Mathematics MCQs in topical order.

Correct Answer: 12xy(x+y)

Factoring out the greatest common divisor, which is 12xy, from both terms yields 12xy(x + y).

Correct Answer: (a+b)(a²-ab+b²)

The sum of two cubes factors into the product of a binomial (a+b) and a trinomial (a²-ab+b²).

Correct Answer: 27

Substituting 3 into x^3 yields 3 * 3 * 3 = 27.

Correct Answer: 1/2

The sum of reciprocals is (x+y)/(xy) = 10/20 = 1/2.

Correct Answer: 400/d

Weekly fruit expense = d/4. Weeks needed = 100 / (d/4) = 400/d.

Correct Answer: -30

Expanding (6x-18)(2x+1) + 41 gives 12x^2 + 6x - 36x - 18 + 41 = 12x^2 - 30x + 23. Thus m = -30.

Correct Answer: 4

For infinitely many solutions, the equations must be equivalent. Multiplying the first equation by 2 gives 6x + 4y = 14, so m must be 4.

Correct Answer: 25 years

Let x be the age. (x + 15) = 4(x - 15). Solving gives x + 15 = 4x - 60, which simplifies to 3x = 75, so x = 25.

Correct Answer: 8 cm

Volume = (1/3)πr²h. So, 216π = (1/3)π(9²)(h) => 216 = 27h => h = 8 cm.

Correct Answer: -1 < d/e < 0

For perpendicular lines, slopes m1 * m2 = -1. If 0 < m1 < 1, then m2 must be between -1 and 0.

Correct Answer: 12 units

The side lengths are 4, 3, and the hypotenuse is 5 (by Pythagorean theorem). Summing these gives a perimeter of 12 units.

Correct Answer: Greater than the area of the square

For equal perimeters, a circle is more efficient at enclosing area than a square; therefore, the circle's area is larger.

Correct Answer: 192 cm²

Using Pythagoras theorem: other side = sqrt(20² - 12²) = sqrt(400 - 144) = sqrt(256) = 16 cm. Area = 12 * 16 = 192 cm².

Correct Answer: 1800

Volume of the cuboid is 10 x 12 x 15 = 1800 cm³. A 1 cm cube has a volume of 1 cm³, so 1800 cubes can be cut.

Correct Answer: 3 cm

By Pythagoras theorem, the radius (r), tangent length (4), and distance to center (5) form a right triangle: r² + 4² = 5², resulting in r² = 9, so r = 3 cm.

Correct Answer: 308 cm²

The curved surface area of a hemisphere is calculated using the formula 2πr². Substituting r=7, 2 * (22/7) * 49 = 308.

Correct Answer: 62.5%

The total parts are 3 + 5 = 8. The percentage of seniors is (5 / 8) * 100 = 62.5%.

Correct Answer: 33.33%

Percentage = (Distance covered / Total distance) * 100 = (13 / 39) * 100 = 33.33%.

Correct Answer: n / (1.36)(0.82)

Let start = x. After turn 1: 0.82x. After turn 2: 0.82x * 1.36 = n. Thus, x = n / (1.36 * 0.82).

Correct Answer: 1.425

To convert a percentage into a decimal, divide by 100. 142.5 / 100 = 1.425.

Correct Answer: 10,000

Let the original salary be x. x + x/5 = 60000. So 6x/5 = 60000, meaning x = 50000. The increase is 60000 - 50000 = 10,000.

Correct Answer: Rs.2125

Discount = 15% of 2500 = 375. Selling price = 2500 - 375 = Rs. 2125.

Correct Answer: 187.5ml

If 8% of the total volume X is 15 mL, then X = (15 * 100) / 8 = 187.5 mL.

Correct Answer: None of these

To find the percentage: (1.19 / 1.6) * 100 = 74.375%. Therefore, none of the provided options (6%, 4%, 60%) are correct.

Correct Answer: 7500000

One million is 1,000,000. Therefore, 7.5 million is 7,500,000.

Correct Answer: 6

Multiplying a square root by itself removes the radical, yielding the base number: √6 × √6 = (√6)² = 6.

