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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.
| 6601. |
What is the sum total of the interior angles of any quadrilateral? |
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Answer» What is the sum total of the interior angles of any quadrilateral? Solution: |
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| 6602. |
Find the exact length of the curve. y = (1 -x2 ), 0 ≤ x ≤ 1/2. |
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Answer» Find the exact length of the curve. y = (1 -x2 ), 0 ≤ x ≤ 1/2. Solution: |
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| 6603. |
Express the area of an equilateral triangle as a function of the length of a side x. |
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Answer» Express the area of an equilateral triangle as a function of the length of a side x. Solution: |
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| 6604. |
How many seconds are in a 24 hour day? |
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Answer» There are 86400 seconds in a day. Hours, minutes, and seconds are the units that are used to measuretime. |
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| 6605. |
Find the area of the shaded region of the rectangle. |
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Answer» The area of the shaded region is 798.86 square units.
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| 6606. |
What is the solution set to the inequality 5(x - 2)(x + 4) > 0? |
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Answer» What is the solution set to the inequality 5(x - 2)(x + 4) > 0? Solution: |
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| 6607. |
Find an equation that models the path of a satellite if its path is a hyperbola, a = 55,000 km, and c = 81,000 km. Assume that the center of the hyperbola is the origin and the transverse axis is horizontal. |
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Answer» Find an equation that models the path of a satellite if its path is a hyperbola, a = 55,000 km, and c = 81,000 km. Assume that the center of the hyperbola is the origin and the transverse axis is horizontal. Solution: |
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| 6608. |
Which of the following shows the factors of 9x2 + 3x - 2? (3x - 1)(3x - 2) (3x + 1)(3x - 2) (3x + 2)(3x - 1) (9x - 2)(x + 1) |
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Answer» Which of the following shows the factors of 9x2 + 3x - 2? Solution: |
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| 6609. |
How to find the perimeter of a right-angle triangle with one side missing? |
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Answer» We can find the missing side and the perimeter of a right-angled triangle using the Pythagoras theorem. Perimeter is defined as the length of the total boundary of a shape. |
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| 6610. |
Prove that (xa/ xb)1/ab (xb / xc)1/bc (xc/ xa)1/ca = 1 |
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Answer» Value of the L.H.S. comes out to be 1 thus the identity holds true. Exponential formulas of multiplication and division can be used to simplify such expressions. |
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| 6611. |
What are the zeroes of f(x) = x2+ 5x + 6? x = -2, -3 x = 2, 3 x = -2, 3 x = 2, -3 |
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Answer» What are the zeroes of f(x) = x2+ 5x + 6? x = -2, -3, x = 2, 3, x = -2, 3 x = 2, -3 Solution: |
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| 6612. |
Which of the following represent the zeros of f(x) = 6x3 - 29x2 - 6x + 5. -5, 1/3, 1/2 5, -1/3, 1/2 5, 1/3, -1/2 5, 1/3, 1/2 |
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Answer» Which of the following represent the zeros of f(x) = 6x3 - 29x2 - 6x + 5. Solution: |
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| 6613. |
Solve the inequality and show the graph of the solution on number line: 3x - 2 < 2x + 1. |
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Answer» Solve the inequality and show the graph of the solution on number line: 3x - 2 < 2x + 1. Solution: |
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| 6614. |
How to find a unit vector u that has the same direction as vector a = 10i + 24j? |
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Answer» The unit vector uthat has the same direction as vector a = 10i + 24j is u is(5/13)i + (12/13)j. Vectors are very important concepts in mathematics, which have many applications in engineering and physics. They are used to calculate the trajectory of an object undergoing projectile motion, as well as the path to be followed by a rocket. |
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| 6615. |
Choose the equation that could be used to find two consecutive integers whose sum is 69. n + (n + 2) = 69 n + (n + 1) = 69 n - (n + 1) = 69 n + 2n = 69 |
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Answer» Choose the equation that could be used to find two consecutive integers whose sum is 69. Solution: |
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| 6616. |
An acute angle θ is in a right triangle with cos θ = 3 / 5 . What is the value of sec θ? |
