Past papers · Mathematics
Mathematics Past Papers MCQs with Answers
565 Mathematics questions from past papers, each with the answer and a quick fact, grouped by topic. These Mathematics past paper MCQs are taken from PPSC, FPSC and other one-paper competitive exams, compiled from unofficial resources.
Browse by topic
565 questions across 9 topics. Open any question for the answer and a quick fact.
Basic Arithmetic & Number Systems
109 MCQsBasic Arithmetic & Number Systems in Mathematics
Integers and Decimals
- What is the value of $0.057 - 0.0041$?
- $0.005 \times 0.2 =$ ?
- What is the sum of the first 5 composite numbers?
- $0.04 \times 0.0162 \times 0.001$ is equal to?
- $0.232323\ldots$ (repeating decimal) can also be expressed in the form of:
- Four people live in a house. There are 22 houses in one street. How many people live in the street?
- A boy saved $4.56 the first month, $3.82 the second month, and $5.06 the third month. How much did he save altogether?
- Convert the binary number $10100$ into decimal.
- What is the result when $4.036$ is divided by $0.04$?
- What is $0.5 \times 0.06$?
- When $52416$ is divided by $312$, the quotient is $168$. What will be the quotient when $52.416$ is divided by $0.0168$?
- What is the result of $50 - 15.5$?
- How many two-digit numbers are divisible by 11?
- If Jack needs $2.5$ pints of cream to make a dessert, how many pints will he need to make $3$ desserts?
- How many pieces of $13.2$ cm can be cut from a $330$ cm long rod?
- A number when divided by 4 and 9 leaves a remainder of 3 in each case. If the number is 39, which of the following correctly represents this calculation?
- If $2994 \div 14.5 = 172$, then $29.94 \div 1.45 = \_\_\_\_\_$?
- The number of prime numbers between 64 and 81 is:
- What is the value of $0.7683 + 0.369 + 0.05 + 0.8$?
- The place value of 9 in 0.06945 is?
- The sum of $3 + 0.3 + 0.03 + 0.003$ is:
- Which positive integer is a multiple of $3$ and less than double the square of $4$?
- What is the value of $0.085 \div 0.017$?
- Find the farthest number from $-1$ on the number line among the following:
- How many two-digit numbers are divisible by 9?
- Express the recurring decimal $0.\overline{125}$ as a rational number.
- Solve: $0.003 \times 0.02 =$ _?
- What is the sum of all prime numbers from 60 to 80?
- Find the value of $\frac{1}{0.02}$.
- The product of two numbers is $72$. If one of the numbers is $9$, find the other number.
Fractions
- A man walked for $\frac{1}{3}$ hour and then got an automobile ride for $\frac{1}{2}$ hour. What part of the total time consumed did he ride on the automobile?
- If the numerator is greater than or equal to the denominator, the fraction is called?
- Solve: $\frac{2}{3} + \frac{3}{4}$
- Simplify: $\frac{3}{4} + \frac{2}{3}$
- If one-third of one-fourth of a number is 15, then three-tenths of that number is:
- If $\frac{3}{11}$ of a number is $22$, what is $\frac{6}{11}$ of that number?
- If $\frac{1}{5}$ of 3000 keyboards are out of order, how many remain functional?
- What is the decimal value of the fraction $\frac{1}{62.5}$?
- What is the value of $\frac{9}{11} + \frac{5}{7}$?
- If $\frac{1}{4}$ of the participants are in writing, $\frac{1}{6}$ in reading, $\frac{1}{8}$ in designing, and there are 33 participants in mathematics, then the total number of participants is:
- Which of the following fractions is less than $\frac{7}{8}$ and greater than $\frac{1}{3}$?
- Which of the following fractions is greater than $\frac{3}{4}$ and less than $\frac{5}{6}$?
- The least value of $\frac{39}{26}$ is?
HCF and LCM
Square Roots and Cube Roots
- What is the value of $\sqrt{10} \times \sqrt{250}$?
- Find the square root of 6492304:
- If $A = \sqrt{5} + 1 + \sqrt{5} - 1$ and $B = \sqrt{5} - 1 + \sqrt{5} + 1$, then $A + B$ is equal to:
- The value of $\sqrt{176} + \sqrt{2401}$ is _?
- What is the nature of the expression $16 + \sqrt{16} + \sqrt[3]{27}$ ?
- $\sqrt[3]{216} = ?$
- $\sqrt{9801} = ?$
- Find $\sqrt[3]{216}$.
BODMAS Rule and Simplification
- Simplify: $51 + 5 - 3 + 7 - 5.1 = \text{?}$
- What is the value of $3.4 \times \frac{1}{4} \div 0.7$?
- The value of $6 \times 10 \times \left(\frac{1000}{3}\right) \times 10 \times 100$ is equal to:
- The value of $\frac{3.5 \times 1.4}{0.7}$ is:
- $5005 - 5000 \div 10.00 = ?$
- Find the value of $X$: $$3889 + 12.952 - X = 3854.002$$
- Solve: $16 \div 4 + 9 - 6$
Average
- David obtained $76$, $65$, $82$, $67$ and $85$ marks (out of $100$) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
- What is the average of the numbers: $0$, $0$, $4$, $10$, $5$, and $5$?
- The average of 50 numbers is 30. If two numbers, 35 and 40, are discarded, then the average of the remaining numbers is nearly:
- Out of three given numbers, the first number is twice the second and thrice the third. If the average of the three numbers is 154, what is the difference between the first and the third number?
- The average age of a group of 13 boys is 13. When two boys join the group, the average rises by 2 years. The sum of the ages of the two new boys is:
- The average of runs of a cricket player in 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4?
- What is the average of the first 100 natural numbers?
- Find the average of $\frac{5}{6}$, $\frac{4}{3}$, $\frac{3}{4}$.
- A class had 14 boys with an average height of $5.3$ feet. A new boy joined the class. Now the average height of the 15 boys in the class is $5.25$ feet. How tall was the new boy?
- The average income of A and B is 50000, the average income of B and C is 60000, and the average income of A and C is 55000. What is the income of B?
- A batsman in his 12th inning makes a score of 80 runs and thereby increases his average score by 3. What is his average after the 12th inning?
- Three years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average age of the family is now the same as it was three years ago. The present age of the baby (in years) is:
- There are two sections A and B of a class, consisting of 36 and 44 students respectively. If the average weight of section A is 40 kg and that of section B is 35 kg, find the average weight of the whole class.
- If the average (arithmetic mean) of $8$, $12$, $15$, $21$, $x$ and $11$ is $17$, then what is $x$?
- The average of five numbers is $27$. If one number is excluded, the average becomes $25$. The excluded number is:
- The average of three numbers is $20$. If two numbers are $16$ and $22$, the third is?
- The average age of 3 friends is 23. Even if the age of the 4th friend is added, the average remains 23. What is the age of the 4th friend?
