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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.
| 6851. |
If the discriminant of an equation is positive, then what can be said for a quadratic equation? |
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Answer» If the discriminant of an equation is positive, then the quadratic equation will have real and distinct roots and the graph of the quadratic equation will cut the x-axis at two real points. We will use the concept of the Sridharacharyas formula also known as the quadratic formulain order to find the required answer. |
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| 6852. |
Find a Vector that has the same Direction as −6, 6, 6 but has Length 6. |
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Answer» A vector with the same direction as (−6, 6, 6) but has length 6 is (−6/√3, 6/√3, 6/√3). We will be using the concept of scaling and the similarity of the vectors. |
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| 6853. |
What are the coordinates of the vertex for f(x) = x2 + 6x + 13? |
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Answer» What are the coordinates of the vertex for f(x) = x2+ 6x + 13? Solution: |
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| 6854. |
Convert 0.15 into fraction. |
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Answer» 0.15 is written as 3/20 in the form of a fraction. A fraction is a portion of any quantity out of a whole. It consists of a numerator and a denominator. |
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| 6855. |
Solve for x : 3 over 3 x plus 1 over quantity x plus 4 equals 10 over 7x |
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Answer» Solve for x : 3 over 3 x plus 1 over quantity x plus 4 equals 10 over 7x Solution: |
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| 6856. |
What is the completely factored form of f(x) = 6x3- 13x2 - 4x + 15? |
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Answer» What is the completely factored form of f(x) = 6x3- 13x2 - 4x + 15? Solution: |
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| 6857. |
What is the equation in point-slope form of the line passing through (-3, -4) and (0, 2)? |
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Answer» What is the equation in point-slope form of the line passing through (-3, -4) and (0, 2)? Solution: |
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| 6858. |
Use the substitution method to solve the following system of equations: 4x − y = 3, 7x − 9y = −2 |
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Answer» Using substitution method, (1, 1) isthe solutionto the givensystem of equations4x − y = 3, 7x − 9y = −2 We will use the substitution method in order to find the values of x and y. |
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| 6859. |
Find the value of x in the equation 2√ x + 20 = 15 + 3√ x |
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Answer» The value of x in the equation 2√ x + 20 = 15 + 3√ x is x = 25. We will use the concept of solving the equation in order to find the value of x. |
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| 6860. |
ABCD is a trapezium in which AB II CD. If angle ADC = twice angle ABC, AD = a cm and CD = b cm, then find the length of AB. |
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Answer» The length of AB is (a + b) cm. A trapeziumis a quadrilateral in which one pair of opposite sides are parallel |
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| 6861. |
What is the probability of drawing a red face card from a deck of cards? |
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Answer» What is the probability of drawing a red face card from a deck of cards? Solution: |
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| 6862. |
Find the absolute maximum and minimum values, and their locations, of the function f(x) in the given interval f(x) = x2−1, −1 ≤ x ≤ 2. |
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Answer» The absolute maximum and minimum values of the given function f(x) = x2−1, −1 ≤ x ≤ 2,are 3and -1respectivelyand they occur at x = 2 and x = 0, respectively. The highest value of thefunctionin the domainis considered the maximum value of a function, and the lowest valueis considered the minimum value of the function. |
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| 6863. |
What is 16 to the power of 1/4? |
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Answer» 16 to the power of 1/4 is 2. A fractional exponent is a method or a technique in which powers and roots are expressed together. |
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| 6864. |
What is the value of 4 to the power of 6 over 4 to the power of 8? |
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Answer» What is the value of 4 to the power of 6 over 4 to the power of 8? Solution: |
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| 6865. |
What fraction is equivalent to 4/5? |
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Answer» The fractions equivalent to 4/5are 8/10, 12/15,16/20, etc. To find the equivalent fractions for any given fraction, we either divide or multiply the numerator and thedenominatorby the same number. |
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| 6866. |
What is the remainder when (x3- 4 x2- 12 x + 9) is divided by (x + 2) ? |
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Answer» What is the remainder when (x3- 4 x2- 12 x + 9) is divided by (x + 2) ? Solution: |
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| 6867. |
