and inversely with z, y = 18 when x = 15 and z = 5. How do you write the equation that models the relationship, then find y when x = 21 and z = 7? Solution: |
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| 7845. |
Find an explicit solution of the given initial-value problem. x2(dy/dx) = y - xy, y(-1) = -1 |
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Answer» Find an explicit solution of the given initial-value problem. x2(dy/dx) = y - xy, y(-1) = -1 Solution: |
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| 7846. |
Find the derivative of sec x. |
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Answer» The derivative of sec x is tan x × sec x. To find the derivative of sec x, we will use the quotient rule. |
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| 7847. |
Choose the correct simplification of the expression (7x - 3)(4x2 - 3x - 6). 28x3 - 33x2 - 33x - 18 28x3 + 33x2 - 33x + 18 28x3 - 51x2 - 33x + 18 28x3 - 33x2 - 33x + 18 |
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Answer» Choose the correct simplification of the expression (7x - 3)(4x2 - 3x - 6) Solution: |
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| 7848. |
Find the first four terms of the sequence. a1 = 1, an= 4 • an -1 |
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Answer» The first four termsof the sequence\(a_{1}\) = 1,\(a_{n}\) = 4 •\(a_{n-1}\) are 1, 4, 16, and 64. We will use the concept of sequence and series in order to find the first 4 terms. |
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| 7849. |
Find the vertex, focus, directrix, and focal width of the parabola. x2 = 28y |
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Answer» Find the vertex, focus, directrix, and focal width of the parabola. x2 = 28y Solution: |
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| 7850. |
Find the horizontal or oblique asymptote of f (x) = 2x2 + 5x + 6, all over x plus 1. |
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Answer» Find the horizontal or oblique asymptote of f (x) = 2x2 + 5x + 6, all over x plus 1. Solution: |
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