- A shopkeeper purchases 5 cartons for 105 rupees and 8 cartons for 155 rupees. If each carton contains 5 items, then the average price per item is _?
- The average weight of 10 people increased by $1.5$ kg when one person weighing $45$ kg is replaced by a new person. What is the weight of the new person?
- The average of 6 numbers is $30$. If the average of the first four is $25$ and that of the last three is $35$, the fourth number is:
- The mean of 5 numbers is 34. Three of them are 29, 26, and 35. If the remaining two numbers are in the ratio $1:3$, find the numbers.
- Find the average of $\frac{5}{6}$, $\frac{4}{3}$, and $\frac{3}{4}$.
- The average marks of four subjects is $120$. If $33$ was misread as $13$ during the calculation, what will be the correct average?
- In a set $S = \{0, 2, 4, 5, 9\}$, which number, if removed from the set, keeps the average unchanged?
- If scores are $75$, $80$, and $85$, what number makes the average $80$?
- There are four numbers. The average of the first three is $15$ and that of the last three is $16$. If the last number is $19$, find the first number.
- If the average weight of 7 people is 70 kg, and one person weighing 80 kg is replaced by another person weighing 60 kg, what will the new average weight be?
- The average of the first five multiples of $9$ is _?
- Roshan bought 5 pants at Rs. 25 each, 10 shirts at Rs. 50 each, and 15 ties at Rs. 35 each. Find the average price of all the articles.
- If the mean of 7 terms is 40, the sum of those terms will be?
Units & Conversions
- One (1) inch is approximately equivalent to how many millimeters?
- One kilometer is equal to metres.
- Kilometre is a unit of distance in ?
- How many seconds are there in 27 minutes?
- 1 kilometer is equal to how many centimeters?
- One mile is equal to ?
- A bag contains 9 KG of sugar which is separated into packages containing 450 grams each. How many such packages can be made?
- One (1) KB (Kilobyte) = ?
- Ali can type at a speed of $25$ words per minute. How many words can he type in one hour?
- How many cubic centimeters ($\text{cm}^3$) are there in 1 liter (L)?
- Convert $80000 \text{ cm}^3$ into liters.
- A picosecond is equal to?
Ratios, Proportions & Percentages
111 MCQsRatios, Proportions & Percentages in Mathematics
Ratio and Proportion
- What is the equation type for A and B working together problems?
- If $40\%$ of a number is equal to $\frac{2}{3}$ of another number, what is the ratio of the first number to the second number?
- The salaries of A, B and C are in the ratio $1 : 3 : 4$. If the salaries are increased by $5\%$, $10\%$ and $15\%$ respectively, then the increased salaries will be in the ratio?
- The ratio of ages of two students is $3 : 2$. One is older than the other by 5 years. What is the age of the younger student?
- What is the ratio of 8 inches to 7 feet?
- What is the ratio of 400 meters to 2 kilometers?
- Find the 4th proportional to $4$, $16$ and $7$.
- If $\frac{2}{3}$ of A = $75\%$ of B = $0.6$ of C, then A : B : C is:
- A truck and a car travel a total distance of 640 km. The ratio of the distance covered by the truck to the distance covered by the car is 4:5. What is the distance covered by the car?
- Simplify the ratio expression: $\frac{2}{3} : \frac{4}{6}$
- If 12 : 68 :: x : 170, find the value of x.
- In a ratio $1 : x : 5$, the sum of the three terms is $11$. Find the value of $x$.
- The price of an item is increased in the ratio $1 : 9$. If the original price was $100{,}000$, what is the new price?
- 6 men, 8 women, and 6 children complete a job for a total sum of Rs. 950. If their individual wages are in the ratio $4 : 3 : 2$, the total money earned by the children is:
- If $x : y = 5 : 2$, then $(8x + 9y) : (8x + 2y)$ is?
- $x$ is $20\%$ more than $z$ and $y$ is $80\%$ more than $z$. Find $x : y$.
- What is the simplest form of the ratio $0.35 : 0.65$?
- Ali has Rs. 20 and Asim has Rs. 16. What is the ratio of Ali's amount to Asim's amount?
- The price of 357 mangoes is Rs. 1517.25. What will be the approximate price of 49 dozen of such mangoes?
- The sum of two numbers is $40$ and their difference is $4$. The ratio of the numbers is:
- If $m:n = 3:2$, then $(4m+5n):(4m-5n)$ is equal to _?
- The mean proportional between $2$ and $8$ is:
- Which of the following ratios is the largest?
- If $A:B = 2:3$, $B:C = 3:4$, and $A:D = 4:5$, then find $C:D$.
- If the current ratio is $2:1$ and working capital is Rs. $60{,}000$, what is the value of current assets?
- What is the ratio of 12 minutes to 1 hour?
- If $\frac{1}{2}$ inch is equal to 12 kilometers, the distance between two points is $5\frac{2}{3}$ inches. What is the distance in kilometers?
- A line segment is divided in the ratio $4:6$. How many total parts are needed to divide it?
- The ratio of ages of two students is $3 : 2$. One is older than the other by $5$ years. What is the age of the younger student?
- Two numbers are respectively $20\%$ and $50\%$ more than a third number. The ratio of the two numbers is:
- If $A : B = 2 : 3$ and $B : C = 4 : 5$, then $A : B : C = ?$
- Two numbers are in the ratio $3:5$. If $9$ is subtracted from each number, the ratio becomes $12:23$. The smaller number is:
- If $2 : 7 :: x : 49$, then what is the value of $x$?
- Which number, when increased in the ratio $7:9$, becomes $224$?
- Find the 4th proportional to $4$, $16$, and $7$.
- Which of the following symbols is commonly used to denote proportion?
- In a mixture of 60 litres, the ratio of milk and water is $2:1$. If this ratio is to be changed to $1:2$, then the quantity of water to be further added is:
- If $\frac{3a - 5b}{3a + 5b} = 5$, then $a : b$ is equal to:
- If 15 toys cost Rs. 234, what will 35 toys cost?
- Total number of students in a class is 95. If the total number of girls in the class is 45, then the ratio of total number of boys to total number of girls is:
- The number of boys and girls in a school are 360 and 240 respectively. What is the ratio of the number of boys to the total number of students?
- A sum of Rs. 95,000 is to be divided among A, B, and C in such a way that $A : B = 2 : 3$ and $B : C = 2 : 3$. What will be the share of A?
- If $\frac{a}{3} = \frac{b}{2}$, then the value of $\frac{2a+3b}{3a-2b}$ is:
- Sum of two numbers is 40 and their difference is 4. The ratio of the numbers is:
- A photograph measuring $5.5$ cm by $9$ cm is enlarged in the ratio $7:5$. What is the new length and width of the picture?
- If $P : Q = 8 : 15$ and $Q : R = 3 : 2$, then find $P : Q : R$.
Percentages
- Two numbers are respectively $20\%$ and $50\%$ more than a third number. The ratio of the two numbers (first to second) is:
- 78 students, which is 30% of the whole class. What is the total number of students in the class?