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Answer» An acute angle θ is in a right triangle with cos θ = 3 / 5. The value of secθ = 5 / 3 We will use the concepts of trigonometry to find the value of secθ. |
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| 6617. |
How much will you save if you buy an item listed at $575.50 at a 30 percent discount? |
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Answer» How much will you save if you buy an item listed at $575.50 at a 30 percent discount? Solution: |
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| 6618. |
What is 2 AM in military time? |
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Answer» 2 AM in military time is 02:00 hours. Military time is a method of measuring the time based on the full 24 hours of the day. |
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| 6619. |
Find the next three terms of the sequence 3, 9, 27, 81, . . . |
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Answer» Find the next three terms of the sequence 3, 9, 27, 81, . . . Solution: |
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| 6620. |
Find all the prime factors of 1729 and arrange them in ascending order. Also, state the relation, if any, between two constructive prime factors. |
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Answer» The prime factors of 1729 arranged in ascending order are 7 < 13 < 19. Prime factorizationis a way of expressing a number as a product of its prime factors. |
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| 6621. |
Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD? y = 2x - 2. y = 2x + 2 y = x + 2 y = x - 2 |
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Answer» Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD? Solution: |
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| 6622. |
What is the Value of given expression? [3 × {(-5) × (-4)}] ÷ {27 + (-13 - 4)} + [{27 × (-2)} ÷ (-3 - 3)] + [{(-3) × (-3) × 5} ÷ (-3)] |
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Answer» What is the Value of given expression? [3 × {(-5) × (-4)}] ÷ {27 + (-13 - 4)} + [{27 × (-2)} ÷ (-3 - 3)] + [{(-3) × (-3) × 5} ÷ (-3)] Solution: |
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| 6623. |
What is the LCM of 7.5, 6, and 5? |
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Answer» LCM of 7.5, 6, and 5 is 30 To find the LCM of three numbers, we need the least number which is exactly divisible by all the three numbers without leaving any remainder. |
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| 6624. |
If y varies inversely as x and y = 40 when x = 5, then the constant is? |
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Answer» If y varies inversely as x and y = 40 when x = 5, then the constant is200. We will use the concept of direct and inversely proportional to find the value of constant. |
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| 6625. |
What is the square root to the power of 4? |
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Answer» What is the square root to the power of 4? Solution: |
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| 6626. |
Find the remainder when f(x) is divided by (x - k). f(x) = 3x3 - 4x2 - 3x + 14; k = 3 50,68,-12,112 |
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Answer» Find the remainder when f(x) is divided by (x - k). f(x) = 3x3- 4x2- 3x + 14; k = 3 Solution: |
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| 6627. |
Why does cos (90 - x) = sin (x) and sin (90 - x) = cos (x) ? |
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Answer» Why does cos (90 - x) = sin (x) and sin (90 - x) = cos (x) ? Solution: |
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| 6628. |
A borrows Rs 800 at the rate of 12% per annum simple interest and B borrows Rs 910 at the rate of 10% per annum, simple interest. In how many years will their amounts of debt be equal: (1) 18 years (2) 20 years (3) 22 years (4) 24 years |
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Answer» Their debts will be equal in 22 years. Simple interestis the interest amount for a particular principal amount of money at some rate of interest. |
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| 6629. |
Determine the standard form of the equation of the line that passes through (0, 5) and (4,0). |
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Answer» Determine the standard form of the equation of the line that passes through (0, 5) and (4,0). Solution: |
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| 6630. |
Does the equation represent a direct variation? If so, find the constant of variation: 5x = 3y. |
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Answer» The equation represents a direct variation, and the constant of variation for 5x = 3y is k = 5 / 3. Proportionality is an important concept which has many day-to-day uses. Various quantities can be compared using proportionality. For example, volume is inversely proportional to density. |
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| 6631. |
AOCB is a quadrilateral in a circle with center O, angle AOC = 130 degrees. Find angle CBA. |
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Answer» The value ofangle CBA is 115 degrees.
