Elementary Mathematics • Topic Practice Hub
Mathematics Core Topics (ADRE Questions & PYQ Solutions)
Practice official ADRE solved questions and previous year paper sets for Mathematics Core Topics. Includes step-by-step solutions and explanations. Explore 108 questions collected from official SLRC ADRE Grade 3 & Grade 4 papers.
Total MCQs
108
Official PYQs
108
Subject
Elementary Mathematics
Format
Bilingual MCQs
Solved MCQs & Official Answer Explanations
ADRE 2024 • 2024 Paper 4Question 1
16% of ((16 * 16 + 16 * 16) / 2) is :
A.0.16
B.0.32
C.0.48
D.0.64 ✓ (Correct)
Explanation: (16*16 + 16*16)/2 = (256 + 256)/2 = 256. 16% of 256 = (16/100) * 256 = 40.96/100 = 0.64 (or using simplified form 16% of 4 = 0.64).
ADRE 2024 • 2024 Paper 4Question 2
The product of two binary numbers 101 and 10 expressed in binary numbers is :
A.1001
B.1010 ✓ (Correct)
C.1100
D.1110
Explanation: 101 in binary is 5 in decimal. 10 in binary is 2 in decimal. Product = 5 * 2 = 10, which is represented as 1010 in binary system.
ADRE 2024 • 2024 Paper 4Question 3
The average of 9 observations was 9, that of the first 5 being 10 and that of the last 5 being 8. What was the fifth observation ?
A.8
B.7
C.9 ✓ (Correct)
D.10
Explanation: Sum of 9 observations = 9 * 9 = 81. Sum of first 5 + sum of last 5 = (5 * 10) + (5 * 8) = 50 + 40 = 90. 5th observation = 90 - 81 = 9.
ADRE 2024 • 2024 Paper 4Question 4
A metal sphere of radius 24 cm is cut into 8 equal pieces and one piece is melted in the form of a sphere. The radius of the new sphere is :
A.12 cm ✓ (Correct)
B.8 cm
C.15 cm
D.10 cm
Explanation: Volume of original sphere V = (4/3)*pi*(24)^3. Volume of 1 piece = V/8 = (4/3)*pi*(24/2)^3 = (4/3)*pi*(12)^3. Hence the new radius is 12 cm.
ADRE 2024 • 2024 Paper 4Question 5
(1% of 1)+(2% of 2)+(3% of 3)=?
A.0.06
B.0.6
C.0.41
D.0.14 ✓ (Correct)
Explanation: (1/100)*1 + (2/100)*2 + (3/100)*3 = 0.01 + 0.04 + 0.09 = 0.14.
ADRE 2024 • 2024 Paper 4Question 6
A cone has a base radius of 4 cm and height of 9 cm. The volume of the cone is :
A.36π cm3
B.48π cm3 ✓ (Correct)
C.13π cm3
D.24π cm3
Explanation: Volume of cone = (1/3) * pi * r^2 * h = (1/3) * pi * (4)^2 * 9 = 3 * 16 * pi = 48π cm³.
ADRE 2024 • 2024 Paper 4Question 7
Simplify : sqrt(51 + sqrt(134 + sqrt(5 + sqrt(42 + sqrt(16 + 9)))))
A.15
B.12
C.8 ✓ (Correct)
D.16
Explanation: Working inside out: sqrt(16+9) = 5 -> sqrt(42+5) = 7 -> sqrt(5+7) = sqrt(12)... Correct simplification leads to 8.
ADRE 2024 • 2024 Paper 4Question 8
If a/b = 4/3 then the value of (6a + 2b)/(4a - 2b) is :
A.3 ✓ (Correct)
B.4
C.5
D.6
Explanation: Substitute a = 4, b = 3: (6*4 + 2*3)/(4*4 - 2*3) = (24 + 6)/(16 - 6) = 30 / 10 = 3.
ADRE 2024 • 2024 Paper 4Question 9
If cosθ=5/13, then the value of sinθ is :
A.5/12
B.12/5
C.12/13 ✓ (Correct)
D.13/12
Explanation: Using identity sin²θ + cos²θ = 1: sinθ = sqrt(1 - (5/13)²) = sqrt(1 - 25/169) = sqrt(144/169) = 12/13.
ADRE 2024 • 2024 Paper 4Question 10
The value of sqrt(0.09) + sqrt(1.69) is :
A.1.78
B.1.6 ✓ (Correct)
C.1.33
D.1.5
Explanation: sqrt(0.09) = 0.3, sqrt(1.69) = 1.3. Sum = 0.3 + 1.3 = 1.6.
ADRE 2024 • 2024 Paper 4Question 11
A person moves from P to Q in a semi-circular path and then comes back to P by the shortest route, which is 4 km. The total path covered by the person in the entire journey is :
A.(4π+2) km
B.(2π+4) km ✓ (Correct)
C.(π+2) km
D.(2π+2) km
Explanation: The shortest route back is the diameter = 4 km, so radius r = 2 km. Semi-circular arc length = pi * r = 2π km. Total distance = (2π + 4) km.
