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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.
| 5851. |
Using the given zero, find one other zero of f(x). If 1 - 6i is a zero of f(x) = x4 - 2x3 + 38x2 - 2x + 37. |
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Answer» Using the given zero, find one other zero of f(x). If 1 - 6i is a zero of f(x) = x4- 2x3+ 38x2- 2x + 37. Solution: |
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| 5852. |
The measures of two angles of a triangle are 35° and 45°. What is the measure of the third angle of the triangle? |
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Answer» The measures of two angles of a triangle are 35° and 45°. The measure of the third angle of the triangle is 100° A triangle has three sides and three angles, one at each vertex, bounded by a pair of adjacent sides. |
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| 5853. |
What is the solution set of the given system of equations 2y = x + 3 and 5y = x - 7? |
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Answer» What is the solution set of the given system of equations 2y = x + 3 and 5y = x - 7? Solution: |
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| 5854. |
Find the least number which when divided by 6, 15, and 18 leave a remainder of5 in each case. |
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Answer» The least number, which when divided by 6, 15, and 18 leave a remainder of5 in each case, is 95. When aleast number is completely divisible by a set of numbers, it is known as the 'Lowest Common Multiple' for those numbers. |
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| 5855. |
Consider the equation below. f(x) = 2x3 + 3x2 - 72x (a) Find the interval on which f is increasing. Find the interval on which f is decreasing. (b) Find the local minimum and maximum values of f. (c) Find the inflection point. (x, y) = find the interval on which f is concave up. Find the interval on which f is concave down. |
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Answer» Consider the equation below. f(x) = 2x3 + 3x2 - 72x. (a) Find the interval on which f is increasing. Find the interval on which f is decreasing. (b) Find the local minimum and maximum values of f. (c) Find the inflection point. (x, y) = find the interval on which f is concave up. Find the interval on which f is concave down. Solution: |
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| 5856. |
If a polynomial function f(x) has roots 3 and square root of 7, what must also be a root of f(x)? |
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Answer» If a polynomial function f(x) has roots 3 and square root of 7, what must also be a root of f(x)? Solution: |
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| 5857. |
How to know if a number is divisible by 7? |
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Answer» The rule is that the last digit of the given number should be multiplied by 2 and then subtracted with the rest of the number leaving the last digit. If the difference is 0 or a multiple of 7, then it is divisible by 7. Let us explore the divisibility rule of7. |
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| 5858. |
Sides of a triangle are in ratio 2 : 3 : 4. Its perimeter is 27 cm. Find the length of each side. |
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Answer» The length of the sides of the triangle are 6 cm, 9cm, and 12 cm. The perimeter of a triangle means the sum of its boundary or all three sides. |
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| 5859. |
What is 4% as a fraction in simplest form? |
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Answer» The value of 4% as a fraction in simplest form is 1/25. To writea fraction in its simplest form means that the numerator and denominatorcan no longer be divided by the same whole number exactly or evenly. |
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| 5860. |
What is the solution to the system of equations? y = 1/3x - 10 and 2x + y = 4 |
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Answer» What is the solution to the system of equations? y = 1/3x - 10 and 2x + y = 4 Solution: |
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| 5861. |
Use the associative property of addition to find the total of 1, 10, and 18 in two different ways. |
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Answer» Use the associative property of addition to find the total of 1, 10, and 18 in two different ways. Solution: |
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| 5862. |
Write the standard form of the equation of the circle with the given characteristics? Center: (3, -2), Solution Point: (-1, 1) |
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Answer» Write the standard form of the equation of the circle with the given characteristics? Solution: |
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| 5863. |
Solve the following system of equations. x + 2y − 6 = z; 3y − 2z = 7; 4 + 3x = 2y − 5z. |
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Answer» For the following system of equations x + 2y − 6 = z; 3y − 2z = 7; 4 + 3x = 2y − 5z, the values of x, y and z are 7/ 4, 3/ 2 and - 5/ 4 respectively. The given system of equations are linear equations in three variables. The standard formof a three variable linear equation is ax + by + cz = k where a,b,c are coefficients, x, y, z are variablesand k is a constant. |
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| 5864. |
The sum of the measures of the interior angles of a polygon is 720°. What type of polygon is it? |
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Answer» The polygon having the sum of interior angles as 720° is Hexagon. We will use the concept of polygons to solve the question.Allinterior anglesof any regular polygon are equal to each other. |
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| 5865. |
Find an equation of the line having the given slope 4 and containing the given point (6, 11). |
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Answer» The equation in slope-intercept form of the line through the point (6, 11) with slope 4is given as y = 4x - 13. In this problem, we use the concept of the point-slope form of the straight line to find the equation. |
