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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.
| 1201. |
Find the volume of the solid that lies within both the cylinder x2+ y2= 1 and the sphere x2+ y2+ z2= 4 |
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Answer» Find the volume of the solid that lies within both the cylinder x2+ y2= 1and the sphere x2+ y2+ z2= 4 Solution: |
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| 1202. |
Find the polar coordinates of the points with cartesian coordinates (−x, y). |
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Answer» The cartesian coordinates (-x, y) can be represented in polar coordinates by (r,Ø), where r = √(x2+ y2) andØ = π- tan-1(y/x). The polar coordinatesystem is a two-dimensionalcoordinatesystem in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. Polar coordinates are used while representing various spherical objects in engineering and science. It is very easy to convert cartesian coordinates to polar coordinates. |
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| 1203. |
Find a polar equation for the curve represented by the given Cartesian equation. y = 5 |
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Answer» The polar equation for the curve represented by the given cartesian equationy = 5isr = 5cosecθ. We will be using the concept of the conversion ofcartesian coordinates to polar coordinatesto solve this. |
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| 1204. |
The ratio of the sum of n terms of two A.P's is (7n + 1) : (4n + 27). Find the ratio of m terms. |
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Answer» The ratio of the sum of n terms of two A.P's is (7n + 1) : (4n + 27). Find the ratio of m terms. Solution: |
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| 1205. |
The measure of an angle in standard position is given. Find two positive angles and two negative angles that are coterminal with the given angle. 3π/4 |
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Answer» The measure of an angle in standard position is given. Find two positive angles and two negative angles that are coterminal with the given angle. 3π/4 Solution: |
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| 1206. |
What does the Cartesian System Mean? |
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Answer» A cartesian system is a system in geometry that is used to describe the location of a point using coordinates. Cartesian coordinates are the foundation of analytic geometry. |
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| 1207. |
Find the value of x such that the data set 31.7, 42.8, 26.4, x has a mean of 35 |
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Answer» Find the value of x such that the data set 31.7, 42.8, 26.4, x has a mean of 35 Solution: |
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| 1208. |
Express: y varies directly as x and inversely as the square of z. |
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Answer» Express: y varies directly as x and inversely as the square of z. We will use the concept of direct and indirect proportion to express the above relation. |
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| 1209. |
Give an example of what it means to say mass and weight are proportional to each other? |
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Answer» An example where mass and weight are proportional to each other is Forcedue to gravity ( Weight ) = mass of the body × acceleration due to gravity We will use the concept of direct and inverse proportion in order to find the required answer. |
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| 1210. |
What is the remainder when the polynomial 5x2+ 10x − 15 is divided by x + 5? |
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Answer» What is the remainder when the polynomial 5x2+ 10x − 15 is divided by x + 5? Solution: |
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| 1211. |
If the Equation of a Circle is (x + 4)2+ (y - 6)2= 25, its Center Point is? |
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Answer» If the Equation of a Circle is (x + 4)2+ (y - 6)2= 25, its Center Point is? Solution: |
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| 1212. |
If 2/3 of n is 4, then 1/2 of n is: |
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Answer» If 2/3 of n is 4, then 1/2 of n is Solution: |
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| 1213. |
Given the sequence 8, 16, 32, 64, ..., which expression would give the thirteenth term? |
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Answer» Given the sequence 8, 16, 32, 64, ..., which expression would give the thirteenth term? Solution: |
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| 1214. |
Which input value produces the same output value for the two functions on the graph? x = -3,x = -2,x = -1,x = 3 |
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Answer» Which input value produces the same output value for the two functions on the graph?