- What is $80\%$ of $700$?
- A village has 5860 voters, of whom 7% usually forget to vote. In order to win an election, a candidate must gain at least 50% of the remaining votes. How many votes does he need to win?
- A student obtained $75\%$, $80\%$ and $85\%$ in three subjects. If the marks of another subject are added, then the number cannot be less than ?
- $20\%$ of $30\%$ of $20\%$ of Rs. $850$ is?
- If Sohail's salary is 10% more than Sajjad's salary, then what is Sajjad's salary as a percentage of Sohail's salary?
- A chemical solution contains $8\%$ acid. If there is $15$ ml acid in the solution, what is the volume of the solution?
- The cost of an article was Rs. 75. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the article is:
- A school has only four classes that contain 10, 20, 30, and 40 students respectively. The pass percentages of these classes are 20%, 30%, 60%, and 100% respectively. Find the pass percentage of the entire school.
- If the price of an article is Rs 945 including 5% GST, then its original price is _?
- A truck weighs $6500$ kg. If $81\%$ of its weight is load, what is the weight of the load?
- What is $20\%$ as a fraction?
- 70% of the students in a school are boys and the number of girls is 504. Find the number of boys in the school.
- $175\%$ of a number is $49$. Find the number.
- If $45\%$ of the total students in a school is $135$, then what is the total number of students?
- Increase from $72$ to $90$: what is the percentage increase?
- In a class of 40 students, 8% are boys. How many boys are there in the class?
- If each side of a square is reduced by $40\%$, by what percentage is the area reduced?
- Total population is $80{,}000$. If $75\%$ attended, how many did not attend?
- The cost of a car is 400% greater than the cost of a bike. If there is an increase in the cost of the car by 15% and that of the bike by 20%, then the total increase in the cost of 5 cars and 10 bikes is:
- A shop has 6224 soaps. If the shop sells 20% of the soaps, how many soaps are left?
- What is $20\%$ of $6440$?
- In a class of 60 students, 18 are girls. What is the percentage of girls?
- Of a class of 40 students, $20\%$ are girls. How many boys are in the class?
- A number is increased by $20\%$ and then decreased by $20\%$. Find the net increase or decrease percent.
- Ali's shell collection share is $80\%$ more than Aslam's. If Aslam has $80$ shells, then the total number of shells will be _?
- What percentage is equivalent to $\frac{21}{4}$?
- $20\%$ is equal to?
- There are 56 boys in a class of 140 students. What is the percentage of boys?
- Of a class of 40 students, 20% are girls. How many boys are in the class?
- Two numbers are respectively $60\%$ and $20\%$ more than a third number. What percentage is the second number of the first?
- Umar paid $7895$ as usher at $10\%$ of the total amount he earned. What was the total amount he earned?
- If an amount increased by $25\%$ becomes $4{,}450{,}000$, what was the original amount?
- $P$ is 6 times greater than $Q$. By what percent is $Q$ smaller than $P$?
- Calculate $30\%$ more than $9{,}000$.
- What is $18\%$ of $600$?
- A man's annual production sells for $3,481,600$. The use of $10\%$ will be _?
- If a person pays Zakat as Rs. 8500, what is the total amount of their wealth?
- $1.14$ expressed as a percent of $1.9$ is?
- 170 teachers out of 200 were present. What percentage of teachers were present?
- Each day, Robert eats $40\%$ of the pistachios left in his jar at that time. At the end of the second day, $27$ pistachios remain. How many pistachios were in the jar at the start of the first day?
- $220\%$ of a number $X$ is $44$. What is $44\%$ of $X$?
- If $X\%$ of $\frac{25}{2}$ is $150$, then the value of $X$ is ?
- A student scores $80\%$ in English and $85\%$ in Math. If the passing percentage in both subjects is $75\%$, what is the percentage of failure?
- A cricket team won 5 matches, with a win percentage of 25%. How many matches did they play in total?
- A man's annual production sells for $75{,}000$. The use of $10\%$ will be _?
- If A's salary is $25\%$ higher than B's salary, then by what percent is B's salary lower than A's?
- There are twice as many boys as girls in a class. If $30\%$ of the boys and $45\%$ of the girls failed in the exams, then what percentage of the class passed the exams?
Direct and Inverse Variations
- A worker is paid Rs. 2130 for 6 days. If his total wages during a month add up to Rs. 9230, find the number of days he worked in the month.
- If a girl jumps 820 times in an hour, how many times does she jump in 30 minutes?
- If 6 persons working 8 hours a day earn Rs. 8400 per week, then how much will 9 persons working 6 hours a day each earn per week?
- A flagstaff $17.5$ m high casts a shadow of length $40.25$ m. The height of the building, which casts a shadow of length $28.75$ m under similar conditions, will be:
- A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
- If $y$ is directly proportional to $x^2$, and when $x = 2$, $y = 20$, what is the value of $y$ when $x = 3$?
- 12 men can complete a work in 24 days. In how many days will 8 men complete the same work?
- Find the value of $x$ when $y = 5$, if $x$ varies directly as $4y - 1$ and $x = 14$ when $y = 2$.
- An army camp of 200 men has enough food for 60 days. How long will the food last if the number of men in the camp is reduced to 160?
- If a 162 km long road can be constructed in 9 months, how many months are required to construct a 306 km long road?
- If $y$ is inversely proportional to $x$, and $y = 10$ when $x = 2$, find $y$ when $x = 5$.
- A car that gets 15 miles per gallon of gasoline can travel 250 miles on a full tank. If the same car got 20 miles per gallon, how many miles could it travel on a full tank?
- A garrison has provisions for 30 days for a certain number of men. If $\frac{2}{3}$ of them do not attend the mess, then the food will last for how many days?
- If the price of a carpet 8 meters long and 3 meters wide is Rs. 6288, what will be the price of a carpet 12 meters long and 6 meters wide?
- 12 water pumps can empty a water tank in 20 minutes. However, 2 pumps are out of order. How long will the remaining pumps take to empty the tank?
Financial Mathematics
45 MCQsFinancial Mathematics in Mathematics
Profit, Loss, and Discount
- A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of another variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percentage is:
- A person buys a shirt for $470$ and sells it for $540$. Find the approximate profit percentage.
- A person bought an item for Rs. 2500 and sold it at a 15% discount on the marked price. If the marked price is the same as the cost price, what was the selling price after the discount?
- At the break-even point:
- A toy is sold for Rs. 220. What was the cost price if the rate of profit was 10% of the cost?
- A person by selling an article for Rs. 180 loses 10%. In order to make a profit of 10%, at what price must he sell the article?
- On a certain item, the price is decreased from $0.62$ to $0.42$. What is the actual percentage of discount?
- The price of a bicycle is Rs. 6480 inclusive of 8% GST. What is the original price of the bicycle?
- Malti bought a TV for ₹ 8,800 including GST at 10%. What is the original cost of the TV?