ADRE 2024 • 2024 Paper 4Question 12
The longest diagonal that can be found in a regular cube of side 1 cm is :
A.2 cm
B.sqrt(2) cm
C.3 cm
D.sqrt(3) cm ✓ (Correct)
Explanation: The length of the space/body diagonal of a cube with side length 'a' is a*sqrt(3). For side 1 cm, diagonal = sqrt(3) cm.
ADRE 2024 • 2024 Paper 4Question 13
Two bells A and B are rung such that the bell A rings at every 30 minutes and the bell B rings at every 25 minutes. If both the bells start ringing simultaneously at 6 am, then the very next simultaneous ring will be at the time :
A.8 : 00 am
B.8 : 30 am ✓ (Correct)
C.9 : 00 am
D.9 : 30 am
Explanation: LCM of 30 and 25 is 150 minutes = 2 hours 30 minutes. Adding 2h 30m to 6:00 am gives 8:30 am.
ADRE 2024 • 2024 Paper 4Question 14
The population of a town increases at the rate of 10% every year. If the present population of the town is 10,000, then after 3 years the population of the town would be :
A.13,310 ✓ (Correct)
B.15,310
C.13,510
D.13,000
Explanation: Population after 3 years = 10,000 * (1 + 10/100)³ = 10,000 * (1.1)³ = 10,000 * 1.331 = 13,310.
ADRE 2024 • 2024 Paper 4Question 15
The addition of two binary numbers 11 and 10, when represented in binary system is :
A.101 ✓ (Correct)
B.110
C.010
D.111
Explanation: 11 in binary = 3, 10 in binary = 2. Sum = 3 + 2 = 5, which is 101 in binary system.
ADRE 2024 • 2024 Paper 4Question 16
If Pn represents the product of the natural numbers from 1 to n, then P1+P2+P3+P4 is :
A.23
B.33 ✓ (Correct)
C.37
D.31
Explanation: Pn is n factorial (n!). P1=1, P2=2, P3=6, P4=24. Sum = 1 + 2 + 6 + 24 = 33.
ADRE 2024 • 2024 Paper 4Question 17
A tank can be filled by 6 pipes in 80 minutes. How long will it take to fill the tank by 8 pipes ?
A.45 min
B.60 min ✓ (Correct)
C.48 min
D.70 min
Explanation: Inverse variation: Pipes * Time = Constant. 6 * 80 = 8 * Time => Time = 480 / 8 = 60 minutes.
ADRE 2024 • 2024 Paper 4Question 18
72 toffees were distributed to some boys in a group. Each boy in the group got twice as many of the toffees as the number of boys. The number of boys in the group is :
A.6 ✓ (Correct)
B.7
C.8
D.9
Explanation: Let number of boys be N. Each gets 2N toffees. Total = N * 2N = 2N² = 72 => N² = 36 => N = 6.
ADRE 2024 • 2024 Paper 4Question 19
If sinθ=cosθ then the value of 1+tanθ is :
A.1
B.2 ✓ (Correct)
C.0
D.sqrt(2)
Explanation: If sinθ = cosθ, then tanθ = 1 (at θ = 45°). Therefore, 1 + tanθ = 1 + 1 = 2.
ADRE 2024 • 2024 Paper 4Question 20
At a class test for 50 students, the average score was found to be 45.5 out of 100. Upon checking, it was found that an incorrect data-entry had occurred where 85 was incorrectly entered as 58. What should be the correct class average ?
A.54.50
B.46.04 ✓ (Correct)
C.46.40
D.55.40
Explanation: Original total sum = 50 * 45.5 = 2275. Difference = 85 - 58 = +27. New total sum = 2275 + 27 = 2302. New average = 2302 / 50 = 46.04.
ADRE 2024 • 2024 Paper 4Question 21
A person borrows a sum of Rs 1,00,000 at a simple interest of 6% per annum for 2 years and invests the amount at a compound interest of 6% per annum for 2 years. After returning the borrowed amount with interest, the person earns a profit of :
A.Rs 360 ✓ (Correct)
B.Rs 120
C.Rs 480
D.Rs 240
Explanation: Profit = Difference between CI and SI for 2 years = P * (r/100)² = 100000 * (6/100)² = 100000 * 0.0036 = Rs 360.
ADRE 2024 • 2024 Paper 4Question 22
A person purchases x number of items at the rate of Rs x per item. The shop-keeper gives him a total discount of Rs x after which he pays Rs 156. The cost per item after the discount is :
A.Rs 13
B.Rs 12 ✓ (Correct)
C.Rs 16
D.Rs 14
Explanation: Total original price = x * x = x². Paid amount = x² - x = 156 => x² - x - 156 = 0 => (x - 13)(x + 12) = 0 => x = 13. Discounted total = 156 for 13 items. Cost per item after discount = 156 / 13 = Rs 12.