If the m∠X = 34° and the m∠Z = 26°, what is the m∠Y? m∠Y = 26°, m∠Y = 34°, m∠Y = 60°, m∠Y = 120° |
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Answer» If the m∠X = 34° and the m∠Z = 26°, what is the m∠Y? Solution: |
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| 6868. |
What is 10/7 as a Mixed Number? |
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Answer» 10/7 in the mixed fraction is 1\(\dfrac{3}{7}\) 10/7 is an improper fraction. Let us represent it asa whole number as well as a fractional part called the mixed number. |
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| 6869. |
What is the ratio of surface area to volume for a sphere? |
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Answer» What is the ratio of surface area to volume for a sphere? Solution: |
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| 6870. |
What is 40%of 20? |
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Answer» 40%of 20 is 8. A percentis a ratio of a number expressed out of100. |
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| 6871. |
Find the height of a square pyramid that has a volume of 8 cubic feet and a base length of 2 feet? 6 feet., 16 feet., 12 feet., 4 feet. |
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Answer» Find the height of a square pyramid that has a volume of 8 cubic feet and a base length of 2 feet? Solution: |
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| 6872. |
What is 2/4as a percent? |
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Answer» 2/4 can be written as 50%. Converting afractionto percent means converting the whole part into 100 and find how many are considered out of 100. |
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| 6873. |
Which of the following represents 3x - 5y + 10 = 0 written in slope-intercept form? y = -3/5x + 2 y = 3/5x - 2 y =3/5 x + 2 |
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Answer» Which of the following represents 3x - 5y + 10 = 0 written in slope-intercept form? Solution: |
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| 6874. |
What value of x is in the solution set of 2x2- 3 ≤ 7? |
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Answer» What value of x is in the solution set of 2x2- 3 ≤ 7? Solution: |
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| 6875. |
How do you subtract a whole number from a fraction? |
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Answer» To subtract a whole number from a fraction, convert the whole number in the fractional form such that both will be like fractions, and then subtract. Whole numbersare all natural numbers including zero. Fractionis a relationship between a part and a whole. |
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| 6876. |
What is the sum of the geometric sequence 1, 3, 9, ... if there are 10 terms? |
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Answer» What is the sum of the geometric sequence 1, 3, 9, ... if there are 10 terms? Solution: |
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| 6877. |
How can x + 2 = −3x + 11 be Set up as a System of Equations? |
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Answer» x + 2 = −3x + 11 can be set up as a system of equations asfollowed: x + 2 = 0 and−3x + 11 = 0. Equations form the basisof mathematics. There are many types of equations, including quadratic, cubic, linear, and many others. |
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| 6878. |
What is 3/10 as a percentage? |
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Answer» 3/10 can be written as 30% as a percentage. Converting a fraction to percent means converting the whole part into100 and find the amountout of 100. |
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| 6879. |
What is the prime factorization of 10? |
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Answer» What is the prime factorization of 10? Solution: |
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| 6880. |
What is the formula of Sin3x? |
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Answer» The formula of Sin3x is (3 sinx - sin3x)/4 We can find the value by using the trigonometric identity of sin3x |
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| 6881. |
Find a vector that has the same Direction as (−6, 6, 2) but has length 6. |
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Answer» A vector that has the same direction as (−6, 6, 2) but has length 6 is(−18/√19, 18/√19, 6/√19). We will be using the concept of scaling and the similarity of the vectors. |
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| 6882. |
Express 75% as a fraction in the simplest form. |
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Answer» 75%is written as 3/4 as a fraction in its simplest form. In mathematics, a percentage is a number or ratio that isrepresented in terms of 100. |
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| 6883. |
Find all the multiples of 9 up to 100 |
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Answer» Themultiples of 9 up to 100 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, and 99 We will find the multiples of 9 to answer this question. |
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| 6884. |
If lcm of a and 18 is 36 and the HCF of a and 18 is 2, then the value of a is? |
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Answer» The value of a is 4. The LCM (least common multiple)and HCF(highest common factor)are connected with an empirical formula: LCM(a,b)× HCF(a,b) = Product of the numbers a and b |
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| 6885. |
How to find the equation of a hyperbola given the centre, focus and vertex? |
