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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.
| 4651. |
Prove that tan(45°+ A) - tan(45°- A)/tan(45°+ A) + tan(45°- A) = 1/sin2A |
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Answer» Hence Proved that tan(45°+A) - tan(45°- A) /tan(45°+A) + tan(45°-A) = 1/sin2A To prove the above equation, we will use trigonometric identities and value of tan45°. |
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| 4652. |
What is 10 to the 7th power? |
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Answer» 10 to the 7thpower is equal to 1,00,00,000 and it is also expressed as 107. 10 to the 7thpower isdenoted by107. |
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| 4653. |
What is the next number? 0, 3, 8, 15, 24, 35 |
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Answer» What is the next number? 0, 3, 8, 15, 24, 35 Solution: |
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| 4654. |
Evaluate 32 + (8 - 2).4 - 6 over 3. |
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Answer» Evaluate 32 + (8 - 2).4 - 6 over 3. Solution: |
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| 4655. |
What is the base of a natural log? |
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Answer» The base of the natural log is e. Denoted bylogeor ln. Logs (or) logarithms are nothing but another way of expressing exponents. |
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| 4656. |
The slope of the line whose equation is x = 6 is |
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Answer» The slope of the line whose equation is x = 6 is Solution: |
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| 4657. |
How do you prove sin 3x = 3sin x - 4sin3x? |
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Answer» sin 3x= 3 sinx- 4 sin3x Trigonometric functions(also calledcircular functions or angle functions) are real functions that relate an angle of a right-angled triangle to the ratio of the other two side lengths. |
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| 4658. |
Evaluate the integral log(x+1) - log x dx/x(x+1). |
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Answer» ∫ log (x + 1) - log x dx/x (x + 1) =-1/2(log (x + 1))2-1/2 (log x)2- log (x + 1) log x + C To evaluate the integral value oflog (x+1) - log x dx/x (x+1), we will use substutitution method. |
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| 4659. |
What is the value of a in the equation a = 2 + 3a + 8? |
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Answer» What is the value of a in the equation a = 2 + 3a + 8? Solution: |
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| 4660. |
How do you find the value of sin 105º? |
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Answer» The value of sin 105º is (√3 + 1) / 2√2 The function sin 105º can be written as sin ( 60º + 45º ). By applying the trigonometric identity sin ( A + B ), we can find the value of sin105º. |
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| 4661. |
The distance between the school and the house of a student's house is 1 km 875 m. Every day she walks both ways. Find the total distance covered by her in six days. |
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Answer» The total distance covered by the student in six days if she walks both ways from her school to house will be 22km 500m. There are 1000m in 1 km. |
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| 4662. |
Solve x2 - 24x = -80 by completing the square. What is the solution set of the equation? {2, 40}, {4, 20}, {5, 16}, {8, 10} |
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Answer» Solve x2 - 24x = -80 by completing the square. What is the solution set of the equation? Solution: |
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| 4663. |
What is the product of (2p + 7)(3p2 + 4p - 3)? |
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Answer» What is the product of (2p + 7)(3p2+ 4p - 3)? Solution: |
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| 4664. |
What are the terminal points determined by π/2, π, -π/2, and 2π? |
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Answer» What are the terminal points determined by π/2, π, -π/2, and 2π? Solution: |
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| 4665. |
What is arough drawing drawn without a scale is called? |
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Answer» A rough drawing drawn without a scale is called a Sketch Map A rough drawing showsthe basic appearance or structure or a schematic representation only. |
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| 4666. |
Let A = {101, 202, 303, 404, 505} and B = {101, 404}. What is A ∩ B? |
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Answer» Let A = {101, 202, 303, 404, 505} and B = {101, 404}. What is A ∩ B? Solution: |
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| 4667. |
How many integers in the range 1 through 140 are integer multiples of 2, 5, or 7? |
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Answer» How many integers in the range 1 through 140 are integer multiples of 2, 5, or 7? Solution: |
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| 4668. |
Solve -2x - 15 = 6x + 9 |
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Answer» Solve -2x - 15 = 6x + 9 Solution: |
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| 4669. |
The product of 9/7 and a number is 63. Find the number. |
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Answer» The product of 9/7 and a number is 63 then the number is 49. The number can be calculated by dividing the productby the given number. |
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| 4670. |
What is a radius of a circle? |
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Answer» The distance from the center point to any endpoint on the circle is called the radius of a circle. Acircleis a collection of points on a two-dimensional plane, which are equidistant from the center point 'O'. |
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| 4671. |
If f(-2) = 0, what are all the factors of the function f(x) = x3 - 2x2- 68x - 120. Use the Remainder Theorem (x + 2)(x + 60) (x - 2)(x - 60) (x - 10)(x + 2)(x + 6) (x + 10)(x - 2)(x - 6) |
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Answer» If f(-2) = 0, what are all the factors of the functionf(x) = x3 - 2x2- 68x - 120. Use the Remainder Theorem Solution: |
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| 4672. |
In quadrilateral PQRS below, sides PS and QR are parallel for what value of x? |
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Answer» In quadrilateral PQRS below, sides PS and QR are parallel for what value of x?