Correct Answer: 47

Calculating 47 squared gives 2209 (47 × 47 = 2209).

Correct Answer: 0.001

5 * 2 = 10. The combined decimals places are 3 + 1 = 4. Placing the decimal gives 0.0010, which is 0.001.

Correct Answer: 17.2

Since 24.94 / 1.45 is equivalent to (2494/100) / (14.5/10), it simplifies to (2494 / 14.5) / 10. Thus, 172 / 10 = 17.2.

Correct Answer: 88

4 people per house multiplied by 22 houses equals 88 people.

Correct Answer: 54.9

5 + 51 = 56; 56 - 3 = 53; 53 + 7 = 60; 60 - 5.1 = 54.9.

Correct Answer: 54.9

Summing the numbers step by step: 5 + 51 = 56; 56 - 3 = 53; 53 + 7 = 60; 60 - 5.1 = 54.9.

Correct Answer: 33 years

Total age of 20 students is 20*12=240. With the teacher, total age is 21*13=273. The teacher's age is 273 - 240 = 33 years.

Correct Answer: 57

Let the average of 59 students be x. Total weight is 59x. Original total for 60 students was 59x + 45. Average was (59x + 45)/60 = x - 0.2. Solving yields x = 57.

Correct Answer: 55000

A+B = 100k, B+C = 120k, A+C = 110k. Summing them: 2(A+B+C) = 330k, so A+B+C = 165k. B = (A+B+C) - (A+C) = 165k - 110k = 55k.

Correct Answer: 42

Total height = 5 * 68 = 340. The sum of the four known heights = 70 + (76 * 3) = 298. Fifth pupil's height = 340 - 298 = 42 inches.

Correct Answer: 60

Let boys be b. 50b + 40(100-b) = 4600. 10b = 600, hence b = 60.

Correct Answer: None of these

Total cartoons = 13. Total items = 65. Total cost = 260. Average = 260 / 65 = Rs. 4 per item.

Correct Answer: 37.25 Kg

Total weight = (36 × 40) + (44 × 35) = 1440 + 1540 = 2980. Average = 2980 / 80 = 37.25 kg.

Correct Answer: 27

The first five multiples are 9, 18, 27, 36, 45. Their sum is 135. Average = 135 / 5 = 27.

Correct Answer: 11:3

Substitute x=3 and y=4. 7(3)+3(4) = 21+12=33. 7(3)-3(4) = 21-12=9. The ratio 33:9 simplifies to 11:3.

Correct Answer: 12.5

The initial 20L mixture is 1:1 ratio. The 15L taken contains 7.5L water and 7.5L milk. Adding 5L more water brings the total water to 12.5L.

Correct Answer: 20

In 12 minutes he irons 4 shirts. In 60 minutes (1 hour) he will iron (60/12) * 4 = 20 shirts.

Correct Answer: 6:4:3

Given 2A = 3B = 4C. Let them equal 12 (the LCM). Then A = 6, B = 4, and C = 3. Therefore, A:B:C = 6:4:3.

Correct Answer: 7/13

0.35 / 0.65 = 35 / 65. Dividing both the numerator and denominator by 5 gives 7 / 13.

Correct Answer: 15 lawns

Lawns per hour = 3 / 2 = 1.5. In 10 hours: 10 * 1.5 = 15 lawns.

Correct Answer: 72 miles

The ratio is 2 recorded : 3 actual. Multiply 48 by (3/2) to find the actual distance: 48 * 1.5 = 72 miles.

Correct Answer: 1:2:3

Since the value of 'b' is 2 in both given ratios, the combined ratio directly becomes a:b:c = 1:2:3.

Correct Answer: 9/125

Multiply the numerators: 1 × 3 × 6 = 18. Multiply denominators: 10 × 5 × 5 = 250. 18/250 simplifies to 9/125 by dividing by 2.

