Mathematics Concepts Quiz

Questions and Answers

What is the spiritual difference between two numbers if their product is 36 and their sum is 13?

5 (correct)

If the greatest common divisor and least common multiple of 264, 1980, and A are 12 and 59400 respectively, what is the maximum possible value of A?

4200

3600

2800 (correct)

5400

In the expression (−63p^4q^5r), what is the coefficient that can be obtained through the combination of factors from (−7p^3q^2r)?

441p^7q^7r^2

9pq^3

9pq^3r

−9pqr (correct)

If the average future value of a manager's assets is four times the average future value of a series of liabilities, how much will the future value of the liabilities equal in 6 years?

2 years Signup and view all the answers

What is the value of x if $2 × 5^x = 3$?

$rac{3}{5}$ Signup and view all the answers

For any positive integer m, what is the quotient of $3m^2 - 9$ divided by $27$?

2 Signup and view all the answers

If the product of two numbers is 36 and their sum is 13, what would be the values of the two numbers?

4 and 9 Signup and view all the answers

In a scenario where 264 and 1980 are involved with A, if A is divisible by both 12 and 59400, what form does A take?

A is a multiple of 4200 Signup and view all the answers

If the average future value of liabilities equals the current value of managers' assets, how are both values represented in terms of years?

They must both be equal in the short term Signup and view all the answers

For any integer value of m in the equation $3m^2 - 9 ext{ divided by } 27$, what is the resultant value when m is substituted?

It will always be an integer Signup and view all the answers

What is the probability that team A wins the competition if the probability of winning any one game is $\frac{8}{15}$?

$\frac{32}{51}$ Signup and view all the answers

In a class of 25 students, what is the probability that neither of the two randomly selected students is passing with a grade of C or better, given that 80% are passing?

$\frac{1}{5}$ Signup and view all the answers

How many kilograms of water are needed to produce 72 kg of a concrete mixture with a gravel, water, and sand ratio of 1:3:5?

24 Signup and view all the answers

What is the square root of $0.4$?

$0.8$ Signup and view all the answers

After applying a 10% discount on a cake priced at Rs. 800, followed by a 10% tax, what is the final selling price?

Rs. 792 Signup and view all the answers

In the ratio of 1 to 3 to 5 for gravel, water, and sand, if the total shift in weight changes, what fraction of water will still be maintained?

$\frac{1}{5}$ Signup and view all the answers

If 80% of students in a class are passing, what percentage represents the students who are not passing?

20% Signup and view all the answers

If team A has an $\frac{8}{15}$ chance of winning a game, what is the probability that team A loses a game?

$\frac{7}{15}$ Signup and view all the answers

Identify the point and its corresponding symmetric axis from the options given.

Point (-1, -2) has symmetric axis x = -1. Signup and view all the answers

What is the mean of the original set of numbers if subtracting 50 from them results in a new mean of 3.5?

56.5 Signup and view all the answers

After a series of movements, what is the final position of Sumeet relative to his starting point?

30 meters towards the South. Signup and view all the answers

What is the probability of Team A winning at least 2 out of 3 games in a series if their probability of winning a single game is 75%?

512/1024 Signup and view all the answers

Given that 80% of students pass a test with grade C or better, what is the probability that none of the two randomly chosen students passed?

2/25 Signup and view all the answers

If the symmetric axis for point (-1, -2) is x = -1, which of the following would modify the point to maintain this symmetry?

Keeping the point unchanged. Signup and view all the answers

What is the average of the original dataset if subtracting 50 from each number gives a mean of 3.5?

53.5 Signup and view all the answers

Considering the positions of Sumeet's movements, which final directional movement yields the shortest distance to his starting position?

He moved South. Signup and view all the answers

If Team A has a probability of winning a single game, how likely are they to win exactly one out of three games?

3 * (0.75) * (0.25)^2 Signup and view all the answers

What is the combined probability of having two students in a random selection pass their test when the passing rate is 80%?

0.36 Signup and view all the answers

What is the value of E in the equation A BC + C BA = DEDD, where A, B, C, D, and E are different digits?

5 Signup and view all the answers

The sum of all odd numbers from 1 to 2019 is divisible by which of the following?

100 and 101 Signup and view all the answers

If a box of dimensions 40 × 35 × 28 is completely filled with smaller boxes with no gaps, what could be the dimensions of the smaller boxes if 100 of them fit?

8 × 7 × 7 Signup and view all the answers

If x is a 5-digit number and its digits sum to y, and the digits of y sum to z, what is the maximum possible value of z?