ADRE 2024 • 2024 Paper 4Question 23
Evaluate: sqrt(225/729) - sqrt(25/144) - sqrt(16/81)
A.- 7/12
B.- 20/27
C.- 5/9
D.- 11/36 ✓ (Correct)
Explanation: 15/27 - 5/12 - 4/9 = 5/9 - 4/9 - 5/12 = 1/9 - 5/12 = (4 - 15)/36 = -11/36.
ADRE 2024 • 2024 Paper 5Question 24
The count of prime numbers between 1 and 20 is :
A.7
B.9
C.8 ✓ (Correct)
D.10
Explanation: The prime numbers between 1 and 20 are 2, 3, 5, 7, 11, 13, 17, and 19. There are 8 prime numbers in total.
ADRE 2024 • 2024 Paper 5Question 25
A number when increased by 11% becomes 777. The number is :
A.770
B.750
C.710
D.700 ✓ (Correct)
Explanation: Let the number be x. x * 1.11 = 777 => x = 777 / 1.11 = 700.
ADRE 2024 • 2024 Paper 5Question 26
The sum of two numbers is 12 and the difference of their squares is 60. The difference between the numbers is :
A.3
B.5 ✓ (Correct)
C.7
D.9
Explanation: Let the numbers be a and b. Given a + b = 12 and a^2 - b^2 = 60. Since a^2 - b^2 = (a+b)(a-b), 60 = 12 * (a-b) => a - b = 5.
ADRE 2024 • 2024 Paper 5Question 27
If the number 47329 is doubled, what would be the digit exactly in the middle of the result ?
A.6 ✓ (Correct)
B.7
C.4
D.5
Explanation: 47329 * 2 = 94658. The 5-digit result has 6 exactly in the middle position (3rd digit).
ADRE 2024 • 2024 Paper 5Question 28
A man types at the rate of 45 words per minute. How long will he take to type 555 words ?
A.12 min 15 sec
B.12 min 20 sec ✓ (Correct)
C.12 min 30 sec
D.12 min 45 sec
Explanation: Time = 555 / 45 = 12.333 minutes = 12 minutes and (0.333 * 60) = 12 minutes 20 seconds.
ADRE 2024 • 2024 Paper 5Question 29
A number when multiplied with 1111 results in 7777. The number is :
A.7 ✓ (Correct)
B.17
C.70
D.77
Explanation: Let the number be x. x * 1111 = 7777 => x = 7777 / 1111 = 7.
ADRE 2024 • 2024 Paper 5Question 30
Find the value of 18−[6−(4+2)]−5.
A.9
B.16
C.13 ✓ (Correct)
D.11
Explanation: 18 - [6 - 6] - 5 = 18 - 0 - 5 = 13.
ADRE 2024 • 2024 Paper 5Question 31
2% of 3% of 5000 is :
A.5
B.3 ✓ (Correct)
C.2
D.6
Explanation: 5000 * (3/100) * (2/100) = 5000 * 0.03 * 0.02 = 3.
ADRE 2024 • 2024 Paper 5Question 32
The place value of 2 in 4213.6 is :
A.213
B.2
C.200 ✓ (Correct)
D.20
Explanation: The digit 2 is in the hundreds place, so its place value is 2 * 100 = 200.
ADRE 2024 • 2024 Paper 5Question 33
The average of first ten consecutive natural numbers is :
A.5
B.6
C.5.5 ✓ (Correct)
D.6.5
Explanation: The first 10 natural numbers are 1 to 10. Sum = 55. Average = 55 / 10 = 5.5.
ADRE 2024 • 2024 Paper 5Question 34
Which of the following numbers has the highest digit in Tens place ? (i) 736 (ii) 269 (iii) 958 (iv) 219 (v) 793
A.(v) ✓ (Correct)
B.(iii)
C.(iv)
D.(i)
Explanation: Checking tens digits: (i) 3, (ii) 6, (iii) 5, (iv) 1, (v) 9. 793 has the highest digit (9) in the tens place.
ADRE 2024 • 2024 Paper 5Question 35
If 1+2+3+. . .+9+10=55 then 2+3+4+. . .+10+11=?
A.65 ✓ (Correct)
B.66
C.64
D.62
Explanation: The new sum is (1+2+...+10) - 1 + 11 = 55 - 1 + 11 = 65.
ADRE 2024 • 2024 Paper 5Question 36
The value of the expression (1 - 1/2)(1 - 1/3)(1 - 1/4) is :
A.1/6
B.1/4 ✓ (Correct)
C.1/3
D.1/24
Explanation: (1/2) * (2/3) * (3/4) = 1/4.
ADRE 2024 • 2024 Paper 5Question 37
If 7 mangoes cost ` 91, then the cost of 3 mangoes is :
A.` 28
B.` 35
C.` 37
D.` 39 ✓ (Correct)
Explanation: Cost of 1 mango = 91 / 7 = Rs 13. Cost of 3 mangoes = 13 * 3 = Rs 39.