- What is the discount percentage if the original price is $1500$ and the selling price is $1200$?
- A shopkeeper buys a watch for Rs. 350 and sells it for Rs. 392. Find his percentage of profit.
- Mr. Rehan ordered a car worth Rs. $6,00,000$ and was given a discount. Given that he paid Rs. $5,70,000$ for his new car, calculate the percentage discount he received.
- A farmer bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?
- The price of a pen is $75$. After a $15\%$ discount, what is its price?
- A shopkeeper sells one-third of his goods at a profit of 10%, another one-third at a profit of 20%, and the rest at a loss of 6%. What is his overall profit percentage?
- The discount price of an item is 20% less than the retail price. James purchases a book at a 30% discount at a special book sale. What percentage of the retail price did James pay?
- A person bought an item for Rs. 2500 and sold it at a 15% discount on the marked price. If the marked price is Rs. 2500, what was the selling price after discount?
- Daniyal sold a chair for Rs. 800 which he had bought for Rs. 1000. What is his percentage loss?
- If $\$28{,}800$ is the actual price, what will be the price after a $20\%$ discount?
- Chand bought a shirt for Rs. 250 and sold it for Rs. 295. Find the profit.
- The selling price of an article is Rs. 118 and the profit earned is 50%. The cost price of the article is:
- On a $20\%$ discount sale, an article costs Rs. $596$. What was the original price of the article?
Simple and Compound Interest
- A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?
- A sum of money doubles in 3 years at compound interest, compounded annually at the same rate. In how many years will it become 4 times itself?
- If $\$1000$ is deposited in a savings account with a $2\%$ annual interest rate, what will be the total interest after $3$ years (simple interest)?
- The price of a printer is Rs 150,000 and it depreciates at 4% annually. What is the price of the printer after 3 years?
- The principal that will amount to Rs. $270.40$ in $2$ years at the rate of $4\%$ per annum compound interest is:
- Ali deposits an amount of Rs. 65800 to obtain simple interest at the rate of 14% per annum for 4 years. What total amount will Ali get at the end of 4 years?
- The value of an article which was purchased 2 years ago depreciates at 12% per annum. If its present value is Rs. 9680, the price at which it was purchased is?
- What will be the compound interest on a sum of Rs. $1875$ after $2$ years if the rate of interest for the first year is $4\%$ and that for the second year is $8\%$?
- A man lends $60{,}000$ at simple interest at the rate of $9\%$ per year. What is the total amount (principal + interest) he receives after $3$ years?
- The simple interest on a sum of money makes it become 3 times of itself in 20 years. In how many years will it become double of itself at the same rate of interest?
- If principal = Rs $1{,}00{,}000$, rate of interest = $10\%$ compounded half-yearly, find the amount after one year.
- Kriya deposits an amount of Rs. 65,800 to obtain a simple interest at the rate of $14\%$ per annum for four years. What is the total amount she will receive at the end of the period?
- Rs. 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.
- What will be the simple interest on Rs 4000 at 12.5% per annum for the period from 4th February 2005 to 18th April 2005?
- Kyle bought a $\$2000$ government bond that yields $6\%$ simple interest per year. Write the equation that gives the total amount $A$, in dollars, Kyle will receive when he sells the bond after $t$ years.
- Hassan borrowed $5000$ with simple interest for five years. He paid an extra $500$, then how much percent does he pay per annum?
- A man takes a loan of $65000$ at an annual interest rate of $3\%$. In how many years will the interest become $68900$?
- Find the time when the Simple Interest is $81$, Principal is $450$, and Rate is $5\%$.
- If the interest on Rs. 800 in 2 years is more than the interest on Rs. 400 by Rs. 40 in 2 years, find the rate of simple interest.
- A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is _?
- Find the compound interest on ₹50,000 at the rate of 12% per annum compounded quarterly for a period of 6 months.
Investment & Risk Management
Time, Work & Distance Problems
65 MCQsTime, Work & Distance Problems in Mathematics
Time, Speed, and Distance
- The diameter of the wheel of a car is $84$ cm and the speed of the car is $72$ km/h. How many revolutions are made by the wheel in $11$ minutes?
- A train covers a certain distance in 5 hours at a speed of $45$ km/h. What speed is required to cover the same distance in $3$ hours?
- In covering a distance of $30$ km, Ali takes $2$ hours more than Raza. If Ali doubles his speed, then he would take $1$ hour less than Raza. What is the speed of Ali?
- A train covers $12$ kilometers in one hour. How many hours will it take to cover $48$ kilometers?
- A train travels $16$ km in $20$ minutes. What is the speed of the train in km/h?
- A train covers a distance of $400$ km at a speed of $20$ km/h. How much time will it take?
- A person crosses a 500 m long street in 5 minutes. What is his speed in km/h?
- Two friends start running in opposite directions from the same point. One runs $2$ km/h faster than the other. After $1$ hour, they are $10$ km apart. What are their speeds?
- A car travels at a speed of $36$ km/h. What is the distance traveled by the car in $20$ seconds, in meters?
- If a car leaves at 21:15 on Wednesday and reaches the destination after $5\frac{1}{2}$ hours, find the time when it reached the destination.
- A train covers $150$ km in $3$ hours. How much distance will it cover in $8$ hours?
- A truck covers 47 km in 10 hours, and a car covers the same distance in 8 hours. What is the ratio of the speed of the car to the truck?
- If a car covers $19$ km at a speed of $57$ km/h, how much distance will it cover at a speed of $110$ km/h in the same time?
- A car travels 100 km at a speed of 60 km/h and returns the same 100 km at a speed of 40 km/h. Calculate the average speed for the whole journey.
- A man faces North and covers $7$ km, turns West and covers $2$ km, then turns South and covers $4$ km, and turns West again and covers $2$ km. How far is he from the starting point?
- If a car travels $120$ miles in $2$ hours, how far will it travel in $3$ hours at the same speed?
Work and Time
- If three lawns are completed in two hours, how many lawns will be completed in ten hours?
- If 42 women can do a work in 18 days, how many women will do the same work in 21 days?
- $P$ and $Q$ need $8$ days to complete a work. $Q$ and $R$ need $12$ days to complete the same work. But $P$, $Q$ and $R$ together can finish it in $6$ days. How many days will be needed if $P$ and $R$ together do it?
- Ali earns Rs 7500 in 2 weeks. What will he earn in 2 days if he works 6 days a week?
- Working $5$ hours a day, A can complete a work in $8$ days and working $6$ hours a day, B can complete the same work in $10$ days. Working $8$ hours a day, they can jointly complete the work in:
- 12 men can do a piece of work in 10 days. How many men would be required to do the same work in 8 days?
- A person irons four shirts in 12 minutes. How many shirts will he iron in one hour?
- A stenographer has been asked to fill out 500 forms. She fills 25 forms by the end of half an hour, when she is joined by another stenographer who fills the forms at the rate of 45 per hour. The entire assignment will be carried out in:
- 125 people can finish a piece of work in 120 days. Find the number of people required to finish this same work in 100 days.
