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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.

7301.

Given the function f(x) = 2x, find the value of f−1(16).

Answer» The value off−1(16) is calculated to be 8.

Theinverse of any function is nothing but replacing the value of x with y in the function and making the subject of formula for x.

7302.

What Transformations Change the Graph of f(x) to the graph of g(x)? f(x) = x2, g(x) = (x – 5)2+ 1.

Answer» If f(x) = x2, g(x) = (x – 5)2+ 1, then the transformations from f(x) to g(x) is right5and up1.

We will be using the formula of transformations to solve this.

7303.

If a data line on a graph slopes down as it goes to the right, it is depicting that 1.as the value of one variable falls, the value of the other also falls (all else constant). 2.the relationship between the variables on the axes is direct. 3.the relationship between the variables on the axes is inverse.

Answer» If a data line on a graph slopes down as it goes to the right, it is depicting that
1.as the value of one variable falls, the value of the other also falls (all else constant).
2.the relationship between the variables on the axes is direct.
3.the relationship between the variables on the axes is inverse.

Solution:

7304.

For what values of a and b is the line 5x + y = b tangent to the parabola y = ax2 when x = 4?

Answer» For what values of a and b is the line 5x + y = b tangent to the parabola y = ax² when x = 4?

Solution:

7305.

What is thearea of thetrapezoid shown below?

Answer» The area of the trapezoid is 63 cm2.

7306.

What are 1000 digits of pi?

Answer» 1000 digits of pi are shown below.

Pi is a constant and its value is estimated as 3.14

7307.

For what values of a and b is the line 4x + y = b tangent to the parabola y = ax² when x = 4?

Answer» For what values of a and b is the line 4x + y = b tangent to the parabola y = ax² when x = 4?

Solution:

7308.

Which of the following constants can be added to x2 - 10x to form a perfect square trinomial? 10,25,100, 250

Answer» Which of the following constants can be added to x2- 10x to form a perfect square trinomial?

Solution:

7309.

What is the circumference of a circle with a radius of 6 units?

Answer» The circumference of a circle with a radius of 6 unitsis 12π or 37.68units

Thecircumference of a circle =2πr units (where r denotes the radius of the circle).

7310.

Find the inverse of the function y = 2x2 + 2.

Answer» The inverse of the function y =2x2 + 2 isf-1(x) =√(x - 2) / √2.

An inverse function is the reverse of an original function with inverse mapping. They have many interesting applications in various fields like calculus and algebra.

7311.

Express the complex number in trigonometric form: 3 - 3i.

Answer» The complex number 3 - 3i can be represented in trigonometric form as 3√2 (cos(−π/4) + i sin(−π/4)).

Complex numbers are very important concepts in mathematics. These are the numbers that can't be represented on the number line or the cartesian plane. They can have both real and imaginary parts.

7312.

A circle has a diameter with endpoints of (-2, 8) and (6, 4). What is the center of the circle?

Answer» A circle has a diameter with endpoints of (-2, 8) and (6, 4). What is the center of the circle?

Solution:

7313.

What is the probability of flipping a coin 3 times and getting all heads?

Answer» The probability of flipping a coin 3 times and getting all heads is 1/8.

We will use the concept of probability to find the required answer.

7314.

Find the value of y for a given value of x, if y varies directly with x. If y = -252 when x = 84, what is y when x = 74?

Answer» Find the value of y for a given value of x, if y varies directly with x. If y = –252 when x = 84, what is y when x = 74?

Solution:

7315.

What is 40 degrees Celsius in Fahrenheit?

Answer» Temperature at 40degrees Celsius is equal to the temperature at 104 degrees Fahrenheit.

The two different types of units or scales to measuretemperatureareCelsiusandFahrenheit.

7316.

Which of the following shows 9x2y - 4x + 3y3x - 2y2 written in standard form. 9x2y - 4x + 3y3x - 2y2 3y3x - 2y2 + 9x2y - 4x 9x2y - 4x - 2y2 + 3y3x 3y3x + 9x2y - 2y2 - 4x

Answer» Which of the following shows 9x2y - 4x + 3y3x - 2y2written in standard form.

Solution:

7317.

Any polygon with two pairs of parallel opposite sides is a parallelogram. True or False?