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| 6632. |
The diameter of a wheel is 1.26 cm. What is the distance covered in 500 revolutions? |
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Answer» The distance covered by the wheel is 1980 cm. The circumference of a circle is equivalent to the distance covered in one revolution of the wheel. |
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| 6633. |
What does it mean for two fractions to be equivalent? |
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Answer» Two fractions are said to be equivalent if both of them get reduced to the same number when they are simplified. Equivalent fractions can be written by multiplying or dividing both thenumeratorand thedenominatorby the same number. |
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| 6634. |
Find two positive numbers such that the sum of the first and twice the second is 100 and their product is a maximum. |
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Answer» Find two positive numbers such that the sum of the first and twice the second is 100 and their product is a maximum. Solution: |
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| 6635. |
What is the difference between a bar graph and a histogram? |
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Answer» The basic differences between a bar graph and a histogram are given in the solution. The fundamental difference between histograms and bar graphs from a visual aspect is that the bars in a bar graph are not adjacent to each other. |
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| 6636. |
Find the center, vertices, and foci of the ellipse with equation 4x2 + 6y2 = 24. |
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Answer» Find the center, vertices, and foci of the ellipse with equation 4x2 + 6y2 = 24. Solution: |
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| 6637. |
How to find the area of a rhombus with one diagonal and perimeter? |
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Answer» When the perimeter and one diagonal of a rhombus is given, we can use the Pythagoras theorem to find the other diagonal and then calculate its area. The area of a rhombus is the product of the lengths of itsdiagonals. |
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| 6638. |
Salle plants 4 saplings in a row in her garden. The distance between two adjacent saplings is 3/4 m. Find the distance between the first and the last saplings. |
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Answer» The distancebetween the first and the last sapling is 9/4 m. The distance of the 2ndsapling from the 1st is 3/4 m; the 3rd sapling from the 2nd is 3/4 m and the last sapling (4th) from the 3rd is 3/4 m. |
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| 6639. |
Find the point on the curve y = sqrt(x) that is closest to the point (3, 0) |
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Answer» Find the point on the curve y = sqrt(x) that is closest to the point (3, 0) Solution: |
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| 6640. |
How do you simplify (1 - tan2(x)) /( 1 + tan2(x))? |
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Answer» (1 - tan2(x)) /(1 + tan2(x)) = cos 2x We’ll use trigonometric identity1 + tan2x = sec2xfor simplifying(1 - tan2(x)) /(1 + tan2(x)) |
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| 6641. |
Determine the standard form of the equation of the line that passes through (-7, 8) and (0, 2). |
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Answer» Determine the standard form of the equation of the line that passes through (-7, 8) and (0, 2). Solution: |
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| 6642. |
Find the length of the curve r(t) = 3t, 3 cos(t), 3 sin(t), -3 ≤ t ≤ 3? |
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Answer» Find the length of the curve r(t) = 3t, 3 cos(t), 3 sin(t) , -3 ≤ t ≤ 3? Solution: |
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| 6643. |
Determine the standard form of the equation of the line that passes through (-5,0) and (0,-9). |
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Answer» Determine the standard form of the equation of the line that passes through (-5,0) and (0,-9). Solution: |
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| 6644. |
Find the probability of rolling two dice and getting a sum of 4. |
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Answer» The probability of rolling two dice and getting a sum of 4 is 1/12. Probability defines the likelihood of occurrence of an event. |
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| 6645. |
If sec θ = x + 1 / 4x, then prove that sec θ + tan θ = 2x or 1 / 2x |
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Answer» The value of sec θ + tan θ = 2x or 1/2x as proved below. We need to consider two different cases. |
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| 6646. |
The ratio between the number of boys and girls in a school is 4:5. If the number of boys are increased by 30% and the number of girls increased by 40 %, then what will the new ratio of boys and girls in the school. |
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Answer» The new ratioof boys and girls in the school is 26:35. The problem can be solved using ratioand percentage increase concepts. |
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| 6647. |
Which polynomial is prime? x3+ 3x2- 2x - 6, x3- 2x2+ 3x - 6, 4x4+ 4x3- 2x - 2, 2x4+ x3- x + 2 |
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Answer» Which polynomial is prime? x³ + 3x² - 2x - 6, x³ - 2x² + 3x - 6, 4x⁴ + 4x³ - 2x - 2, 2x⁴ + x³ - x + 2 Solution: |
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| 6648. |
Determine the standard form of the equation of the line that passes through (6,0) and (2,-7). |
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Answer» Determine the standard form of the equation of the line that passes through (6,0) and (2,-7). Solution: |
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| 6649. |
How to find the exact value of trig functions without a unit circle? |
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Answer» To find the exact value of trig functions without a unit circle, we need to check the quadrant in which the angle falls. Trigonometryis a branch of mathematics that studies relationships between side lengths and angles of triangles. |
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| 6650. |
The population of a city is 20000. Find the population of the city after 3 years if the population increase by 5% every year. |
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Answer» The population of the city after 3 years will be 23,153. The problem can be solved by the compound interest concept. |
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