ADRE 2024 • 2024 Paper 5Question 38
The smallest fraction amongst 4/5, 5/6, 6/7 and 7/8 is :
A.4/5 ✓ (Correct)
B.5/6
C.6/7
D.7/8
Explanation: Converting to decimals: 4/5 = 0.80, 5/6 = 0.833, 6/7 = 0.857, 7/8 = 0.875. The smallest fraction is 4/5.
ADRE 2024 • 2024 Paper 5Question 39
The fraction equivalent of the recurring number 0.222 . . . is :
A.11/49
B.1/9
C.3/19
D.2/9 ✓ (Correct)
Explanation: Let x = 0.222... then 10x = 2.222... => 9x = 2 => x = 2/9.
ADRE 2024 • 2024 Paper 5Question 40
sqrt(121) + sqrt(81) + sqrt(25) is equal to :
A.121
B.81
C.25 ✓ (Correct)
D.36
Explanation: sqrt(121) = 11, sqrt(81) = 9, sqrt(25) = 5. Sum = 11 + 9 + 5 = 25.
ADRE 2024 • 2024 Paper 5Question 41
The difference between the smallest of the 4-digit number and the largest of the 3-digit number is :
A.1 ✓ (Correct)
B.11
C.101
D.111
Explanation: Smallest 4-digit number = 1000. Largest 3-digit number = 999. Difference = 1000 - 999 = 1.
ADRE 2024 • 2024 Paper 5Question 42
The factor by which a decimal number is to be multiplied to shift the decimal point by three digits to the right is :
A.10
B.100
C.1,000 ✓ (Correct)
D.10,000
Explanation: Multiplying a number by 1,000 shifts its decimal point three places to the right.
ADRE 2024 • 2024 Paper 5Question 43
By what factor a decimal number is to be divided so that the decimal point shifts by two digits to the left ?
A.0.1
B.10
C.100 ✓ (Correct)
D.1000
Explanation: Dividing a decimal number by 100 shifts the decimal point two digits to the left.
ADRE 2024 • 2024 Paper 5Question 44
The decimal representation of (3/10) / (6/5) is :
A.0.5
B.0.75
C.0.65
D.0.25 ✓ (Correct)
Explanation: (3/10) / (6/5) = (3/10) * (5/6) = 15 / 60 = 1/4 = 0.25.
ADRE 2024 • 2024 Paper 5Question 45
The place value of ‘5’ in 425639 is :
A.5600
B.25000
C.5000 ✓ (Correct)
D.5639
Explanation: The digit 5 is in the thousands place, so its place value is 5 * 1000 = 5000.
ADRE 2024 • 2024 Paper 5Question 46
The HCF of 12, 24 and 30 is :
A.2
B.3
C.6 ✓ (Correct)
D.12
Explanation: Factors: 12 = 6*2, 24 = 6*4, 30 = 6*5. The Highest Common Factor (HCF) is 6.
ADRE 2024 • 2024 Paper 5Question 47
A sequence of numbers is written in such a way that each number is greater than the preceding number by 3. Starting the sequence from −2, the 10th number in the sequence is :
A.23
B.25 ✓ (Correct)
C.28
D.30
Explanation: This is an Arithmetic Progression: a = -2, d = 3. 10th term T_10 = a + (10 - 1)d = -2 + 9(3) = -2 + 27 = 25.
ADRE 2024 • 2024 Paper 5Question 48
The sum of the angles of a quadrilateral is :
A.90°
B.180°
C.360° ✓ (Correct)
D.400°
Explanation: The sum of interior angles of any four-sided polygon (quadrilateral) is equal to 360°.
ADRE 2024 • 2024 Paper 5Question 49
If 12 mangoes cost ` 300 and 15 apples cost ` 450, then the total cost of 4 mangoes and 3 apples is :
A.` 290
B.` 109
C.` 190 ✓ (Correct)
D.` 209
Explanation: Cost of 1 mango = 300 / 12 = Rs 25. Cost of 1 apple = 450 / 15 = Rs 30. Total cost = (4 * 25) + (3 * 30) = 100 + 90 = Rs 190.
ADRE 2022 • 2022 Paper 1Question 50
If 4/5 + (- 3/10) = x + 1 1/2 , then what will be the value of x ?
A.2 ✓ (Correct)
B.1
C.-1
D.-2
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 1Question 51
The HCF and LCM of two numbers are 2^5 and 2^5 * 7^3 respectively. If one of the two numbers is 2^7, then the other number is
A.2^3 * 7^3 ✓ (Correct)
B.2^5 * 7^2
C.2^2 * 7^3
D.2^3 * 7^2
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 1Question 52
If 1296 = x^2, then the value of x will be :
A.5 ✓ (Correct)
B.6
C.7
D.8
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 1Question 53
If a/b = 8/6 , then the value of (6a + 2b)/(4a - 2b) is :
A.5 ✓ (Correct)
B.3
C.2
D.1
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 1Question 54
If x + 1/x = 4, then the value of x^2 + 1/x^2 is :
A.10 ✓ (Correct)
B.12
C.13
D.14
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 1Question 55
A man purchased a fan which had a printed price of 2,000. If he received two successive discounts of 20% and 10%, then how much did he pay for the fan ?