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| 4673. |
What is the derivative of tan2x? |
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Answer» The value when wedifferentiate tan2x is2 tanx sec2x. Differentiationmeans finding the derivative which is the process of finding the instantaneous rate of change of a function. |
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| 4674. |
Find the length of the missing leg of a right triangle given a leg of length 8 and a hypotenuse of length 10? |
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Answer» Find the length of the missing leg of a right triangle given a leg of length 8 and a hypotenuse of length 10? Solution: |
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| 4675. |
Graph the first six terms of a sequence where a1 = -10 and d = 3. |
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Answer» Graph the first six terms of a sequence where a1= -10 and d = 3. Solution: |
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| 4676. |
What is x squared plus x squared? |
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Answer» What is x squared plus x squared? Solution: |
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| 4677. |
1 out of 6 is what percent? |
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Answer» 1 out of 6 is 16.67%. The percentage is a fraction or a ratio in which the value of the whole is always 100. |
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| 4678. |
Find the integral of (sinx + cosx) / [3+sin2x] dx. |
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Answer» The integral of (sinx + cosx) / [3+sin2x] dx is 1/4log {(2 + sinx - cosx) / (2 - sinx + cosx)} + C. Integration is exactly the reverse of differentiation. The integral of (sinx + cosx) / [3+sin2x] dx can be found using substitution method. |
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| 4679. |
What is 10 to the 1 power? |
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Answer» 10 to the 1 power is 101= 10. 10 to the 1 power can be re-written as 101. |
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| 4680. |
Use synthetic division to solve (x3 + 1) ÷ (x - 1). What is the quotient? |
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Answer» Use synthetic division to solve (x3+ 1) ÷ (x - 1). What is the quotient? Solution: |
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| 4681. |
A coin is tossed 400 times. use the normal curve approximation to find the probability of obtaining (a) between 185 and 210 heads inclusive; (b) exactly 205 heads; (c) fewer than 176 or more than 227 heads. |
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Answer» A coin is tossed 400 times. use the normal curve approximation to find the probability of obtaining(a) between 185 and 210 heads inclusive; (b) exactly 205 heads; (c) fewer than 176 or more than 227 heads. Solution: |
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| 4682. |
What is 15/16 as a decimal? |
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Answer» 15/16 is written as 0.9375 in the decimal form. Bothdecimalsandfractionsare just two ways to represent the same number. |
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| 4683. |
How to integrate sin squared? |
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Answer» The final integralof sin2x is(1/2)x- (1/4)sin(2x) + C We will use the concept of cos double angle formula forIntegrationof sin square. |
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| 4684. |
Find a third-degree polynomial equation with rational coefficients that has the given numbers as roots. 1 and 3i |
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Answer» Find a third-degree polynomial equation with rational coefficients that has the given numbers as roots. 1 and 3i Solution: |
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| 4685. |
Solve the equation: 2x -3 + 4x = 21 x = -12,x = -6,x = 4,x = 6 |
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Answer» Solve the equation: 2x -3 + 4x = 21 Solution: |
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| 4686. |
What are the Amplitude, Period, Phase Shift, and Midline of f(x) = 2 sin(x + π) − 4? |
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Answer» The Amplitude, Period, Phase Shift, and Midline of f(x) = 2 sin(x + π) − 4 are 2, 2π,π, and y = -4 respectively. We will be using the phase shift standard form to solve this. |
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| 4687. |
If x is rational and y is irrational then x + y is irrational(True or false) |
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Answer» If x is rational and y is irrational then x + y is irrational(True or false) Solution: |
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| 4688. |
A couple decided to have 4 children. What is the probability that they will have at least two boys? |
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Answer» A couple decided to have 4 children. What is the probability that they will have at least two boys? Solution: |
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| 4689. |
Write the following equation in the general form ax + by + c = 0. 2x + y = 6 |
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Answer» Write the following equation in the general form ax + by + c = 0. 2x + y = 6 Solution: |
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| 4690. |
The new number, 200, is 400 less than the original number. What is the approximate percent change? |
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Answer» The new number, 200, is 400 less than the original number. What is the approximate percent change? Solution: |
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| 4691. |
How to find the surface area,when the volume of a sphere is given. |
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Answer» The surface area of asphere when the volume of a sphere is given is given by 4× π× [3V / (4π)]2/3 A sphere is a set of points connected with one common point at equal distances. |
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| 4692. |
Use an appropriate half-angle formula to find the exact value of the expression. tan(15°) |
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Answer» Use an appropriate half-angle formula to find the exact value of the expression. tan(15°) Solution: |
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| 4693. |
What is 2.5 as a Fraction? |
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Answer» Fractional form of 2.5 is 5/2. A fraction is a part of the whole quantity. |
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| 4694. |
Prove that 3+ √5 is an irrational number. |
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Answer» 3+ √5 is an irrational number Irrational numbers are those real numbers that cannot be represented in the form of a/b. |
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| 4695. |
Find the radius of the circle if the center is at (1, 2) and the point (-3, 4) lies on the circle? |
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Answer» Find the radius of the circle if the center is at (1, 2) and the point (-3, 4) lies on the circle? Solution: |
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| 4696. |
What is the value of y if the segment outside the circle is tangent to the circle |
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Answer» What is the value of y if the segment outside the circle is tangent to the circle
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| 4697. |
Is there a number that is exactly 3 more than its cube? |
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Answer» Is there a number that is exactly 3 more than its cube? Solution: |
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| 4698. |
For f(x) = 0.01(2)x, find the average rate of change from x = 3 to x = 8. 0.08,0.426,2.48,5 |
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Answer» For f(x) = 0.01(2)x, find the average rate of change from x = 3 to x = 8. Solution: |
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| 4699. |
Using the substitution u(x) = y + x, solve the differential equation dy/dx = (y + x) 2 . |
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Answer» Using the substitution u(x) = y + x, solve the differential equation dy/dx = (y + x) 2 . Solution: |
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| 4700. |
Read the numbers and decide what the next number should be. 1, 1.25, 7, 7.50, 2, 2.25, 8,…? |
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Answer» Read the numbers and decide what the next number should be. 1, 1.25, 7, 7.50, 2, 2.25, 8,…? Solution: |
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