Correct Answer: 144

Let total = X. German = 0.25X. Remaining = 0.75X. Italian = (4/5)*0.75X = 0.6X. Remaining = 0.15X. French = (2/3)*0.15X = 0.1X. Japanese = 0.05X = 12. So, X = 240. Italian = 0.6 * 240 = 144.

Correct Answer: 72

Let total be x. x/4 + x/6 + x/8 + 33 = x. Multiplying by 24 gives 6x + 4x + 3x + 792 = 24x => 11x = 792 => x = 72.

Correct Answer: 4/5

Decimal conversions show 3/4 is 0.75 and 5/6 is ~0.833. The fraction 4/5 equals 0.8, which mathematically sits right between them.

Correct Answer: 2 2/3

Let fraction be x. Equation: (x * x) / (1/x) = x^3. Since 18 26/27 = 512/27, we take the cube root of 512/27, which equals 8/3 or 2 2/3.

Correct Answer: 7/8

Converted to decimals: 3/4 = 0.75, 5/6 ≈ 0.833, 7/12 ≈ 0.583, 7/8 = 0.875. Therefore, 7/8 is the largest.

Correct Answer: 2.67

Let the fraction be x. Equation is x * x / (1/x) = x^3. So x^3 = 512/27. x = 8/3 = 2.666..., which rounds to 2.67.

Correct Answer: 1/3

Multiplying the fractions: (5/6) * (2/5) = 10/30, which simplifies to 1/3.

Correct Answer: Rs.8000

Let original price be P. P + 10% of P = 8800. Therefore, 1.1P = 8800, giving P = 8000.

Correct Answer: Rs. 3000

For maximum profit, books are bought at the lowest price (150) and sold at the highest (350). Profit per book = 350 - 150 = 200. Total profit for 15 books = 200 * 15 = 3000.

Correct Answer: 4% Loss

Cost = (200*10) + 500 = 2500. Total oranges = 200*12 = 2400. Revenue = 2400*1 = 2400. Loss = 100. Loss % = (100/2500)*100 = 4%.

Correct Answer: 200

Selling Price = Cost Price + Profit. 220 = CP + 0.1(CP) -> 1.1(CP) = 220 -> CP = 200.

Correct Answer: 16

Using the formula: Profit% = ((CP of given qty - SP of given qty)/SP given qty) * 100. -> 25 = ((20 - X) / X) * 100. Solving this gives X = 16.

Correct Answer: 200

Since Selling Price = Cost Price * (1 + Profit Margin), 250 = CP * 1.25. Therefore, CP = 250 / 1.25 = 200.

Correct Answer: 10%

Assuming Rs 250 is the Cost Price (as per the question context), Profit % = (25 / 250) * 100 = 10%.

Correct Answer: 5.26%

Profit = 60,000 - 57,000 = 3,000. Profit % = (3,000 / 57,000) * 100 = 5.263%.

Correct Answer: 5 days

Total work = 10 * 20 = 200 units. 20 persons at double efficiency act like 40 persons. Days required = 200 / 40 = 5 days.

Correct Answer: 10 days

2(A+B+C)'s one-day work = 1/12 + 1/15 + 1/20 = 12/60 = 1/5. (A+B+C)'s one-day work = 1/10. Time = 10 days.

Correct Answer: 3 days

A takes 40 hours total, B takes 60 hours total. Joint 1-hour work = 1/40 + 1/60 = 1/24. They need 24 hours. At 8 hours a day, 24/8 = 3 days.

Correct Answer: 36

Using inverse proportion: Women * Days = Constant. 42 * 18 = W * 21. W = (42 * 18) / 21 = 36 women.

Correct Answer: 06 days

In 2 days, they finish 2/3 work. A finishes remaining 1/3 in 2 days. A's 1 day work = 1/6. B's 1 day work = (1/3) - (1/6) = 1/6. B takes 6 days.

Correct Answer: 12 days

If B takes 12 days, A takes 6 days. Together: (1/12) + (1/6) = 3/12 = 1/4, meaning 4 days to finish. Thus, B takes 12 days.

Correct Answer: None of these

Total work = 40 x 25 = 1000 units. For 12 men: 1000 / 12 = 83.33 days, which is not listed in the standard options.