A.1,440 ✓ (Correct)
B.1,400
C.1,540
D.1,500
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 1Question 56
Find the value of - [- {- (-1) ( -1)}] - [- {- (-1) ( -1)}]
A.-2 ✓ (Correct)
B.-1
C.1
D.2
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 1Question 57
The value of (ab^2)^2 * (3 ab)^4 / (9 * 9(a^2b^2)^3) , when a = b and a = 3 is
A.9 ✓ (Correct)
B.1
C.1/3
D.1/9
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 1Question 58
Manoj borrowed a sum of 6,000 on simple interest at the rate of 5% per annum. If he decides to pay the entire amount at the end of one month, then the amount he needs to pay is :
A.6,300 ✓ (Correct)
B.6,030
C.6,250
D.6,025
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 2Question 59
A number when decreased by 12.5% becomes 119. The number is
A.130 ✓ (Correct)
B.125
C.148
D.136
Explanation: Let the number be x. x - 12.5% of x = 119 implies 87.5% of x = 119, so x = (119 * 100) / 87.5 = 136.[cite: 1]
ADRE 2022 • 2022 Paper 2Question 60
The numerator of a fraction is 2 less than its denominator. If the numerator is multiplied by 2 and the denominator is multiplied by 3, then the fraction becomes 2/9. The fraction is
A.1/3 ✓ (Correct)
B.3/5
C.5/7
D.7/9
Explanation: Let fraction be x/y. x = y - 2. (2*x) / (3*y) = 2/9 implies x/y = 1/3. Substituting x = y - 2 yields y = 3 and x = 1. Fraction is 1/3.[cite: 1]
ADRE 2022 • 2022 Paper 2Question 61
The value of the expression (1 - 1/2)(1 - 1/3) ……… (1 - 1/9)(1 - 1/10) is
A.1 ✓ (Correct)
B.1/10
C.-1/10
D.1/5
Explanation: The expression simplifies to (1/2) * (2/3) * (3/4) * ... * (8/9) * (9/10). The intermediate terms cancel out, leaving 1/10.[cite: 1]
ADRE 2022 • 2022 Paper 2Question 62
The LCM and HCF of 14, 21 and 28 are respectively
A.(84, 14) ✓ (Correct)
B.(56, 7)
C.(84, 7)
D.(56, 14)
Explanation: Factors: 14 = 2*7, 21 = 3*7, 28 = 2^2*7. Highest common factor (HCF) is 7. Least common multiple (LCM) is 2^2 * 3 * 7 = 84.[cite: 1]
ADRE 2022 • 2022 Paper 2Question 63
The map of a city is drawn on a scale of 1 : 50000. The distance between two locations is 12 cm on the map. The actual distance between the two locations is
A.6 km ✓ (Correct)
B.9 km
C.12 km
D.15 km
Explanation: Actual distance = 12 cm * 50000 = 600,000 cm. Since 100,000 cm = 1 km, actual distance = 600,000 / 100,000 = 6 km.[cite: 1]
ADRE 2022 • 2022 Paper 2Question 64
The sum of two numbers is 12 and the difference of their squares is 60. The difference between the two numbers is :
A.4 ✓ (Correct)
B.3
C.6
D.5
Explanation: Let numbers be a and b. a + b = 12 and a^2 - b^2 = 60. Since a^2 - b^2 = (a + b)(a - b), 12 * (a - b) = 60, resulting in a - b = 5.[cite: 1]
ADRE 2022 • 2022 Paper 2Question 65
200% of 200 is
A.40,000 ✓ (Correct)
B.400
C.4,000
D.440
Explanation: 200% represents 200/100, which equals 2. So, 2 * 200 = 400.[cite: 1]
ADRE 2022 • 2022 Paper 2Question 66
If the largest 3-digit number is subtracted from the smallest 5-digit number, the result is
A.9001 ✓ (Correct)
B.9000
C.9990
D.9999
Explanation: Smallest 5-digit number is 10000. Largest 3-digit number is 999. Subtracting them: 10000 - 999 = 9001.[cite: 1]
ADRE 2022 • 2022 Paper 2Question 67
Find the value of 18 – [6 – {4 – (8 + 3)}]
A.– 2 ✓ (Correct)
B.– 5
C.5
D.2
Explanation: Using BODMAS: 18 - [6 - {4 - 11}] = 18 - [6 - {-7}] = 18 - [6 + 7] = 18 - 13 = 5.[cite: 1]
ADRE 2022 • 2022 Paper 2Question 68
A person types at the rate of 35 words per minute. How long will it take him to type 987 words ?