- $A$ and $B$ can do a piece of work in $12$ days, $B$ and $C$ in $15$ days, and $C$ and $A$ in $20$ days. The number of days taken by $A$, $B$, and $C$ together to finish the work is:
- If a certain job can be finished by 18 workers in 26 days, how many workers are needed to finish the job in 12 days?
- A takes 6 days less than the time taken by B to finish a piece of work. If both A and B together can finish it in 4 days, find the time taken by B to finish the work.
- 21 binders can bind 1400 books in 15 days. How many binders will be required to bind 800 books in 20 days?
- If 10 persons can do a job in 20 days, then 20 persons with twice the efficiency can do the same job in how many days?
- 24 workers working 7 hours a day produce 4000 units in 30 days. In how many days will 30 workers working 8 hours a day produce 3500 units?
- If 8 men or 12 women can do a piece of work in 25 days, in how many days can the same work be done by 6 men and 11 women?
- If 30 men working 9 hours per day can reap a field in 16 days, in how many days will 36 men reap the field, working 8 hours per day?
- A group of five clerks has been assigned to insert 24,000 letters into envelopes. The clerks perform this work at the following rates: Clerk A, 1100 letters/hour; Clerk B, 1450 letters/hour; Clerk C, 1200 letters/hour; Clerk D, 1300 letters/hour; Clerk E, 1250 letters/hour. At the end of two hours of work, Clerks C and D are assigned to another task. From the time that Clerks C and D were taken off the assignment, the number of hours required for the remaining clerks to complete this assignment is:
- 15 cattle can graze a field in 20 days. 20 cattle can graze 3 such fields in how many days?
- If person A completes a work in 12 days and person B completes the same work in 6 days, and they start working together, in how many days will they complete the work?
- If 60 women spin 48 kg of cotton by working 8 hours daily, how much cotton will 30 women spin by working 12 hours daily?
- A washerman irons 4 shirts in 12 minutes. How many shirts does he iron in one hour?
- A dishwasher can wash 12 dishes in 6 minutes. At this rate, how many dishes can be washed in 3 hours?
- If $A$ and $B$ together can complete a piece of work in $15$ days and $B$ alone can complete it in $20$ days, then in how many days can $A$ alone complete the work?
- $A$ is $4$ times as fast as $B$ and therefore is able to finish the work in $45$ days less than $B$. In how many days can $A$ and $B$, working together, complete the work?
- A completes a work in $12$ days whereas B completes the same work in $24$ days. If both A and B work together, the work will be completed in
- If a school cafeteria needs $C$ cans of soup each week for each student, and if there are $S$ students in the school, for how many weeks will $X$ cans of soup last?
- 12 men and 15 women can reap a field in 14 days. Find the number of days that 7 men and 5 women will take to reap the same field.
- 15 men were hired to plough a piece of land in 10 days. How many more men will be required to do the same job in 3 days?
- If a dishwasher cleans 1350 dishes in 1 hour, how many dishes will it wash in 16 minutes?
- $A$ and $B$ can do a piece of work in $12$ days, $B$ and $C$ in $8$ days, and $C$ and $A$ in $6$ days. How long would $B$ take to do the same work alone?
- A can do a piece of work in 4 hours, B and C together can do it in 3 hours, and A and C together can do it in 2 hours. How long will B alone take to do the work?
- A basket is filled at a rate such that $\frac{2}{3}$ of the basket is filled in $\frac{15}{2}$ hours. How many hours will it take to fill the entire basket?
- A and B together can complete a piece of work in 12 days. A alone can complete the same work in 20 days. In how many days can B alone complete the work?
- If 5 men can complete a piece of work in 6 days, how many days will 6 men take to complete the same work?
- A and B together can complete a work in 3 days. They start together but after 2 days, B left the work. If the work is completed after two more days, B alone could do the work in how many days?
- A man makes a basket in $\frac{2}{3}$ hours. How many baskets can he make in $7.5$ hours?
- A can complete a work alone in 10 days. A and B together can complete the same work in 8 days. In how many days can B alone complete the work?
Clocks and Calendar Problems
- What is the angle between the minute hand and hour hand of a clock at 8:30?
- A train leaves at 21:30 and reaches its destination at 7:30 the next morning. How much time does the journey take?
- How many times in a day are the hands of a clock in a straight line but opposite in direction?
- If the day before yesterday was Saturday, what day will it be the day after tomorrow?
- How many times do the hands of a clock coincide in a day?
- A train arrives at 15:06. If it started its journey $5\frac{1}{4}$ hours ago, what was the starting time?
- According to a timetable, a coach was due to leave a station at 22:55 and arrive at the destination at 06:05 the next day. Find the time taken for the journey.
Pipes and Cisterns
Problems on Ages
Algebra
111 MCQsAlgebra in Mathematics
Algebraic Expressions and Identities
- If $P * Q = P + Q + \frac{P}{Q}$, then $8 * 2$ is?
- The simplified value of $\left(1+\frac{1}{x}\right)\left(1+\frac{1}{x+1}\right)\left(1+\frac{1}{x+2}\right)\left(1+\frac{1}{x+3}\right)$ is:
- If $(2x+3)(ax-5)=12x^2+bx-15$ for all values of $x$, what is the value of $b$?
- If $a = 7$, $b = 5$, and $c = 3$, then the value of $a^2 + b^2 + c^2 - ab - bc - ca$ is?
- If $x = 3 + \sqrt{8}$, find the value of $x^2 + \frac{1}{x^2}$.
- Simplify: $\frac{(x^2 - 4x + 4) - (x^2 - 6x + 9)}{x - 3}$
- What is the value of $(892)^2$?
- An expression is a collection of:
- What is the value of $8.73 \times 8.73 \times 8.73 + 4.27 \times 4.27 \times 4.27$?
- Simplify the algebraic expression: $3x + 2y + x$
- Simplify: $(5p - 6q)^2 + (5p + 6q)^2$
- $(x + 3)(x - 2) = ?$
- The product of the first four consecutive natural numbers plus one is:
- Find the perimeter of a rectangle where the height is 6 more than the width.
- Simplify the expression: $3x^2 - 4\sqrt{x} + xy + \sqrt{25x} + 7x^2$
- If $x = 5$ and $y = 2$, then $x + y$ is equal to?
- $201 \times 199 =$ ?
- To solve a polynomial equation by putting a given value of $x$, we are actually?
- If x = 7 − 4√3, then the value of x − 1/x is?
- Simplify: $\frac{(2.39)^2 - (1.61)^2}{2.39 - 1.61}$
- Simplify: $\frac{3x + 3y + x^2 - y^2}{x + y}$
- If $a+b+c=0$, then the value of $\left(\frac{a+b}{c} + \frac{b+c}{a} + \frac{c+a}{b}\right)\left(\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}\right)$ is:
- The sum of two numbers is $37$ and the difference of their squares is $185$. The difference of the two numbers is:
- The sum of the squares of two numbers is 97 and the square of their difference is 25. The product of the two numbers is:
- If $a * b = a + b + ab$, then $3 * 4 - 2 * 3$ is equal to?
