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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.
| 4101. |
What is the y-intercept of the quadratic function f(x) = (x - 8)(x + 3)? (8, 0),(0, 3),(0, -24),(-5, 0) |
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Answer» What is the y-intercept of the quadratic function f(x) = (x - 8)(x + 3)? Solution: |
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| 4102. |
Evaluate the integral (use c for the constant of integration) ∫8tan4(x) sec6(x) dx |
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Answer» Evaluate the integral (use c for the constant of integration) ∫8tan4(x) sec6(x) dx Solution: |
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| 4103. |
What is an equation in standard form of an ellipse centered at the origin with vertex (-6, 0) and covertex (0, 4)? |
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Answer» What is an equation in the standard form of an ellipse centered at the origin with vertex (-6, 0) and covertex (0, 4)? Solution: |
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| 4104. |
Which of the following represents the range of the function f(x) = -4x + 1 for the domain (-5, -1, 0, 2, 10) (-39, -7, 1, 5, 21) (-41, -9, 1, 5, 21) (-19, -3, 1, 5, 21) (-41, -9, -3, -19) |
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Answer» Which of the following represents the range of the function f(x) = -4x + 1 for the domain (-5, -1, 0, 2, 10) Solution: |
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| 4105. |
Angle Ais a right angle in △ABC. Which side is opposite to angle A? |
| Answer» In the above triangle△ABC, the side opposite to angle A is BC. | |
| 4106. |
Solve the equation 3x2- 5 x + 2 = 0 by completing the square method. |
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Answer» The value of x is 1 or 2/3 for the equation3x2- 5 x + 2 = 0 The method of completing the squareis one of the methods to solve quadratic equations by changing their form. |
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| 4107. |
If x2 - 6x + 8 = 0, then x - 4 = 0 or x - 2 = 0. State True or False. |
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Answer» It is true that, if x2 - 6x + 8 = 0, then x - 4 = 0 or x - 2 = 0. Quadratic equations are those equations that have a degree equal to two. They have many applications in various fields of engineering and science. |
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| 4108. |
Which three lengths could be the lengths of the sides of a triangle? |
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Answer» Which three lengths could be the lengths of the sides of a triangle? Solution: |
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| 4109. |
On which axis does the complex number z = x + iy, which satisfies the equation ∣z − 5i| / |z+5i∣=1 lies? |
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Answer» The complex number z lies on the x-axis. A complex numberis neededto be converted into its real values to solve it further. |
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| 4110. |
If PR = 4x - 2 and RS = 3x - 5, which expression represents PS? x - 7, x - 3, 7x - 7, 7x + 3 |
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Answer» 7. If PR = 4x - 2 and RS = 3x - 5, which expression represents PS? x - 7, x - 3, 7x - 7, 7x + 3
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| 4111. |
What is the radius of the circle whose equation is x2 + y2 = 8? |
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Answer» What is the radius of the circle whose equation is x2+ y2= 8? Solution: |
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| 4112. |
Prove: cos A/ (1+ sin A ) + (1+ sin A) / cos A = 2 sec A |
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Answer» Hence Provedcos A / (1 + sin A) + (1 + sin A) / cos A = 2 sec A To prove this, we will use trigonometric identities. |
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| 4113. |
What is the equation of the line that passes through (4, -1) and (-2, 3)? |
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Answer» What is the equation of the line that passes through (4, -1) and (-2, 3)? Solution: |
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| 4114. |
In the diagram of circle C, m∠VWX is 43°. What is the measure of arc VX? |
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Answer» In the diagram of circle C, m∠VWX is 43°. What is the measure of arc VX?