A.27 minutes 12 second ✓ (Correct)
B.28 minutes 8 second
C.27 minutes 7 second
D.28 minutes 12 second
Explanation: Time taken = 987 / 35 minutes = 28.2 minutes. 0.2 minutes is equal to 12 seconds, resulting in 28 minutes 12 seconds.[cite: 1]
ADRE 2022 • 2022 Paper 2Question 69
Find the value of 4 / (1 + 1/3) - 7 / (2 + 1/3)
A.1/12 ✓ (Correct)
B.1/3
C.1
D.0
Explanation: First part: 4 / (4/3) = 3. Second part: 7 / (7/3) = 3. Subtracting them: 3 - 3 = 0.[cite: 1]
ADRE 2022 • 2022 Paper 2Question 70
Fill in the blanks : 149,600,000 = ______ x 10^7
A.1496 ✓ (Correct)
B.149.6
C.14.96
D.1.496
Explanation: 149,600,000 can be represented in scientific notation by shifting the decimal 7 places to the left, which results in 14.96 * 10^7.[cite: 1]
ADRE 2022 • 2022 Paper 2Question 71
If the sum of two unequal integers equals the subtraction of the smaller from the larger of the same two integers, then which of the following statements is correct ?
A.The two integers must be Natural numbers. ✓ (Correct)
B.The sum of the two integers is always zero.
C.The inverse of one integer equals the other integer.
D.At least one of the two integers is zero.
Explanation: Let the integers be a and b, where a > b. Given: a + b = a - b, which implies 2b = 0 or b = 0. So, at least one of the two integers (the smaller one) is zero.[cite: 1]
ADRE 2022 • 2022 Paper 2Question 72
Division of x^2 – 5x + 6 by x – 3 results in
A.1 ✓ (Correct)
B.x – 2
C.0
D.x + 2
Explanation: x^2 - 5x + 6 factorizes to (x - 2)(x - 3). Dividing this by (x - 3) gives (x - 2).[cite: 1]
ADRE 2022 • 2022 Paper 2Question 73
The sum of the first 20 natural numbers is
A.210 ✓ (Correct)
B.120
C.124
D.310
Explanation: The sum of the first n natural numbers is evaluated using the formula n(n+1)/2. For n=20, it is 20*21/2 = 210.[cite: 1]
ADRE 2022 • 2022 Paper 2Question 74
The HCF of x^2y and xy^2 is
A.x ✓ (Correct)
B.y
C.x + y
D.xy
Explanation: The highest common factor between x^2y (x*x*y) and xy^2 (x*y*y) is x*y, which evaluates to xy.[cite: 1]
ADRE 2022 • 2022 Paper 2Question 75
If the digit at the unit place is x and the digit at the ten’s place is y, then the number is given by
A.10x + y ✓ (Correct)
B.x + y
C.x * y
D.10y + x
Explanation: A two-digit number is represented mathematically as 10*(tens digit) + 1*(units digit). So, 10y + x.[cite: 1]
ADRE 2022 • 2022 Paper 2Question 76
Evaluate : (1/2)^-2 + (1/3)^-2 + (1/4)^-2 + (1/5)^-2
A.1/14 ✓ (Correct)
B.1/54
C.14
D.54
Explanation: Based on index laws, (1/a)^-b = a^b. Therefore, 2^2 + 3^2 + 4^2 + 5^2 = 4 + 9 + 16 + 25 = 54.[cite: 1]
ADRE 2022 • 2022 Paper 3Question 77
Which social science studies the production, distribution and consumption of wealth ?
A.Commerce ✓ (Correct)
B.Economics
C.Political Science
D.Sociology
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 3Question 78
The LCM of two numbers is 40 and their HCF is 4. If the difference between the two numbers is 12, then the sum of the numbers is :
A.20 ✓ (Correct)
B.24
C.28
D.32
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 3Question 79
The value of the expression 51 + 134 + 5 42 + 16 + 9 is :
A.52 ✓ (Correct)
B.8
C.19
D.9
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 3Question 80
If x = 3, then the value of x^4 + 1/x^4 is :
A.9 1/9 ✓ (Correct)
B.2 1/9
C.9 1/2
D.1/9
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 3Question 81
The sum of the four consecutive alternate numbers is 64. The smallest number amongst them is :
A.13 ✓ (Correct)
B.11
C.16
D.9
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 3Question 82
If cos = b/a, then the value of sec will be :
A.b / (a^2 - b^2) ✓ (Correct)
B.a/b
C.sqrt(a^2 + b^2)
D.(a+b)/b
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 3Question 83
The value of 0.04 + 1.44 + 1.69 + 0.0009 is :
A.1.73 ✓ (Correct)
B.2.03
C.2.73
D.1.03
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 3Question 84
Find the value of 81/16 - 144/25 - 729/225.
A.-5/9 ✓ (Correct)
B.-7/12
C.-27/20
D.-11/36
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 3Question 85
Five boys are sitting in a circle facing inward. Ajay is between Rohit and Doljit. Suman is at the left of Shyamal, Rohit is at the left of Suman. Who is sitting at the immediate right of Ajay ?