- What is the simplified result of the expression: $\frac{X+1}{7} - \frac{X-1}{8}$?
- $x(yz) - (xy)z$ is a representation of the:
- Amy buys $d$ dollars worth of groceries each week and spends one-fourth of those dollars on fruit. In terms of $d$, how many weeks will it take Amy to spend a total of $100$ just on fruit?
- The value of $\left(1+\frac{1}{x}\right)\left(1+\frac{1}{x+1}\right)\left(1+\frac{1}{x+2}\right)\left(1+\frac{1}{x+3}\right)$ is equal to:
- An internet service provider charges a one-time setup fee of $\$100$ and $\$50$ each month for service. If $c$ customers join at the same time and are on the service for $m$ months, which of the following expressions represents the total amount, in dollars, the provider has charged these customers?
- The sum of two numbers is $10$, and their product is $20$. What is the sum of their reciprocals?
- If $T^3 - 3T + 1 = 0$, find $T^3 + \frac{1}{T^3}$.
- In the equation $\frac{12x^2 + mx + 23}{2x + 1} = 6x - 18 + \frac{41}{2x + 1}$, where $m$ is a constant and $x \neq -\frac{1}{2}$, what is the value of $m$?
- A carpenter lays $x$ bricks per hour for $y$ hours and then lays $\frac{x}{2}$ bricks per hour for $2y$ more hours. In terms of $x$ and $y$, how many bricks did he lay in total?
Linear Equations
- If $(7x - 1) = (4x + 8)$, what is the value of $x$?
- In the system of equations above, $ax + 2y = 5$ and $3x - 6y = 20$, $a$ is a constant. If the system has one solution, which of the following CANNOT be the value of $a$?
- The sum of five consecutive even numbers of set $x$ is $440$. Find the sum of a different set of five consecutive integers whose second least number is $121$ less than double the least number of set $x$.
- The numerator of a fraction is 5 less than the denominator. If 1 is added to both the numerator and the denominator, the fraction becomes $\frac{2}{3}$. Find the fraction.
- The numerator of a fraction is 5 less than the denominator. If 1 is added to both the numerator and the denominator, the fraction becomes $\frac{2}{3}$. What is the original fraction?
- If the sum of two numbers is $30$ and their difference is $8$, what is their product?
- If $k \leq x \leq 3k + 12$, which of the following must be true? I. $x - 12 \leq 3k$ II. $k \geq -6$ III. $x - k \geq 0$
- The sum of two numbers is $25$, and their difference is $13$. What is the product of the two numbers?
- The sum of two numbers, if one number is two-third of the second, is equal to 45. Find the smaller number.
- Jerry estimates that there are $m$ marbles in a jar. Harry, who knows the actual number of marbles in the jar, notes that the actual number, $n$, is within 10 marbles (inclusive) of Jerry's estimate. Which of the following inequalities represents the relationship between Jerry's estimate and the actual number of marbles in the jar?
- Solve: $3(x - 1) = -6$
- Two numbers whose sum is 67 and difference is 3, the numbers are?
- A 3-digit number is reversed, and the new number is 297 greater than the original. The sum of the first and third digits is 7. What is the product of the first and third digits?
- If $4x + 13 = 7 - 2x$, what is the value of $x$?
- What is the value of $x$ in the equation: $4 - 3x = 8 - x$?
- A fraction becomes $\frac{4}{5}$ when 1 is added to each of the numerator and denominator. However, if we subtract 5 from each, then it becomes $\frac{1}{2}$. The fraction is?
- The numerator of a fraction is 4 less than its denominator. If 1 is added to both its numerator and denominator, the fraction becomes $\frac{1}{2}$. Find the fraction.
- Three-fourths of a number is 60 more than its one-third. The number is:
- A and B have the same amount of money at first. After A gives B $50, B has 5 times as much money as A has left. How much do A and B each have at first?
- If $A + B = 12$ and $A + B + C = 8$, then find the value of $C$.
- If $2a - 2 = 20$, then what is the value of $a$?
- If $4x + y = 3x + 5y$, find $\frac{3x}{16y}$.
- Three times the first of three consecutive odd integers is $3$ more than twice the third. What is the third integer?
- For the system of equations $3x + 2y = 7$ and $6x + my = 14$, the system has infinitely many solutions when $m =$ ?
- A certain two-digit number is three times the sum of its digits. If 45 is added to the number, the digits are reversed. The number is:
- Pair of equations $y = 2$ and $y = -5$ has?
- Solve for $x$ in the equation $3889 + 12.950 - x = 47.97$. What is the value of $x$?
- If $6n + 5$, what is the value of $n$?
- If $6 + 5x = 30 - x$, then $x =$ ?
- The fuel after the 4th lap is 22 liters and it is 18 liters after the 7th lap. How many laps are made at the end when the fuel runs out?
- Verification refers to:
- If there are 27 students in a class and the number of girls is 7 more than the number of boys, how many total girls are in the class?
- The total cost of placing an advertisement in a newspaper comprises a fixed cost of $3.50 and a variable cost that depends on the number of words. Each word costs 25 cents. Find the total cost of placing an advertisement containing 22 words.
- Aaron has 3 times as much money as Josh. If Aaron gives Josh $50, Josh will then have 3 times as much money as Aaron. How much money do the two of them have together?
- If $|n - 2| = 10$, what is the sum of the two possible values of $n$?
- If $54$ is subtracted from $3$ times a certain number, the result is $36$. Find the number.
- What is the value of $x$ in the equation $\frac{x}{5} - \frac{3x}{2} = 7 + \frac{x}{2}$?
Quadratic Equations
- If a number is multiplied by three-fourths of itself, the result is 10700. What is the number?
- If the sum of the ages of two children is $12$ years and their product is $32$, which one is the elder?
- The sum of the reciprocals of A's ages (in years) 2 years ago and 2 years from now is $\frac{1}{3}$. The present age of A is:
- If a number is multiplied by two-third of itself, the value so obtained is 864. What is the number?
- The sum of the squares of two positive integers is $100$ and the difference of their squares is $28$. What is the sum of the numbers?
- The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:
- If one factor of the quadratic equation $x^2 - 3x - 10 = 0$ is $(x - 5)$, what is the other factor?
- If the sum of the roots of a quadratic equation is $-2$ and the product of the roots is $3$, find the quadratic equation.
- Solve the equation: $2x^2 + 5x - 12 = 0$. Find the value of $x$.
- If $2x^2 - 3x - 2 = 0$, then $x = ?$
- A positive number when decreased by 4 is equal to 21 times the reciprocal of the number. The number is?
- Solve: $x^2 + 18x + 81 = 0$. What is the factor form?