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| 4115. |
Given (x - 1)2= 50, select the values of x. |
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Answer» Given (x - 1)2 = 50, select the values of x. Solution: |
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| 4116. |
Find an equation of the plane that passes through the points (4, 1, 4), (5, -8, 6), and (-4, -5, 1)? |
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Answer» Find an equation of the plane that passes through the points (4, 1, 4), (5, -8, 6), and (-4, -5, 1)? Solution: |
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| 4117. |
How to determine whether a function has a minimum or maximum value? |
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Answer» To determinewhether a function has a minimum or maximum value, we have to double differentiate the function and check whether it has a negative or a positive value in the given domain. Maxima and minima are very important and interesting concepts in the field of mathematics. Finding the maximum or minimum value of a function can be done in various ways like using graphical techniques, using calculus etc. We will have a look at an example in which we have to determine whether a function has a maximum or a minima value. |
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| 4118. |
Which of the following constants can be added to x2 - 6x to form a perfect square trinomial? 6,9,36,None of the above |
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Answer» Which of the following constants can be added to x2- 6x to form a perfect square trinomial? Solution: |
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| 4119. |
What is the general solution of the differential equation y'' + 4y =0? |
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Answer» What is the general solution of the differential equation y'' + 4y =0? Solution: |
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| 4120. |
What are the zeros of the quadratic function f(x) = 2x2 + 8x - 3? |
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Answer» What are the zeros of the quadratic function f(x) = 2x2+ 8x - 3? Solution: |
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| 4121. |
What is the reciprocal of 1/2? |
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Answer» What is the reciprocal of 1/2? Solution: |
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| 4122. |
What is 9 to the power of 1/2? |
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Answer» 9 to the power of 1/2 is 3. In algebra, a fractional exponentis a method for expressing roots and powerstogether is known as. |
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| 4123. |
How much is 81 to the power of 1/4? |
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Answer» 81 to the power of 1/4 is 3. In algebra, a method for expressing roots andpowers together is known as a fractional exponent. |
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| 4124. |
How to find the expected value of a discrete random variable? |
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Answer» Expected Value of a discrete random variable is given by (E(X))= Σ x P(X=x). The expected value is equal to the sum of the product of each possible outcome with its probability and is expressed as the formula for the expected value. |
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| 4125. |
What is the lcm of two numbers that have no common factors greater than 1 |
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Answer» What is the lcm of two numbers that have no common factors greater than 1 Solution: |
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| 4126. |
If a man earns $420 interest in one year at 7%, what was the amount of money invested? |
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Answer» If a man earns $420 interest in one year at 7%, what was the amount of money invested? Solution: |
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| 4127. |
If sinθ = 2 over 7 and tanθ > 0, what is the value of cosθ? |
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Answer» If sinθ = 2 over 7 and tanθ > 0, what is the value of cosθ? Solution: |
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| 4128. |
What is 23/6 as a Mixed Number? |
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Answer» 23/6 as a mixed number is \(3\dfrac{5}{6}\) 23/6 being an improper fraction, it can be further written as a mixed number consisting of a whole and a fractional part. |
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| 4129. |
Find an equation of the tangent line to the curve y = 8x sin(x) at the point (π/2, 4π). |
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Answer» Find an equation of the tangent line to the curve y = 8x sin(x) at the point (π/2, 4π). Solution: |
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| 4130. |
Verify that sin(A + B) + sin(A - B) = 2sinA.sinB |
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Answer» Hence, verified thatsin(A + B) + sin(A - B) = 2sinA.sinB To verify this, we will use the trigonometric identity |
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| 4131. |
In the circle shown below, segment BD is diameter and the measure of arc CB is 54°. What is the measure of ∡DBC? |
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Answer» In the circle shown below, segment BD is diameter and the measure of arc CB is 54°. What is the measure of ∡DBC?