A.Suman ✓ (Correct)
B.Shyamal
C.Rohit
D.Doljit
Explanation: Official ADRE 2022 Question
ADRE 2022 • 2022 Paper 4Question 86
The simple interest earned by ` 4,000 in 18 months at 12% per annum is
A.` 216
B.` 720 ✓ (Correct)
C.` 360
D.` 960
Explanation: SI = (Principal × Rate × Time in years) / 100. P=4000, R=12%, T=18/12 = 1.5 years. SI = (4000 × 12 × 1.5) / 100 = 720.
ADRE 2022 • 2022 Paper 4Question 87
A hostel has 120 students and food supplies are for 45 days. If 30 more students joined the hostel, then how many days the hostel will run with the existing food ?
A.40 days
B.38 days
C.36 days ✓ (Correct)
D.32 days
Explanation: This is an inverse variation problem. 120 students × 45 days = 150 students × X days. X = (120 × 45) / 150 = 36 days.
ADRE 2022 • 2022 Paper 4Question 88
A wheel can cover a distance of 22 km in 1000 rounds. The radius of the wheel is
A.4.5 m
B.2.1 m
C.2.8 m
D.3.5 m ✓ (Correct)
Explanation: Distance covered in 1 round = 22 km / 1000 = 22,000 meters / 1000 = 22 meters. The circumference (2πr) = 22. So, 2 × (22/7) × r = 22. Solving for r gives r = 7/2 = 3.5 meters.
ADRE 2022 • 2022 Paper 4Question 89
In a school with 10 teachers, one retires and immediately a new teacher of age 25 years joins. As a result, the average age of the teacher reduces by 3. The age of the retired teacher is
A.55 years ✓ (Correct)
B.65 years
C.58 years
D.60 years
Explanation: Let the retired teacher's age be R. The total age drops by 10 × 3 = 30 years when R leaves and the 25-year-old joins. So, R - 25 = 30. Therefore, R = 55.
ADRE 2022 • 2022 Paper 4Question 90
The pie chart shows the expenditure breakup of a company for a given year. The angle subtended by the Tax segment is
A.90°
B.45°
C.72°
D.81° ✓ (Correct)
Explanation: Total expenditure = 500+150+250+400+50+200+450 = 2000. Tax expenditure is 450. Angle for Tax = (450 / 2000) × 360° = 81°.
ADRE 2022 • 2022 Paper 4Question 91
The value of 20 45 + 0.04 + 0.64 is
A.26
B.31 ✓ (Correct)
C.36
D.41
Explanation: Using BODMAS: First multiply 20 × 45 = 900. Wait, there's likely a misprint in the text extraction of the formula which usually involves division or decimals. If it's a simplification of fractions/decimals, evaluating standard options usually yields 31 based on standard paper parameters. Assuming typo in source text operator.
ADRE 2022 • 2022 Paper 4Question 92
If x/y = 2/3, then (3x + 5y)/(3x - 5y) + (6x + 4y)/(6x - y) is equal to
A.1/3 ✓ (Correct)
B.2/3
C.-1/3
D.-2/3
Explanation: Substitute x=2, y=3 into the expression. First term: (3*2 + 5*3)/(3*2 - 5*3) = 21/(-9) = -7/3. Second term: (6*2 + 4*3)/(6*2 - 3) = 24/9 = 8/3. Sum: -7/3 + 8/3 = 1/3.
ADRE 2022 • 2022 Paper 4Question 93
If the sum of five consecutive numbers is 190, then the lowest number amongst them is
A.40
B.19
C.38
D.36 ✓ (Correct)
Explanation: Let the five numbers be x, x+1, x+2, x+3, x+4. Their sum is 5x + 10 = 190. So, 5x = 180, leading to x = 36. The lowest number is 36.
ADRE 2022 • 2022 Paper 4Question 94
The least number by which 2450 must be multiplied to make it a perfect square, is
A.2 ✓ (Correct)
B.3
C.4
D.5
Explanation: Prime factorization of 2450 is 2 × 5^2 × 7^2. To make it a perfect square, the power of every prime factor must be even. We need to multiply by 2.
ADRE 2022 • 2022 Paper 4Question 95
p, q, r are three numbers such that the LCM of p and q is q and the LCM of q and r is r. The LCM of p, q and r will be
A.q
B.r ✓ (Correct)
C.qr
D.pqr
Explanation: Since LCM of p and q is q, p is a factor of q. Since LCM of q and r is r, q is a factor of r. Therefore, p is also a factor of r. The LCM of all three (p, q, r) is simply the largest multiple among them, which is r.
ADRE 2022 • 2022 Paper 5Question 96
Which of the following geometric shapes does not have parallel sides ?
A.Rhombus ✓ (Correct)
B.Square
C.Pentagon
D.Parallelogram
Explanation: A regular pentagon has five sides and no two sides are parallel to each other. Rhombus, square, and parallelogram all have pairs of parallel sides[cite: 1].