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| 1215. |
Which equation represents the line that passes through the points (6, -3) and (-4, -9). y + 4 = 3 over 5 (x + 9) y + 4 = 5 over 3 (x + 9) y - 3 = 3 over 5 (x + 6) y + 3 = 3 over 5(x- 6) |
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Answer» Which equation represents the line that passes through the points (6, -3) and (-4, -9). Solution: |
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| 1216. |
Which of the following is an even function? f(x) = (x - 1)2 f(x) = 8x f(x) = x2 - x f(x) = 7 |
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Answer» Which of the following is an even function? f(x) = (x - 1)2, f(x) = 8x , f(x) = x2 - x , f(x) = 7 Solution: |
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| 1217. |
Which of the following is a trinomial? c2 + c + 6,c2 - 16,- 8c,c3 + 4c2 - 12c + 7 |
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Answer» Which of the following is a trinomial? c2 + c + 6,c2 - 16,- 8c,c3 + 4c2 - 12c + 7 Solution: |
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| 1218. |
What is the value for ƒ(x) = 42x - 100 when x = 2 ? |
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Answer» What is the value for ƒ(x) = 42x- 100 when x = 2 ? Solution: |
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| 1219. |
Which of the following is true for f(x) = -2sin(x) - 3? The range of the function is the set of real numbers -2 is less than or equal to y and y is less than or equal to 2 The graph of the function is the graph of f(x) = -2sin(x) shifted 3 units up The amplitude of the function is 2 The period of the function is 4pi |
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Answer» Which of the following is true for f(x) = -2sin(x) - 3? Solution: |
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| 1220. |
What is the greatest common factor of 8m, 36m3, and 12? |
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Answer» What is the greatest common factor of 8m, 36m3, and 12? Solution: |
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| 1221. |
Find the midpoint of the segment with the given endpoints, D(1, 2) and E(-3, 6). |
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Answer» Find the midpoint of the segment with the given endpoints, D(1, 2) and E(-3, 6). Solution: |
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| 1222. |
Which set represents the domain of the function shown? {(-3, 6), (0, 2), (4, 7), (11, 15)} |
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Answer» Which set represents the domain of the function shown? {(-3, 6), (0, 2), (4, 7), (11, 15)} Solution: |
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| 1223. |
Use the double intercept approach to find the graph of -1 = -y + x. |
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Answer» Use the double intercept approach to find the graph of -1 = -y + x. Solution: |
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| 1224. |
Which set represents the range of the function shown? {(-1, 5), (2, 8), (5, 3), (13, -4)} {-1, 2, 5, 13} {-4, 3, 5, 8} {(5, -1),(8, 2),(3, 5),(-4, 13)} {-4, -1, 2, 3, 5, 5, 8, 13} |
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Answer» Which set represents the range of the function shown? {(-1, 5), (2, 8), (5, 3), (13, -4)} Solution: |
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| 1225. |
The domain of g(x) is {x| –4 < x ≤ 3}. |
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Answer» Which values are within the domain of the function? Check all that apply.
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| 1226. |
The range of g(x) is {y| –1 < y ≤ 4}. |
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Answer» Which values are within the domain of the function? Check all that apply.
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| 1227. |
The maximum value of the domain is 3. |
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Answer» Which values are within the domain of the function? Check all that apply.
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| 1228. |
The maximum value of the range is 4. |
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Answer» Which values are within the domain of the function? Check all that apply.
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| 1229. |
The function g(x) is defined for all real numbers x. |
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Answer» Which values are within the domain of the function? Check all that apply.
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| 1230. |
Which values are within the domain of the function? Check all that apply. |
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Answer» Which values are within the domain of the function? Check all that apply.