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| 5866. |
Find the Exact Length of the Curve. x = 1/3 √y (y − 3), 9≤ y ≤ 25 |
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Answer» The ExactLength of the Curvex = 1/3 √y (y − 3), 9≤ y ≤ 25is 92/3. We will be using the formula of integration to calculatethe exact length of the curve to solve this. |
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| 5867. |
What is a 10 out of 15? |
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Answer» 10 out of 15 is equivalent 2/3 or 66.7 %.10/15 =2/3= 0.6667 = 66.67 % The question is based on definitions of fractions and percentages. |
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| 5868. |
Find the derivative of the function logarithmic function (logx)using the first principle ofderivative. |
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Answer» The derivative of the logarithmic function (logx) by using the first principle of the derivative is 1/(x ln a). The symboldy/dx iscalled the derivative of the dependent variable y with respect to the independent variablex. The process of finding the derivatives is called differentiation. |
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| 5869. |
What is the formula for the circumference C of a circle of radius r? |
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Answer» The formula to find the circumference C of a circle of radius risC = 2π r. The circumference of a circle is the length of the boundary of the circle. |
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| 5870. |
A sequence has a common ratio of 3/2 and f(5) = 81. Which explicit formula represents the sequence? f(x) = 24 f(x) = 16 f(x) = 24 f(x) = 16 |
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Answer» A sequence has a common ratio of 3/2 and f(5) = 81. Which explicit formula represents the sequence? Solution: |
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| 5871. |
Holly finds that (11m - 13n + 6mn) - (10m - 7n + 3mn) = m - 20n + 9mn. What error did Holly make? |
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Answer» Holly finds that (11m - 13n + 6mn) - (10m - 7n + 3mn) = m - 20n + 9mn. What error did Holly make? Solution: |
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| 5872. |
Find the Exact Length of the Curve. x = 1/3 √y (y − 3), 1 ≤ y ≤ 9 |
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Answer» The ExactLength of the Curvex = 1/3 √y (y − 3), 1 ≤ y ≤ 9 is 32/3 units. We will be using the formula of the exact length of the curve to solve this. |
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| 5873. |
How many sides does a regular polygon have if one exterior angle is 1? |
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Answer» For an exterior angle equal to 1, the total number of sides is equal to 360°. We will use the relationship between the exterior angle and the number of sides of a regular polygon. |
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| 5874. |
Prove that cos 20°· cos40°· cos60°. cos80° = 1/16 |
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Answer» It's proved thatcos 20° · cos40° · cos60°. cos80° = 1/16 Trigonometric ratios help us to calculate the sides of a right angled triangle with the help of a given angle and a given side. Trigonometric angle value is a collective term for values ofdifferent ratios, such as sine, cosine, tangent, secant, cotangent, and cosecant. |
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| 5875. |
An acute angle θ is in a right triangle with sin θ = 6/7. What is the value of cot θ? |
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Answer» In a right triangle with sin θ = 6/7, the value of cot θ = (√13) / 6. Trigonometryis a branch of mathematics that deals with the relation between the angles and sides of a right triangle. |
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| 5876. |
If y equals 32, then what is x in this equation? y = 192 ÷ x |
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Answer» If y equals 32, then what is x in this equation? y = 192 ÷ x Solution: |
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| 5877. |
Find the measure of each angle in triangle ABC. Triangle ABChas angles labeled as follows: A =(x minus 26) degrees,B = (2x minus 227) degrees,C =(one half x plus 13) degrees |
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Answer» The measure of each angle of triangle ABC withA =(x minus 26) degrees,B = (2x minus 227) degrees,C =(one half x plus 13) degrees is 94°,13° and 73° A triangle is a three-sided polygonwith 3 edges, angles, and vertices |
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| 5878. |
How to use the properties of rational numbers in the questions? |
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Answer» To use the different properties of rational numbers, we use the definition of the properties involved with different mathematical operations. A rational number is formed when any two integers, such as p and q,are expressed in the form of p/q, where q≠ 0. |
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| 5879. |
Find the roots of the equation x2- 5x + 6 = 0 using the quadratic formula. |
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Answer» Using the quadratic formula, the roots of the equation x2- 5x + 6 are 2 and 3. A quadratic equation is an equation in the form of ax2- bx + c= 0 where a is a non-zero value. |
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| 5880. |
Find the sample space for tossing 2 coins,then find p(exactly 1 head). |
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Answer» The sample space for tossing 2 coins is{ TT, TH, HT, HH }and p(exactly 1 head) is 1/2. Sample space, in probability, is referred to as the collectionof all possible outcomes in any random experiment. It is denoted by "S". |
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| 5881. |
A man sells two houses at the rate of rupees 1.95 lacs each. On one, he gains 5% and on the otherhe lost 5%. Find his gain or loss percent in the whole transaction. |
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Answer» A man who sells two houses at the rate of rupees 1.95 lacs each, gaining5% and on oneandloosing 5% on the other faces a loss percent in the whole transaction which is 0.25%. A profit or loss is the difference between the cost price and the selling price. If the cost price is more than the selling price, then the transaction results in a loss, whereas if the selling price is more than the cost price then the transaction results in a profit. |