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Answer» We can find the equation of hyperbola by finding the values of a and b from the given vertex, focus and centre and substitute in the general equation of the hyperbola. Hyperbola is a type of curve that has an equation of the form (x - h) / a2- (y - k) / b2 = 1, where a,b, h and kare constants, and a,bare not equal to zero. They have many applications in various fields. |
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| 6886. |
Explain circle with the help of conic sections. |
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Answer» According to conic sections, a circle is a locus of a point equidistant from a fixed point. Conics sections are planes, cut at varied angles from a cone. The shapes vary according to the angle at which it is cut from the cone. |
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| 6887. |
How do you divide a whole number by a decimal? |
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Answer» To divide a whole number by a decimal number, multiply both the numbers with the power of 10 with the same number of zeros as the number of decimal places in the divisor. Then, divide them as we divide 2 whole numbers. Whole numbersare all natural numbers including zero. Adecimalnumber can bedefinedas a number whose whole number part and the fractional part are separated by adecimalpoint. |
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| 6888. |
Find an equation for the nth term of the arithmetic sequence. a16 = 21, a17 = -1 |
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Answer» Find an equation for the nth term of the arithmetic sequence. a16 = 21, a17 = -1 Solution: |
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| 6889. |
Find dy/dx. x = t / (9 + t) y = √(9 + t). |
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Answer» Find dy/dx. x = t / (9 + t) y = √(9 + t). Solution: |
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| 6890. |
Find the vertex of the graph of the function. f(x) = 3x2- 18x + 24 |
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Answer» Find the vertex of the graph of the function. f(x) = 3x2- 18x + 24 Solution: |
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| 6891. |
Simplify the following expression: 2x - 6y + 3x2 + 7y -14x. |
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Answer» We obtain3x2- 12x+ y by simplifying the expression: 2x - 6y + 3x2 + 7y -14x. The given algebraic expression can be simplified by combining like terms. |
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| 6892. |
Find the exact values of cos 150° and sin 150°? |
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Answer» The exact value of cos (150∘) is −√3/2 and sin (150∘) is 1/2. To find the exact values of cos 150° and sin 150°, we will use the trigonometric identitycos (180° - Θ) andsin (180° - Θ). |
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| 6893. |
If sin θ = √3 / 2 and tan θ < 0, what is the value of cos θ? |
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Answer» If sin θ = √3 / 2 and tan θ < 0, the value of cosθ = -1 / 2. We will use the concepts of trigonometry to find the value ofcos θ. |
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| 6894. |
How to express 2 to the power of 5? |
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Answer» 2 to the power 5 can be expressed as 25= 2× 2× 2× 2 × 2 = 32 Power or exponents is defined as the total number of times we use the number ina multiplication.For example, 2 to the power 3 means 2 is multiplied 3 times. |
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| 6895. |
Find all solutions to the equation cos 4x - cos 2x = 0 in the interval [0, 2π). |
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Answer» Find all solutions to the equation cos 4x - cos 2x = 0 in the interval [0, 2π). Solution: |
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| 6896. |
If 7 1/4 boxes of parts weigh a total of 68 7/8 pounds, what does one box of parts weigh? |
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Answer» If 71/4 boxes of parts weigh a total of 687/8 pounds, what does one box of parts weigh? Solution: |
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| 6897. |
Read the numbers and decide what the next number should be. 15, 14, 13, 12, 11, 10, 9,…? |
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Answer» Read the numbers and decide what the next number should be. 15, 14, 13, 12, 11, 10, 9,…? Solution: |
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| 6898. |
Place value and face value are always equal at which place: (1) Hundreds (2) Ones (3) Thousands (4) Tens |
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Answer» The place valueand face value are always equal at ones place. Place value can be defined as the value represented by a digit in a number on the basis of its position in the number. |
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| 6899. |
What is the 32nd term of the arithmetic sequence where a1 = 13 and a13 = -59? |
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Answer» What is the 32nd term of the arithmetic sequence where a1= 13 and a13 =-59? Solution: |
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| 6900. |
What is the area of the region in the first quadrant bounded by the graph of y = ex/2 and the line x = 2? |
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Answer» What is the area of the region in the first quadrant bounded by the graph of y = ex/2 and the line x = 2? Solution: |
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