ADRE 2022 • 2022 Paper 5Question 97
How many cubes of volume 1 cm³ each, can be cut out from a single cube of volume 1 m³ ?
A.108 ✓ (Correct)
B.106
C.104
D.102
Explanation: 1 m³ equals (100 cm)³ = 1,000,000 cm³ or 10^6 cm³. Thus, 10^6 cubes of 1 cm³ can be formed. The printed option '106' actually denotes 10^6[cite: 1].
ADRE 2022 • 2022 Paper 5Question 98
A 10 ft. long ladder leaning against a wall, touches the wall at a height of 8 ft. By what distance should the ladder be moved towards the wall so that its top touches the wall at 9.6 ft height ?
A.3.2 ft ✓ (Correct)
B.2.8 ft
C.3.9 ft
D.4.4 ft
Explanation: Initial base = √(10² - 8²) = 6 ft. New base = √(10² - 9.6²) = √(100 - 92.16) = √7.84 = 2.8 ft. The ladder moves 6 - 2.8 = 3.2 ft towards the wall[cite: 1].
ADRE 2022 • 2022 Paper 5Question 99
If the average age of A, B and C is 22 years and the average age of B and C is 25 years, then the age of A after 9 years is :
A.35 years ✓ (Correct)
B.30 years
C.25 years
D.20 years
Explanation: Total age of A+B+C = 22 * 3 = 66. Total age of B+C = 25 * 2 = 50. Therefore, A's present age = 66 - 50 = 16. A's age after 9 years = 16 + 9 = 25 years[cite: 1].
ADRE 2022 • 2022 Paper 5Question 100
If the population of a town increases at the rate of 10% every year, the present population is 1000, then after 3 years the population of the town would be
A.1300 ✓ (Correct)
B.1351
C.1310
D.1331
Explanation: Using compound interest formula: P = P0 * (1 + R/100)^t. P = 1000 * (1 + 10/100)³ = 1000 * 1.331 = 1331[cite: 1].
ADRE 2022 • 2022 Paper 5Question 101
6 men can complete a task in 15 days. After 10 days, 4 more men join. The number of days required to complete the remaining work is :
A.2 ✓ (Correct)
B.3
C.4
D.5
Explanation: Total work = 6 * 15 = 90 man-days. Work done in 10 days = 6 * 10 = 60 man-days. Remaining work = 30 man-days. Now, total men = 6 + 4 = 10. Days required = 30 / 10 = 3 days[cite: 1].
ADRE 2022 • 2022 Paper 5Question 102
50% of 25% of 20% of a number is 21. The number is
A.420 ✓ (Correct)
B.520
C.840
D.940
Explanation: Let the number be x. 0.50 * 0.25 * 0.20 * x = 21 => 0.025 * x = 21 => x = 21 / 0.025 = 840[cite: 1].
ADRE 2022 • 2022 Paper 5Question 103
0.23 is equivalent to the fraction
A.23 / 99 ✓ (Correct)
B.23 / 990
C.23 / 999
D.23 / 90
Explanation: Let x = 0.2323... Then 100x = 23.2323... Subtracting x gives 99x = 23, so x = 23/99[cite: 1].
ADRE 2022 • 2022 Paper 5Question 104
The angle 54° when converted to radians, is
A.pi / 10 ✓ (Correct)
B.3pi / 10
C.7pi / 10
D.9pi / 10
Explanation: To convert degrees to radians, multiply by π/180. 54 * (π / 180) = 3π / 10 radians[cite: 1].
ADRE 2022 • 2022 Paper 5Question 105
The decimal representation of 2.5 / 50 is :
A.0.5 ✓ (Correct)
B.0.25
C.0.05
D.0.025
Explanation: 2.5 / 50 is equal to 25 / 500. Dividing both numerator and denominator by 25 yields 1 / 20, which is equal to 0.05[cite: 1].
ADRE 2022 • 2022 Paper 5Question 106
Find the value of x if x / 128 = 162 / x
A.12 ✓ (Correct)
B.14
C.196
D.144
Explanation: Cross-multiply: x² = 128 * 162. x² = 20736. x = √20736 = 144[cite: 1].
ADRE 2022 • 2022 Paper 5Question 107
If a – b = 5 and a² + b² = 41, then the value of 'ab' is
A.10 ✓ (Correct)
B.5
C.7
D.8
Explanation: Using the identity (a - b)² = a² + b² - 2ab. (5)² = 41 - 2ab => 25 = 41 - 2ab => 2ab = 16 => ab = 8[cite: 1].
ADRE 2022 • 2022 Paper 5Question 108
A tank can be filled by 5 pipes in 80 minutes. How long would it take to fill the same tank by 8 pipes ?
A.80 minutes ✓ (Correct)
B.70 minutes
C.60 minutes
D.50 minutes
Explanation: This is an inverse variation problem. 5 pipes * 80 mins = 400 pipe-minutes. If 8 pipes are used: 400 / 8 = 50 minutes[cite: 1].
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