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| 1231. |
What is the solution to the system of equations y+2x = 4 and 2y−6x = −12? |
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Answer» What is the solution to the system of equations y+2x = 4 and 2y−6x = −12? Solution: |
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| 1232. |
The product of two consecutive positive integers is 5 more than their sum. Find the integers. |
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Answer» The product of two consecutive positive integers is 5 more than their sum. Find the integers. Solution: |
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| 1233. |
Solve 1/5ln((x + 2)5) + 1/2[ln x - ln((x2+ 3x + 2)2)] |
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Answer» Solve 1/5ln((x + 2)5) + 1/2[ln x - ln((x2+ 3x + 2)2)] Solution: |
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| 1234. |
What are the cylindrical coordinates of the point whose rectangular coordinates are (x=−4, y=4, z=3)? |
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Answer» What are the cylindrical coordinates of the point whose rectangular coordinates are (x=−4, y=4, z=3)? Solution: |
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| 1235. |
If segment LN is congruent to segment NP and ∠1 ≅ ∠2, prove that ∠NLO ≅ ∠NPM. Overlapping triangles LNO and PNM. The triangles intersect at point Q on segment LO of triangle LNO and segment MP of triangle PNM. |
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Answer» If segment LN is congruent to segment NP and ∠1 ≅ ∠2, prove that ∠NLO ≅ ∠NPM. Overlapping triangles LNO and PNM. The triangles intersect at point Q on segment LO of triangle LNO and segment MP of triangle PNM. Solution: |
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| 1236. |
Prove that cosA + cosB + cosC is always positive in triangle ABC. |
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Answer» Prove that cosA + cosB + cosC is always positive in triangle ABC. Solution: |
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| 1237. |
Simplify the difference. (-7x - 5x4 + 5) - (-7x4 - 5 - 9x) |
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Answer» Simplify the difference. (-7x - 5x4 + 5) - (-7x4 - 5 - 9x) Solution: |
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| 1238. |
a) One angle and two sides are congruent. b) Two angles and one side are congruent. c) Two corresponding sides and one angle are congruent. d) Two corresponding sides and two corresponding angles are congruent. |
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Answer» Options (b) and (d) are correct. We will use the concept of congruency of triangles to answer this question. |
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| 1239. |
Which of the following conditions make a pair of triangles congruent? |
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Answer» Options (b) and (d) are correct. We will use the concept of congruency of triangles to answer this question. |
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| 1240. |
What is the distance between the points (7 3 4) and (5 2 9)? |
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Answer» What is the distance between the points (7 3 4) and (5 2 9)? Solution: |
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| 1241. |
Which is a zero of the quadratic function f(x) = 16x2 + 32x -9? |
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Answer» Which is a zero of the quadratic function f(x) = 16x2 + 32x -9? Solution: |
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| 1242. |
If x - (1 / x) = 3 then what will be thevalue of x3- (1 / x3) ? |
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Answer» If x - (1 / x) = 3 then what will be thevalue of x3- (1 / x3) ? Solution: |
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| 1243. |
Do you include the median when finding the upper and lower quartiles? |
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Answer» Do you include the median when finding the upper and lower quartiles? Solution: |
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| 1244. |
If f(x) and f-1(x) are inverse functions of each other and f(x) = 2x + 5, what is f-1(8). |
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Answer» If f(x) and f-1(x) are inverse functions of each other and f(x) = 2x + 5, what is f-1(8). Solution: |
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| 1245. |
Find a vector that has the same direction as but has length 6. |
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Answer» Find a vector that has the same direction as <-2, 4, 2> but has length 6. Solution: |
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| 1246. |
What is the solution to the equation 9(w - 4) - 7w = 5(3w - 2)? |
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Answer» What is the solution to the equation 9(w - 4) - 7w = 5(3w - 2)? Solution: |
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| 1247. |
Simplify open parenthesis x to the 2 fifths power close parentheses to the 5 sixths power. |
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Answer» Simplify open parenthesis x to the 2 fifths power close parentheses to the 5 sixths power. Solution: |
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| 1248. |
If 2x2 + 8y= 121.5 and x2 - 8y= 121.5, then x =? |
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Answer» If 2x2+ 8y= 121.5 and x2- 8y= 121.5, then x =? Solution: |
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| 1249. |
How do you find an equation of the line having the given slope and containing the given point m = -8, (4, 5)? |
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Answer» How do you find an equation of the line having the given slope and containing the given point m = -8, (4, 5)? Solution: |
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| 1250. |
Find an equation of the line that passes through the point and has the indicated slope m which is undefined. Point (-3, 6) |
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Answer» Find an equation of the line that passes through the point and has the indicated slope m which is undefined. Point (-3, 6) Solution: |
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