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| 5882. |
What is1/4of 12? |
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Answer» 1/4of 12 is 3. Themultiplication of fractionsstarts with the multiplication of the given numerators, followed by the multiplication of the denominators. |
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| 5883. |
How to find the radius and diameter of a circle? |
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Answer» Using the formula d= Circumference/π and r = d/2we can find the diameter and radius of a circle Diameteris the longest chordof the circle and radiusis half of the diameter. |
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| 5884. |
What is 3/8 as a decimal? |
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Answer» 3/8 as a decimal is0.375 Adecimalnumber can bedefinedas a number whose whole number part and the fractional part are separated by adecimalpoint. |
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| 5885. |
Find x in (2x + 5)/3= 3x - 10. |
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Answer» The value of x in the given equation(2x + 5)/3= 3x - 10 is 5. In algebra, we use the balancing or the transposition method to solve for the unknown variable 'x'. |
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| 5886. |
What is the mean of a discrete random variable? |
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Answer» The mean of adiscrete random variable is given by ux= x1p1+ x2p2+ x3p3..........xnpn =Σ xipi We will use the concept of probability and random variables to find the mean of discrete random variables. |
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| 5887. |
How can the triangles be proven similar by the sss similarity theorem? |
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Answer» Triangles ABC and QPR are both similar by SSS since the ratio of their corresponding sides is equal. Similarity can be proven, either by SSS, SAS, or AAS. |
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| 5888. |
Find an equation of the tangent line to the curve at the given point. y = sin(sin(x)), (π, 0)? |
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Answer» Find an equation of the tangent line to the curve at the given point. y = sin(sin(x)), (π, 0)? Solution: |
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| 5889. |
Find the next three terms of the sequence -8, 24, -72, 216, . . .? |
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Answer» Find the next three terms of the sequence -8, 24, -72, 216, . . .? Solution: |
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| 5890. |
What are the vertical and horizontal asymptotes for the function f(x) = 3x2/x2 - 4 |
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Answer» What are the vertical and horizontal asymptotes for the function f(x) = 3x2/x2 - 4 Solution: |
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| 5891. |
Express 4/5 × 4/5 as a fraction. |
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Answer» The product of the fractionin its simplest form 4/5 × 4/5 is 16/ 25. A fraction is apart of the whole. It is in the form of a/b where a represents the part and b represents the whole, and b cannot be zero. |
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| 5892. |
Find the common factors of: (a) 4, 8 and 12 (b) 5, 15 and 25 |
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Answer» Common factors of (a) 4, 8 and 12 are1, 2 and 4 and(b) 5, 15 and 25 are1 and 5. A factor is nothing but a divisor of the given number. |
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| 5893. |
Find the solutions of the equation, 1/2x2 - x + 5 = 0. |
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Answer» Find the solutions of the equation, 1/2x2 - x + 5 = 0. Solution: |
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| 5894. |
If the product of two whole numbersis 1, can we say that one or both of them will be 1? Justify through examples. |
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Answer» If the product of two whole numbers is 1, thenboth of them will be 1 Natural numbers refer to aset of positive integers and on the other hand,natural numbers along with zero (0) form a set, referred to aswhole numbers. |
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| 5895. |
What is 6PM in military time? |
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Answer» 6 PM in military time is 18:00 hours. Military time is a method of measuring the time based on the full 24 hours of the day. |
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| 5896. |
Simplify the following expression: 35 + (-13) + (+8) -(-6). |
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Answer» 35 + (-13) + (+8) - (-6) = 36. The question is based on the operation ofintegers. |
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| 5897. |
How do you know if a graph is one-to-one? |
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Answer» Any function that follows the horizontal line test, can only be classified as a one-to-one function. A one-to-one function is afunction in which for each value of thedomain, there is a unique output/range in the graph of the function. |
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| 5898. |
What are the solutions of the equation x4 - 9x2 + 8 = 0? Use u substitution to solve. |
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Answer» What are the solutions of the equation x4- 9x2+ 8 = 0? Use u substitution to solve. Solution: |
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| 5899. |
Non terminating non-repeating |
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Answer» Thus, conversion of decimal numbers to p/q depends upon the type of decimal we have Explanation: |
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| 5900. |
Non terminating repeating |
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Answer» Thus, conversion of decimal numbers to p/q depends upon the type of decimal we have Explanation: |
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