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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your General Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 8201. |
In the kite, AC = 10 and BD = 6. What is the area of kite ABCD? |
| Answer» <strong style="font-size: 15px; line-height: 20px !important;">In the kite, AC = 10 and BD = 6. What is the area of kite ABCD?</strong><p><b id="docs-internal-guid-e9a34df0-7fff-2afa-670a-df602b941586"><img alt="pic3" src="https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/q306-1-1634917410.png" style="width: 300px;"/></b></p> | |
| 8202. |
(iv) tan-1 (2 cos (2π/3) ) |
| Answer» <strong style="font-size:14px; line-height:20px !important;"> The value ofinverse tan ratios are (i) is π / 6, (ii) is - π / 6,(iii) is 0 and (iv) is- π / 4.</strong><p>To find the values of the above inverse trigonometric ratios, we will use <a href="https://www.cuemath.com/trigonometry/trigonometric-identities/">trigonometric identities</a>.</p> | |
| 8203. |
(iii) tan-1 (cos (π/2) ) |
| Answer» <strong style="font-size:14px; line-height:20px !important;"> The value ofinverse tan ratios are (i) is π / 6, (ii) is - π / 6,(iii) is 0 and (iv) is- π / 4.</strong><p>To find the values of the above inverse trigonometric ratios, we will use <a href="https://www.cuemath.com/trigonometry/trigonometric-identities/">trigonometric identities</a>.</p> | |
| 8204. |
(ii) tan-1 (-1/√3) |
| Answer» <strong style="font-size:14px; line-height:20px !important;"> The value ofinverse tan ratios are (i) is π / 6, (ii) is - π / 6,(iii) is 0 and (iv) is- π / 4.</strong><p>To find the values of the above inverse trigonometric ratios, we will use <a href="https://www.cuemath.com/trigonometry/trigonometric-identities/">trigonometric identities</a>.</p> | |
| 8205. |
(i) tan-1 (1/√3) |
| Answer» <strong style="font-size:14px; line-height:20px !important;"> The value ofinverse tan ratios are (i) is π / 6, (ii) is - π / 6,(iii) is 0 and (iv) is- π / 4.</strong><p>To find the values of the above inverse trigonometric ratios, we will use <a href="https://www.cuemath.com/trigonometry/trigonometric-identities/">trigonometric identities</a>.</p> | |
| 8206. |
Find the value of each of the following: |
| Answer» <strong style="font-size:14px; line-height:20px !important;"> The value ofinverse tan ratios are (i) is π / 6, (ii) is - π / 6,(iii) is 0 and (iv) is- π / 4.</strong><p>To find the values of the above inverse trigonometric ratios, we will use <a href="https://www.cuemath.com/trigonometry/trigonometric-identities/">trigonometric identities</a>.</p> | |
| 8207. |
Write an equation in slope-intercept form, given that the line passes through the point (2, 7) and has a slope of 2? |
| Answer» <strong style="font-size: 15px; line-height: 20px !important;">Write an equation in slope-intercept form, given that the line passes through the point (2, 7) and has a slope of 2?</strong><p><strong>Solution:</strong></p> | |
| 8208. |
Which quadratic equation is equivalent to (x2- 1)2- 11(x2- 1) + 24 = 0? |
| Answer» <strong style="font-size: 15px; line-height: 20px !important;">Which quadratic equation is equivalent to (x<sup>2</sup>- 1)<sup>2</sup>- 11(x<sup>2</sup>- 1) + 24 = 0?</strong><p><strong>Solution:</strong></p> | |
| 8209. |
Solve the equation 8 - 2x = - 8x + 14 |
| Answer» <strong style="font-size: 15px; line-height: 20px !important;">Solve the equation8 - 2x = - 8x + 14</strong><p><strong>Solution:</strong></p> | |
| 8210. |
How do you find the mode of a data set? |
| Answer» <strong> Mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all.</strong><p>Themode is one of the most frequently used metrics in statistics.</p> | |
| 8211. |
Find the taylor polynomial t3(x) for the function f centered at the number: f (x) = 7 tan-1(x), a = 1, t3(x) |
| Answer» <strong style="font-size: 15px; line-height: 20px !important;">Find the taylor polynomial t3(x) for the function f centered at the number:<br/> f (x) = 7 tan - 1(x), a = 1 t3(x)</strong><p><strong>Solution:</strong></p> | |
| 8212. |