Answer» It is false that any polygon with two pairs of parallel opposite sides is a parallelogram.

Parallelograms are interesting shapes with many interesting properties. Even the shape rectangle is a type of parallelogram. They have an immensely large number of applications across many fields including engineering and science. They are one of the most steady shapes. Let's explore one of their properties in this blog.

7318.

Solve the following system of equations and show all work. y = x2 + 3, y = x + 5.

Answer» The solution to the given system of equations y = x2 + 3, y = x + 5, is x = -1 and x = 2.

Equations form the basisof mathematics. There are many types of equations, which include quadratic, biquadratic, cubic, linear, and many others.

7319.

What is 7.5% as a decimal?

Answer» 7.5% as a decimal is equal to 0.075

Adecimalnumber can bedefinedas a number whose whole number part and the fractional part is separated by adecimalpoint

7320.

How to find the area of a triangle with 3 sides?

Answer» UsingHeron's formula -√s (s - a)(s - b)(s - c) to find the area of a triangle.

We will use Heron's formula to find the area.

7321.

The ratio of two numbers is 2:3. If 2 is subtracted from first and 8 fromsecond, the ratio becomes reciprocal of the original ratio. Find the Numbers.

Answer» The numbers are 8 and 12.

The given problem is an application of ratio and linear equations in one variable.

7322.

p varies directly as q. when q = 31.2, p = 20.8. Find p when q = 15.3.

Answer» p varies directly as q. when q = 31.2, p = 20.8. Find p when q = 15.3.

Solution:

7323.

Find a Vector that has the same Direction as −4, 6, 4 but has Length 6.

Answer» A vector with the same direction as (−4, 6, 4) but has length 6 is (−12/√17, 18/√17, 12/√17).

We will be using the concept of scaling and the similarity of the vectors.

7324.

Consider a parallelogramABCD. AE is perpendicular to DC and CF is perpendicular to AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, Find AD.

Answer» Fora parallelogramABCD,where AE is perpendicular to DC and CF is perpendicular to AD with AB = 16 cm, AE = 8 cm and CF = 10 cm,AD is 12.8 cm.

Aparallelogramis a quadrilateral, whose opposite sidesare parallel and equal to each other.

7325.

What is 5 degrees Celsius in Fahrenheit?

Answer» 5°Celsiusis equal to 41°Fahrenheit.

The two different types of units to measuretemperatureareCelsiusandFahrenheit.

7326.

Which number comes next in this series of numbers? 2, 3, 5, 7, 11, 13,… ?

Answer» Which number comes next in this series of numbers? 2, 3, 5, 7, 11, 13,… ?

Solution:

7327.

For which of the following equations are x = 5 and x = -5 both solutions (a) x²- 25 (b) x-5 (c) x+5 (d) x²+25

Answer» - 25 is the required equation for which x = 5 and x = -5 both are solution.

We will use the concept of factorization to find the equation.

7328.

A bag contains 25 paise coins, 50 paise coins, and 1 rupee coin whose values are in the ratio of 8:4:2. The total values of coins are 840. Then, find the total number of coins.

Answer» The total number of coins is 2520.

The problem can be solved using linear equations in one variableand ratio calculation.

7329.

What is the common denominator of y + [(y - 3)/3] in the complex fraction {y + [(y - 3)/3]}/(5/9 + 2/3y)? 5y + 6,y(y - 3),3y,3

Answer» What is the common denominator of y + [(y - 3)/3] in the complex fraction {y + [(y - 3)/3]}/(5/9 + 2/3y)?

Solution:

7330.

Each exterior angle of a regular decagon has a measure of (3x + 6)°. What is the value of x?

Answer» Each exterior angle of a regular decagon has a measure of (3x + 6)°. What is the value of x?

Solution:

7331.

How can we tell if a number is divisible by 4?

Answer» If the number formed by the last two digits of the given number is divisible by 4, then the number is divisible by 4

A divisibility rule is a kind of shortcuttofiguring outifa given integer is divisible by adivisor, without performing the whole division processbutby examining its digits.

7332.

2 + (x + y) = (2 + x) + y is an example of which algebraic property ?