Exponents and Powers
- Convert into radical form: $X^{\frac{2a}{b}}$ is
- If $3^{(x+3)} + 7 = 250$, then $x$ is equal to?
- If $1 < x < 2$, then the value of $\sqrt{(x - 1)^2} + \sqrt{(3 - x)^2}$ is:
- If $\left(\frac{3}{5}\right)^3 \times \left(\frac{3}{5}\right)^{-6} = \left(\frac{3}{5}\right)^{2x-1}$, what is the value of $x$?
- If $n$ is a natural number, then $9^{2n} - 4^{2n}$ is always divisible by:
- Given that $10^{0.48} = x$, $10^{0.70} = y$ and $x^z = y^2$, then the value of $z$ is closest to _?
- If $\sqrt{t} = \frac{1}{2}$, evaluate $\sqrt{\frac{\log 2}{t^2}}$.
- Simplify: $(x^2)^2$
- If $y = \sqrt{\frac{64}{3x + 1}}$, find $x$ when $y = 4$.
- Simplify: $(m^{\frac{1}{3}} n^{-2})^{\frac{3}{5}}$
- Evaluate: $(-1)^{300}$
- If $a + b = -2$, then $(a + b)^3 =$
- The value of $(100)^{1.5}$ is?
- Find the value of $a$ if $11^a = 1331$
- Solve: $(0.49)^4 \times (0.343)^4 \div (0.2401)^4 = \left(\frac{70}{100}\right)^{?+3}$
- If $(7^a)(7^b) = (7^c)(7^d)$, what is $d$ in terms of $a$, $b$, and $c$?
- Which of the following is equal to $3.14 \times 10^6$?
- Solve for $x$: $4^{7} \times 4^{x} = 1$
- If $x = 0.5$ and $y = 0.2$, then the value of $\sqrt{0.6} \times (3y)^x$ is equal to?
- If $4^{4x+1} = \frac{1}{64}$, then the value of $x$ is?
- If the initial population of rats was 20 and grew to 25 after the second year, which of the following functions best models the population of rats $P$ with respect to the number of years $t$ if the population growth of rats is considered to be exponential?
- If $x$, $y$ are two positive real numbers and $x^{13} = y^{14}$, then which of the following relations is true?
- If $x = 7 - 4\sqrt{3}$, find $x + \frac{1}{x}$.
- If we multiply a fraction by itself and divide the product by its reciprocal, the fraction thus obtained is $18\frac{26}{27}$. What is the original fraction?
Logarithms
Sets & Functions
7 MCQsSets & Functions in Mathematics
Sets and Venn Diagrams
- In a class, $\frac{3}{4}$ of the students do not know either Hindi or English. $\frac{1}{6}$ of the students know English and $\frac{1}{8}$ of the students know Hindi. What part of the students know both English and Hindi?
- If the number of elements in set $A$ is $20$, in set $B$ is $30$, and the number of elements in the union of sets $A$ and $B$ is $40$, what is the number of elements in the intersection of sets $A$ and $B$?
- In an examination, $25\%$ candidates failed in Mathematics and $20\%$ students failed in English. If $5\%$ students failed in both the subjects, find the percentage of students who passed in both the subjects.
Geometry & Mensuration
71 MCQsGeometry & Mensuration in Mathematics
Lines and Angles
- Who is known as the Father of Geometry?
- The distance between two parallel lines is always:
- Sum of angles on a straight line is:
- The spacing between parallel lines remains _ throughout their length.
- Two angles that have a common vertex, a common arm, and no common interior points are known as _?
- The sum of adjacent angles on a straight line is?
Triangles
- The angle of elevation of a ladder leaning against a wall is $60^\circ$ and the foot of the ladder is $4.6$ m away from the wall. The length of the ladder is:
- The ratio of the length of a rod and its shadow is $1 : \sqrt{3}$. The angle of elevation of the sun is _?
- The angle of elevation of the top of a tower from a point 20 m away from its base is $45^\circ$. What is the height of the tower?
- A ladder makes an angle of $60^\circ$ with the ground when placed against a wall. If the foot of the ladder is $2$ m away from the wall, then the length of the ladder (in meters) is:
- The angle of elevation of a ladder leaning against a wall is $60^\circ$ and the foot of the ladder is $12.4$ m away from the wall. The length of the ladder is:
- If the angle of elevation of a tower from a distance of 100 metres from its foot is $60^\circ$, the height of the tower is _?
- The angle of depression of a point situated at a distance of $70$ m from the base of a tower is $60^\circ$. The height of the tower is:
- If the height of a triangle is 4 cm less than its base, and the hypotenuse is 10 cm, find the other two sides.
- A ladder is placed against a wall such that its foot is at a distance of $2.5$ m from the wall and its top reaches a window $6$ m above the ground. Find the length of the ladder.
- A ladder makes an angle of $45^\circ$ with the ground when placed against a wall. If the foot of the ladder is $5$ m away from the wall, then the height of the wall is:
- The angles of a triangle are $(x-35)^\circ$, $(x-25)^\circ$, and $\left(\frac{1}{2}x - 10\right)^\circ$. Find the value of $x$.
- The angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree, is?
Quadrilaterals and Polygons
Circles
- How many tangents can be drawn to a circle?
- What is the angle of a semi-circle?
- If the circumference of a circle is equal to the perimeter of a square, then the area of the circle is:
- Find the area of a circle whose circumference is $31.4$ centimeters.
- If the area of a circle is $38.5 \text{ m}^2$, then its circumference will be _?
- If the tire of a car makes 4000 revolutions to cover 8 km, what is the diameter of the tire?
- Find the circumference of a circle with radius $r = 8$ units. (Use $\pi \approx 3.14$)
- Find the circumference of a circle whose radius is $8$ cm. (Take $\pi = 3.14$)
- The area of a circle is $98.56 \text{ cm}^2$. Find its circumference.
- The radius of a circle is $10$ cm and the length of one of its chords is $12$ cm. Find the distance of the chord from the center.
- If the radius of a circle is increased to twice its original length, how much will the area of the circle increase?
- The diameter of a round table is 7 meters. How much distance will a person walk around it?
Area, Perimeter and Volume
- The radius of a circle is $1$ cm. Find its area.
- If the volumes of two cubes are in the ratio $8:1$, then the ratio of their edges is
- The area of a triangle is $126$ square units and its base is $28$ units. Find the height of the triangle.
- The perimeter of a square is $256$ cm. Find the length of its side.
- A cube is painted on all its faces. If the total painted surface area of the cube is $96 \text{ cm}^2$, what is the side length of the cube?
- If a rectangle's length is $6$ cm greater than its width and its perimeter is $48$ cm, find its width.
- If a sphere has a diameter of 12 cm, then the surface area of the sphere is?
- A cylinder has a base diameter of $8$ cm and height equal to half of its radius. Find its volume.