A polygon has an angle sum of 360° and each angle measures 90°. What is the polygon? |
| Answer» <strong> Rectangle andsquare are polygons that have an angle sum of 360° and each angle measures 90°.</strong><p>A closed shape having sides and vertices is known as a polygon. If a polygon hasinterior angles and sides are equal, it is known as a regular polygon.</p> | |
| 8213. |
How many crores make 10 million? |
| Answer» <strong> 1 crore makes 10 million.</strong><p>Crore is a place value that is used in the Indian place value chart, whereas, million is a place value that is used in the International place value chart.</p> | |
| 8214. |
Show that (sinθ -cosθ + 1) / ( sinθ + cosθ - 1) = 1 /(secθ - tanθ ) |
| Answer» <strong>Answer : (sinθ -cosθ + 1) / ( sinθ + cosθ - 1) = 1 /(secθ - tanθ )</strong><p>We can use the <a href="https://www.cuemath.com/trigonometry/trigonometric-identities/">trigonometric identity</a> (sec<sup>2</sup>θ = 1 + tan<sup>2</sup>θ)</p> | |
| 8215. |
Let f(x) = x2− 8x + 5. Find f(−1). |
| Answer» <strong> For f(x) = x<sup>2</sup>− 8x + 5, f(-1) = 14</strong><p>We have the functionf(x) = x<sup>2</sup>− 8x + 5</p> | |
| 8216. |
Find the exact length of the curve. y = 2 + 8x3/2, 0 ≤ x ≤ 1? |
| Answer» <strong> The exact length of the curve is 7.995.</strong><p>The length of a curve is a geometrical concept that addressed by <a href="https://www.cuemath.com/calculus/integral/">integral calculus</a>. It is a method for calculating the exact lengths of <a href="https://www.cuemath.com/geometry/line-segment/">line segments</a>.</p> | |
| 8217. |
Prove that: sin6x + cos6x = 1 - 3 sin2x cos2x. |
| Answer» <strong> sin<sup>6</sup>x + cos<sup>6</sup>x = 1 - 3 sin<sup>2</sup>x cos<sup>2</sup>x</strong><p><a href="https://www.cuemath.com/trigonometry/cosine-function/">Cosine </a>and <a href="https://www.cuemath.com/trigonometry/sine-function/">Sine </a>are primary trigonometric functions. They are also known as complemetary functions</p> | |
| 8218. |
In Triangle ABC, ∠A is a Right Angle and ∠B = 45°. Find BC. If your answer is not an Integer, Leave it in Simplest Radical Form. |
| Answer» <strong>If∠A is a Right Angle and ∠B = 45°, then BC = AB√2</strong><p>We will be using the Angle Sum Theorem and the Pythagorastheorem to solve this.</p> | |
| 8219. |
Explain the term Jacobian. |
| Answer» <strong style="font-size: 15px; line-height: 20px !important;">Explain the term Jacobian.</strong><p><strong>Solution:</strong></p> | |
| 8220. |
Multiples that are shared by two or more numbers are called __________ |
| Answer» <strong> Multiples that are shared by two or more numbers arecalled the common multiples of the two numbers.</strong><p>A <a href="https://www.cuemath.com/numbers/multiples/">multiple</a> is a product that we get when one number is multiplied by another number.</p> | |
| 8221. |
Using divisibility test, determine which of the following numbers are divisibly by 4, by 8 (a) 572 (b) 726352 (c) 5500 (d) 6000 (e) 12159 (f) 14560 (g) 21084 (h) 31795072 (i) 1700 (j) 2150 |
| Answer» <strong> The numbers which are divisible by 4 are a), b), c), d), f), g), h) and i) while the numbers divisible by 8 are b),d),f) and h).</strong><p>A <a href="https://www.cuemath.com/numbers/divisibility-rules/">divisibility rule </a>is a kind of shortcut to figure out if a given <a href="https://www.cuemath.com/numbers/integers/">integer</a> is divisible by a divisor, without performing the whole division process but by examining its digits.</p> | |
| 8222. |
How to convert kilometers per hour to meters per second? |
| Answer» <strong> To convert kilometers per hour tometers per second, we multiply the given value by 5/18</strong><p>Kilometers per hour can be easily converted intometers per second by using a conversion factor.</p> | |
| 8223. |
What is 15% of 20? |
| Answer» <strong> 15% of 20 is 3.</strong><p>A percentis a ratio of a number expressed out of100.</p> | |
| 8224. |
Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1. |
| Answer» <strong style="font-size: 15px; line-height: 20px !important;">Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1.</strong><p><strong>Solution:</strong></p> | |