Answer» 2 + (x + y) = (2 + x) + y is an example of aasociative property of addition.

The associative property of additionsays that the change in the order of the number does not change the resultant sum.

7333.

What is the 22nd term of the arithmetic sequence where a1= 8 and a9 = 56?

Answer» What is the 22nd term of the arithmetic sequence where a1 = 8 and a9 = 56?

Solution:

7334.

Write the next three natural numbers after 10999

Answer» Write the next three natural numbers after 10999

Explanation:

7335.

Let f(x) = x2 + 3x - 4 and g(x) = x + 5. Find f(x) . g(x) ?

Answer» Let f(x) = x2 + 3x - 4 and g(x) = x + 5. Find f(x) . g(x) ?

Solution:

7336.

What is 0.75 as a Fraction?

Answer» 0.75 as a fraction is 3/4.

Fractions can be used to depict a part of some whole quantity.

7337.

Find the least natural number that is divisible by three different primes.

Answer» The least natural number that is divisible by three different primes is 30

To find the least natural number that isdivisible by three different primes, we need to find the LCM of the set of the three smallest prime numbers.

7338.

Using a directrix of y = 2 and a focus of (3, -4), what quadratic function is created?

Answer» Using a directrix of y = 2 and a focus of (3, -4), what quadratic function is created?

Solution:

7339.

If f and g are both even functions, is f+ g even?

Answer» If f andg areeven functions, then f + gis an even function.

We will use the concept of an even function to find whether f + g is an even function or not.

7340.

How do you find the radius of a circle with the area?

Answer» The radius of a circle is equal to⎷(Area/π).

The area of a circle isthe amount of space enclosed within the boundary of a circle.

7341.

For the equation y = 3x2− 4x + 11, choose the correct application of the quadratic formula.

Answer» Thevalue of x for the equation y = 3x2− 4x + 11 using quadratic formulais2/3 + i√29 / 3 or 2/3 -i√29 / 3

An algebraic expression in the form of ax2+ bx + c = 0 is called a quadratic equation, a≠ 0.

7342.

Solve the given Differential Equation by Undetermined Coefficients:1/4 y'' + y' + y = x2− 3x

Answer» Solve the given Differential Equation by Undetermined Coefficients:1/4 y'' + y' + y = x2− 3x

Solution:

7343.

How to find the perimeter of a rectangle with only the area?

Answer» Perimeter = 2(L + Area/L) unitsor2(B+ Area/B) units, where L and B are length and breadth respectively.

The area is the product of the length and the breadth of the rectangle. And, the perimeter is the sum of the lengths and breadths of the rectangle.

7344.

Find the limit: lim x➝0 sin | x | / x

Answer» The limit does not exist.

We will use the concept of limits and function to find our required limit

7345.

How do you turn a fraction into a whole number?

Answer» Toconvert a fraction into a whole number:Divide the numerator by the denominator, only if the numerator is a multiple of thedenominator.

Wholenumbers are part of real numbers including allthe positive integers andzero, but not thefractions,decimals, ornegative numbers.

7346.

What is 10to the 8th power?

Answer» The value of 10 raised to the 8thpower is equal to 100,000,000.

The exponentor power of a number shows how many times the number is multiplied by itself.

7347.

What is 30% of 100?

Answer» 30% of 100 is 30.

A percentis a ratio of a number expressed out of100.

7348.

Find HCF of 65 and 117 and find a pair of integral values of m and n. Such that HCF = 65m + 117n.

Answer» HCF of 65 and 117 is 13, the values of m and n are:m = 2 and n = -1

The largest possible number which divides the given numbers exactly without any remainder is called the HCF (Highest Common Factor).

7349.

How many solutions does this linear system have? y = 2x - 5 and -8x - 4y = -20

Answer» How many solutions does this linear system have? y = 2x - 5 and -8x - 4y = -20

Solution:

7350.

If x is real, the maximum valueof expression (x2+ 14x + 9) / (x2+ 2x + 3) will be what?

Answer» If x is real, the maximum valueof expression(x2+ 14x + 9) / (x2+ 2x + 3) will be 4.

Algebra is the branch of mathsdealing with expressions and variables. It has many applications. In this article, we will calculate the maximum valueof the given expression.