Correct Answer: 20 days

If A takes x days, B takes 2x. Since 2x - x = 30, A takes 30 days and B takes 60. Combined rate = 1/30 + 1/60 = 1/20, so 20 days together.

Correct Answer: Continuous variable

A continuous variable can take an infinite number of possible values within a given range, unlike discrete variables.

Correct Answer: Ratio scale

A ratio scale possesses a true, meaningful zero point, allowing for the calculation of ratios between values.

Correct Answer: Arithmetic mean

In general parlance, when people speak of an 'average', they are specifically referring to the arithmetic mean.

Correct Answer: Heteroscedasticity

In statistics, the White test is used to establish whether the variance of the errors in a regression model is constant, meaning it tests for heteroscedasticity.

Correct Answer: Variables

Multicollinearity occurs in multiple regression models when independent variables are highly correlated with one another.

Correct Answer: Geometric mean

The geometric mean is the mathematically correct way to calculate average rates of return and compound growth over multiple periods.

Correct Answer: Arithmetic mean

The arithmetic mean is simply the sum of a collection of numbers divided by the count of numbers in the collection, commonly referred to as the average.

Correct Answer: Square root

Standard deviation is mathematically defined as the square root of the variance, measuring the dispersion of a dataset.

Correct Answer: c = 12(3,000 + 2,500x)

The monthly cost is the fixed cost plus the variable cost (3000 + 2500x). For an entire year, this monthly sum is multiplied by 12.

Correct Answer: 15

Let the brother's age be x. Ali's age is 2x. Their difference is 2x - x = 15. Thus, x = 15.

Correct Answer: 10

Let C = x. Then B = 2x and A = 2x + 2. Summing them: (2x + 2) + 2x + x = 27. 5x = 25, x = 5. So, B = 2(5) = 10.

Correct Answer: 0.6

Total time = 1/3 + 1/2 = 5/6 hours. Fraction on automobile = (1/2) / (5/6) = 3/5 = 0.6.

Correct Answer: None of these

Tank capacity = 250 / 15 = 16.66 gallons. At 20 mpg, distance = 16.66 × 20 = 333.3 miles.

Correct Answer: $75

If both start with 75, A gives 50, leaving A with 25. B now has 75 + 50 = 125. Since 125 is 5 times 25, $75 is correct.

Correct Answer: $100

Let Josh = J, Aaron = 3J. After transfer: Josh has J+50, Aaron has 3J-50. Eq: J+50 = 3(3J-50) => J+50 = 9J-150 => 8J = 200 => J = 25. Aaron = 75. Total = 100.

Correct Answer: 16

Fuel consumed per lap = (22 - 18) / (7 - 4) = 4/3 units. Total laps from 22 units = 22 / (4/3) = 16.5, completing 16 full laps.

Correct Answer: 35

The pattern involves multiplying the number by an increasing integer: 4x2=8, 5x3=15, 6x4=24. Following this, 7x5=35.

Correct Answer: 127

The pattern follows multiplying the previous number by 2 and adding 1 (e.g., 63 × 2 + 1 = 127).

Correct Answer: 82

The gaps between terms are 2, 6, 18 (each gap is multiplied by 3). The next gap is 18 × 3 = 54. 28 + 54 = 82.

Correct Answer: 28

The first five prime numbers are 2, 3, 5, 7, and 11. Their sum is 2 + 3 + 5 + 7 + 11 = 28.

Correct Answer: 64

The series consists of two alternating patterns: odd positions are cubes (1³, 2³, 3³, 4³=64) and even positions are squares (1², 2², 3², 4²=16).

Correct Answer: 18

The pattern adds sequential integers: +1, +2, +3, +4. So 13 + 5 = 18.

Correct Answer: 31

The series increases by even numbers: 7+6=13, 13+8=21, 21+10=31, 31+12=43.

Correct Answer: 56

The differences are increasing even numbers: +4, +6, +8, +10, +12, +14. So 42 + 14 = 56.