| 8225. |
What is 7 to the power of 0? |
| Answer» <strong> 7 to the power of 0 is 1.</strong><p>We will solve this question by using the zero <a href="https://www.cuemath.com/algebra/exponent-rules/">property of exponents</a>.</p> | |
| 8226. |
What is 33(1/3)%as a fraction? |
| Answer» <strong> 33(1/3)%as a fraction is 1/3</strong><p>Percent means per hundred or for every hundred. We represent percentage with the symbol %.</p> | |
| 8227. |
Write an equation in slope-intercept form when the slope and a point are given. |
| Answer» <strong style="font-size: 15px; line-height: 20px !important;">Write an equation in slope-intercept form when the slope and a point are given.</strong><p><strong>Solution:</strong></p> | |
| 8228. |
What is the difference between an outcome and an event? |
| Answer» <strong> Thedifference between an outcome and an event is - an event is the total number of outcomes whereas an outcome is the result of an event.</strong><p>Outcome and Event are both <a href="https://www.cuemath.com/data/terms-of-probability/">terms of Probability</a> that will be discussed here.</p> | |
| 8229. |
What number fills in the blank to complete the factorization of 3x + 24? _____(x + 8) |
| Answer» <strong style="font-size: 15px; line-height: 20px !important;">What number fills in the blank to complete the factorization of 3x + 24? _____(x + 8)</strong><p><strong>Solution:</strong></p> | |
| 8230. |
Find the 12th partial sum of the summation of negative 2i minus 10, from i equals 1 to infinity. |
| Answer» <strong> The12th partial sum of the summation of negative 2i minus 10, from i equals 1 to infinity is -276.</strong><p>A <a href="https://www.cuemath.com/algebra/Sum-of-arithmetic-sequence/">partial sum</a> is basically the sum of part of a sequence. Sometimes partial sums are called "Finite Series".</p> | |
| 8231. |
What is 105% as a fraction? |
| Answer» <strong> 105% can be represented as 21/20in fraction form.</strong><p>A<a href="https://www.cuemath.com/numbers/fractions/">Fraction</a>can be a portion or section of any quantity out of a whole, where, the whole can be any number, a specific value, or a thing. All fractions consist ofa <a href="https://www.cuemath.com/numbers/numerator/">numerator</a> and a <a href="https://www.cuemath.com/numbers/denominator/">denominator</a>.</p> | |
| 8232. |
Find the volume of the cylinder in terms of pi? |
| Answer» <strong style="font-size: 15px; line-height: 20px !important;">Find the volume of the cylinder in terms of pi?</strong><p><strong>Solution:</strong></p> | |
| 8233. |
If the diameter of circle c is 3 times the diameter of circle d, then what is the ratio of their areas? |
| Answer» <strong> The ratio of the area of circle 'c' to the area of circle 'd' is 9:1</strong><p>The area of a circle is given by the formula: π/4 × (diameter)<sup>2</sup></p> | |
| 8234. |
How many cubic centimeters cm3 are in a cubic meter m3? |
| Answer» <strong> 1 cubic meter = 10<sup>6</sup> cubic centimeter</strong><p>We will use the concept of measuring systems in order to find the required answer. We will use the fact that 1 meter is equal to 100 centimeters.</p> | |
| 8235. |
How many faces edges and vertices does a cube have? |
| Answer» <strong> A cube has 6 faces,12edges, and 8 vertices</strong><p>A <a href="https://www.cuemath.com/measurement/volume-of-cube/">cube</a> is a 3-dimensional object with edges of equal length.</p> | |
| 8236. |
How to measure the height of a tree using trigonometry? |
| Answer» <strong> B<span style="color:null;">asic trigonometric formulas for tangent functions can easily help us to find the height of the tree.</span></strong><p>We can make use of the tangent function in trigonometry to find the height of the triangle.</p> | |
| 8237. |
If xy + 3ey = 3e, find the value of y'' at the point where x = 0. |
| Answer» <strong style="font-size: 15px; line-height: 20px !important;">If xy + 3e<sup>y</sup> = 3e, find the value of y'' at the point where x = 0.</strong><p><strong>Solution:</strong></p> | |