10 Signup and view all the answers

What is the minimum product of combining four numbers chosen from the set {2, 3, 5, 7, 8, 10, 12}?

60 Signup and view all the answers

In a café, 120 students are drinking either gold coffee or black coffee. If 10 male students drink black coffee, how many female students drink gold coffee?

26 Signup and view all the answers

Which of the following is the correct sum of the first ten odd numbers?

55 Signup and view all the answers

If the volume of a box is given as 2520 cm³, which of the following sets of dimensions could represent this volume?

5 × 21 × 24 Signup and view all the answers

If an integer is randomly selected from 1 to 100, what is the probability that the number is even?

1/2 Signup and view all the answers

Given a number set, what is the median of the numbers {7, 5, 1, 3, 9}?

5 Signup and view all the answers

If a circle and a square have the same perimeter, which statement is true regarding their areas?

The area of the circle is greater. Signup and view all the answers

What is the correct sequence of the number of days in each of the 4 sheets of a 2019 calendar?

(90, 92, 91, 92) Signup and view all the answers

What are the vertex and the axis of symmetry for a quadratic function at (-1,-2)?

The vertex is at (-1,-2) and axis of symmetry is x = -1. Signup and view all the answers

If the mean of the resulting numbers, after subtracting 50 from each, is 3.5, what is the mean of the original set of numbers?

56.5 Signup and view all the answers

What is Sumedh's final position and distance from his original point after his journey?

30 meters to the west. Signup and view all the answers

In a best of 3 games badminton finals, what could be the potential outcomes for the two teams?

A wins 2 games, B wins 1. Signup and view all the answers

What is the axis of symmetry for a quadratic function with vertex (-2,-1)?

x = -2 Signup and view all the answers

If each game in a badminton finals results only in a win or a loss, what outcome represents the scenario where both teams win one game?

A wins the second, loses the first. Signup and view all the answers

Study Notes

Ratios

Ratios presented: 4:9, 9:4, 3:4, 4:3.

Circle and Square

A circle and a square have the same perimeter.
Area Comparisons:
- Areas are not equal.
- Area of the circle is greater, or
- Area of the square is π times the area of the circle, or
- Area of the square is π² times the area of the circle.

Calendar 2019

Calendar made with 4 sheets, each containing three months.
Total days on each sheet options:
- (90, 91, 92, 92)
- (90, 92, 91, 92)
- (90, 92, 91, 92)
- (90, 92, 92, 91).

Quadratic Functions

Vertex and axis of symmetry of a quadratic function can be identified:
- Options presented include vertex at (-1,-2) with axes at x = -1 or y = -2, or vertex at (-2,-1) with axes at x = -2 or y = -1.

Mean Calculation

Original set of numbers: Mean needs to be calculated if 50 numbers subtracted from 53 yielding a mean of 3.5 after subtraction.

Path Calculation

Sumedh's journey involves multiple directional changes, resulting in a final position.
Possible end positions:
- 15 meters west
- 30 meters east
- 30 meters west
- 45 meters east.

Probability in Badminton

Team A and B in best of 3 games competition, probability that Team A wins is evaluated.

Class Statistics

In a class of 25, with 80% passing a grade of C or better; calculating probability for random selection suggests possible outcomes.

Concrete Mixture Ratio

Concrete mixture composed of gravel, water, and sand in a 1:3:5 ratio by weight – calculation for water in a 72 kg mixture needed.

Square Root Calculation

Square root of 0.4 with options available for assessment: 0.6, 0.7, 0.8, 0.9.

Cake Pricing

A cake originally priced at 800 with a 10% discount followed by a 10% tax, requires calculation of the final selling price.

Variable Problems

Given an algebraic equation involving variables A, B, C, D satisfying the budget of Rs. 96.

Summation Problem

Sum of all odd integers from 1 to 2019 requiring divisibility checks.

Box Size Calculation

Specified dimensions for small boxes fitting uniformly within a larger box.

Maximum and Minimum Values

A series of problems involving finding maximum and minimum possible values from given conditions.

Coffee Consumption

Survey of student coffee preferences, determining female student preferences based on male statistics.

Harmonic Relationship

Problems related to products and sums of roots under specific conditions.

Professor's Assignment

Evaluating cumulative properties of polynomial roots from given expressions and finding specific coefficients.

Miscellaneous

Various mathematical problems including logical deductions and ratio calculations.

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Description

Test your understanding of various mathematical concepts including ratios, area comparisons between shapes, calendar calculations, quadratic functions, mean calculations, and pathfinding. This quiz covers essential principles and problem-solving skills in math.