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| 4132. |
Find the integral of log(sinx+cosx) from -pi/4 to pi/4. |
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Answer» The value ofintegral of log (sin x + cos x) from -pi/4 to pi/4 is- π / 4log 2. Integral is the antiderivative of a function. |
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| 4133. |
How do you prove cos4(x) - sin4(x) = cos (2x)? |
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Answer» Hence proved thatcos4(x) - sin4(x) = cos (2x) sin(θ) is the ratio of the opposite (base) side to the hypotenuse, while cos(θ) is the ratio of the adjacent (perpendicular) side to the hypotenuse. |
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| 4134. |
Find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = 15x3 - 3xy + 15y3. |
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Answer» Find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = 15x3- 3xy + 15y3. Solution: |
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| 4135. |
Which number line represents the solution set for the inequality -4(x + 3) ≤ -2 -2x? |
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Answer» Which number line represents the solution set for the inequality -4(x + 3) ≤ -2 - 2x? Solution: |
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| 4136. |
What is the missing coefficient of the x-term of the product (-x - 5)2 after it has been simplified? |
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Answer» What is the missing coefficient of the x-term of the product (-x - 5)2after it has been simplified? Solution: |
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| 4137. |
How do you find the exact values of cos 22.5 degrees using the half-angle formula? |
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Answer» The exact valueof cos 22.5 degreesis 0.92387953... The half-angle formula for cos is cos x/2 = ± √ (1 + cosx) / 2. |
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| 4138. |
Explain how to make six 9's equal to 100. |
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Answer» 8 possible ways are there to convert six 9's into 100. We may make use of only mathematical operations like+ , -, ×, and / |
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| 4139. |
How do you find the derivative of y = tan2x? |
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Answer» The derivative of y = tan2x is dy/dx = 2 sec2x tan x The derivative of any functiony=f(x)of a variablexis a measure of the rate at which the valueychanges with respect to the change ofx. |
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| 4140. |
Find the general solution of the given differential equation. x2y' + xy = 8. y(x) = give the largest interval over which the general solution is defined. |
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Answer» Find the general solution of the given differential equation. x2y' + xy = 8. y(x) = give the largest interval over which the general solution is defined. Solution: |
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| 4141. |
Find the value of the integral (1 + 2cos x) / (2 + cos x)2dx from 0 to π/2 |
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Answer» The value of the integral (1 + 2cos x)/(2 + cos x)^{2}dx from 0 to π/2 is 1 / 2. Integrationis the inverse of differentiation. Given a derivativeof a function, the process of finding the original function is called integration. |
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| 4142. |
Solve 3[-x + (2 x + 1)] = x - 1. |
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Answer» Solve 3[-x + (2 x + 1)] = x - 1. Solution: |
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| 4143. |
What is the area of triangle LMN? 3 square units,4 square units,6 square units,8 square units |
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Answer» What is the area of triangle LMN? 3 square units,4 square units,6 square units,8 square units Solution: |
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| 4144. |
Using the quadratic formula to solve 5x = 6x2-3, what are the values of x? |
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Answer» Using the quadratic formula to solve 5x = 6x2-3, what are the values of x? Solution: |
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| 4145. |
What does Descartes'rule of signs tell you about the real roots of the polynomial? |
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Answer» We useDescartes'rule of signs to determine the number of positive real roots or negative real roots for the given polynomial function. Real roots of the polynomial mean zeros of the polynomial in real numbers. |
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| 4146. |
Find the area of the parallelogram with vertices a (-3, 0), b(-1, 7), c(9, 6), and d(7, -1)? |
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Answer» Find the area of the parallelogram with vertices a (-3, 0), b(-1, 7), c(9, 6), and d(7, -1)? Solution: |
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| 4147. |
Find the exact location of all the relative and absolute extrema of the function.f(x) = -x3 - 6x2- 9x - 2. |
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Answer» Find the exact location of all the relative and absolute extrema of the function. f(x) = -x3 - 6x2- 9x - 2 Solution: |
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| 4148. |
Find the sum of the summation of 3 i plus2, from i equals 5 to 13. |
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Answer» Find the sum of the summation of 3 i plus2, from i equals 5 to 13. Solution: |
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| 4149. |
Find 2r2 + 3s3-r2 + 4t2-r2 if r = −2, s = −3, and t = 5. |
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Answer» Find 2r2 + 3s3-r2 + 4t2-r2 if r = −2, s = −3, and t = 5. Solution: |
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| 4150. |
If the area of the triangle BGC is 28 square units and the centroid of the triangle is G. Then, find the area of the triangle ABC |
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Answer» If the area of the triangle BGC is 28 square units and the centroid of the triangle is G. Then, find the area of the triangle ABC Solution: |
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