| 8238. |
How to find the average of a set of numbers? |
| Answer» <strong> The average of a set of numbers is obtained by dividing the sum of the values by the number of values in the set.</strong><p>The <a href="https://www.cuemath.com/data/average/">average</a> of a set of values is equal to the sum of the values divided by the number of values.</p> | |
| 8239. |
What is the value of (-7 + 3i) - (2 - 6i)? -9 + 9i,-9 - 3i,-5 - 3i,- 5 + 9i |
| Answer» <strong style="font-size: 15px; line-height: 20px !important;">What is the value of (- 7 + 3i) - (2 - 6i)?</strong><p><strong>Solution: </strong></p> | |
| 8240. |
What is 14/9 as a mixed number? |
| Answer» <strong> 14/9 as a mixed number is 1 5/9.</strong><p>An<a href="https://www.cuemath.com/numbers/improper-fractions/">improper fraction</a>is a typeof fractionwhere the numerator is greater than or equal to the denominator.</p> | |
| 8241. |
Find the derivative of the function using the definition of derivative. g(x) = 5 - x |
| Answer» <strong style="font-size: 15px; line-height: 20px !important;">Find the derivative of the function using the definition of derivative. g(x) = 5 - x</strong><p><strong>Solution:</strong></p> | |
| 8242. |
What is the Equation of the Line that Passes through the Points (−3, 2) and (−5, 8)? |
| Answer» <strong style="font-size: 15px; line-height: 20px !important;">What is the equation of the line that passes through the points (-3, 2) and (-5, 8)?</strong><p><strong>Solution:</strong></p> | |
| 8243. |
Determine if 25110 is divisible by 45 Hint: 5 and 9 are co-prime numbers. Test the divisibility of the number by 5 and 9. |
| Answer» <strong> Yes, 25110 is divisible by 45</strong><p>We can check the <a href="https://www.cuemath.com/numbers/divisibility-rules/">divisibility</a>by using the numbers 5 and 9 which are <a href="https://www.cuemath.com/numbers/coprime-numbers/">co-prime numbers</a>. The divisibility can be tested by using the prime factorization method.</p> | |
| 8244. |
Find an equation for the nth term of the arithmetic sequence. a18 = 97, a20 = 281. |
| Answer» <strong style="font-size: 15px; line-height: 20px !important;">Find an equation for the nth term of the arithmetic sequence. a18 = 97, a20 = 281.</strong><p><strong>Solution:</strong></p> | |
| 8245. |
How do you verify the identity: cos2x− sin2x= 1 − 2sin2x |
| Answer» <strong> The identitycos<sup>2</sup>x− sin<sup>2</sup>x= 1 − 2sin<sup>2</sup>xis verified.</strong><p><a href="https://www.cuemath.com/trigonometry/trigonometric-identities/">Trigonometric identities</a> are <a href="https://www.cuemath.com/algebra/equation/">equations </a>that relate different trigonometric functions using different mathematical operations.</p> | |
| 8246. |
Find the limit: lim x➝0 sin | x | / 2x |
| Answer» <strong> The limit: lim x➝0 sin | x | / 2x does not exist.</strong><p>We will use the concept of limits and <a href="https://www.cuemath.com/calculus/What-are-functions/">function</a> to find our required limit</p> | |
| 8247. |
What is 10% of 20? |
| Answer» <strong> 10% of 20 is 2.</strong><p>A <a href="https://www.cuemath.com/commercial-math/percentages/">percent</a>is a ratio of a number expressed out of100.</p> | |
| 8248. |
What is the solution set of {x | x < -5} ∩ {x | x > 5}? |
| Answer» <strong style="font-size: 15px; line-height: 20px !important;">What is the solution set of {x | x < -5} ∩ {x | x > 5}?</strong><p><strong>Solution:</strong></p> | |
| 8249. |
If Sam has 6 different hats and 3 different scarves, how many different combinations could he wear? |
| Answer» <strong style="font-size: 15px; line-height: 20px !important;">If Sam has 6 different hats and 3 different scarves, how many different combinations could he wear?</strong><p><strong>Solution:</strong></p> | |
| 8250. |
5,7,19,24,10,17,21,6,22,5,9 |
| Answer» <strong>The mean, median, and mode for the given data set are 13.18, 10, 5 respectively.</strong><p>Mean, median, and mode are important statistics parameters to analyze any data set.</p> | |