- The length and breadth of the floor of a room are $20$ feet and $10$ feet respectively. Square tiles of $2$ feet length of different colours are to be laid on the floor. Black tiles are laid in the first row on all sides. If white tiles are laid on one-third of the remaining area and blue tiles on the rest, how many blue tiles will be there?
- A square of area $64\,\text{m}^2$ is made of wire. The wire is then bent to form a circle. Find the area of the circle.
- Find the perimeter of a square if its area is $256 \text{ cm}^2$.
- A rectangular lawn $80$ meters by $60$ meters has two roads each $10$ m wide running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling them at Rs. $30$ per square meter.
- A mason fixed black tiles of square shape around a square room. There are 21 tiles on each side of the room. How many tiles did he need altogether?
- Total surface area of a sphere of radius $3$ cm is?
- If a square has a side length of $5$ cm, what is its area?
- What is the cost of fencing a square park with a side of $50$ meters at the rate of Rs. $8$ per meter?
- A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm³, then the weight of the pipe is:
- The volume of a cone is $245\pi$ cm$^3$ and its radius is $7$ cm. Find the height of the cone.
- If the volume and surface area of a sphere are numerically equal, what is its radius?
- The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length is 2.5 m and its depth is 10 m.
- Find the volume of a cylinder if the radius is $4$ cm and the height is $10$ cm.
- How many sides does a prism have?
- What is the height of a parallelogram with an area of $54\,\text{cm}^2$ and a base of $15\,\text{cm}$?
- How many cubes of side $1$ cm can be cut from a cuboid having dimensions $10 \times 12 \times 15$ cm?
- 16 hemispheres of radius $2$ cm are melted to make a single sphere. Find the radius of the sphere.
- The size of a single tile is $2 \times 2$ feet. How many tiles are required to fill a $17 \times 12$ feet floor?
- An open rectangular tank that is $4$ m long, $2$ m wide, and $4.8$ m high, is initially three-quarters filled with water. Find the depth of water in the tank after $4000$ liters of water are added to it.
- What is the area of a rectangle with a length of $7$ cm and a width of $2$ cm?
- What is the radius of a basketball whose volume is $6400 \text{ cm}^3$? (Use $\pi = 3.14$)
- An open rectangular tank that is $4$ m long, $2$ m wide, and $4.8$ m tall is initially three-quarters filled with water. What is the depth of water in the tank after $4{,}000$ litres of water are added to it?
- If sin x = 15/17, then cos x equals?
Coordinate Geometry
- The distance of the point $P(2,3)$ from the X-axis is _?
- In the $xy$-plane, points $(-3,5)$ and $(6,8)$ lie on line $l$. Which of the following points is also on line $l$?
- The perimeter of the triangle with vertices $(0,4)$, $(0,0)$, and $(3,0)$ is:
- If point $A$ is $(4, -1)$ and point $B$ is $(3, 5)$, what is the square of the distance $AB^2$ between them?
- The point $(0, -7)$ lies in which quadrant?
- Two perpendicular lines are given by the equations $y = \frac{a}{b}x + c$ and $y = \frac{d}{e}x + c$, where $a, b, c, d, e$ are constants. If $0 < \frac{a}{b} < 1$, which of the following must be true?
- Distance of point $(-6, 8)$ from the $x$-axis is:
- What is the distance of the point $(-6, 8)$ from the origin?
- If $ABCD$ is a square where $A(2,3)$, $B(6,7)$, $C(10,1)$, then $D = ?$
Statistics & Probability
14 MCQsStatistics & Probability in Mathematics
Mean, Median, and Mode
Permutations & Combinations
- The letters of the word SAP taken all at a time can be arranged in how many ways?
- $\frac{10!}{7!} = ?$
- In how many ways can 2 students be chosen from a class of 20 students?
- Find the number of triangles which can be formed by joining the angular points of a polygon of 8 sides as vertices.
- What is the number of ways that 4 boys and 3 girls can be seated in a row so that boys and girls alternate?
- In how many ways can a President, Vice President, and Water-boy be selected from a group of 10 people?
Probability
Data Interpretation (Tables, Graphs)
Series, Patterns & Logical Reasoning
32 MCQsSeries, Patterns & Logical Reasoning in Mathematics
Number Series
- Which one is odd in the sequence: $19, 26, 33, 40, 47, 53$?
- Complete the number series: $7, 6, 5, 9, 3, 12, 1, 15, \_\_\_\_\_\_\_?$
- What number should come next in the series: $14, 28, 20, 40, 32, 64, ?$
- Which term of the AP $2, 11, 20, 29, \dots$ is $290$?
- The prize money of Rs. 60,000 will be distributed among eight teams according to their positions determined in a match series. The award increases by the same amount for each higher position. If the last place team is given Rs. 4,000, how much is awarded to the first place team?
- If $a_{n-3} = 2n - 5$, then its $n$th term is:
- How many terms are there in the sequence $20, 25, 30, \dots, 140$?
- What comes next in the following series? $64, 48, 40, 36, 34, \_\_\_\_\_\_$
- Find the missing number in the series: $6$, $?$, $21$, $33$, $48$.
- What is the missing figure in the series? $48, 45, 40, 33, 24, \_\_\_\_\_$?
- Which number will come next in the series? $3, 5, 7, 10, 12, 14, 24, 26, \_\_\_\_?$
- Find the 15th term of the arithmetic progression: $12, 9, 6, \dots$
- Find the value of $x_{11}$ in the sequence defined by $x_n = 4n + 3$.
- What is the next term in the sequence: $2, 1, 3, 4, 7, 11, \_\_\_$?
- Complete the sequence: $2, 6, 18, \_\_\_\_, 486$. Find the 4th term from the last?
- There are 12 numbers between $A$ and $B$. All these numbers are multiples of $6$. The first number after $A$ is $18$. Find the value of $B$.
- Find the 15th term of the sequence: $12, 9, 6, \_\_\_\_\_\_$?
- $12 : 68 :: 30 : ?$
- What is the next number in the sequence $1, 1, 2, 6, 24$?
- Complete the number series: $6, 9, 18, 45, 126, ?$
- Find the value of $x$ in the series: $x, 9, 25, 48, 81, 121$
- Complete the series: $2, 4, 12, 48, 240, \_\_\_\_\_?$
- What is the 101st term of the sequence: $1, 4, 7, 10, \dots$ ?
- Considering the following pattern: $2^2 + 1 = 5$, $3^2 + 1 = 10$, $4^2 + 1 = 17$, $5^2 + 1 = 26$, … The 8th line in the pattern is:
- What is the sum of the first 1000 positive integers?
- Which of the following numbers in the sequence is wrong? $$140, 340, 540, 730, 940, 1140$$
- The next number in the series is $\frac{1}{5}, \frac{1}{9}, \frac{1}{13}, \frac{1}{17}, \_\_\_?$
- Find the odd one out: $140, 340, 540, 730, 940, 1140$
- If an object falls 27 m and rebounds two-thirds of the distance each time, what is the total distance traveled before it comes to rest?