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Subject: Mathematics
Q1. [+1, -0.25] Mathematics
What is the sum of the first 20 natural numbers?
Show Answer Correct Answer: BSum of first n natural numbers = n(n+1)/2. For n=20, sum = 20×21/2 = 210.
Q2. [+1, -0.25] Mathematics
Which of the following is a prime number?
Show Answer Correct Answer: C97 is prime as it has no divisors other than 1 and itself. 87=3×29, 91=7×13, 99=9×11.
Q3. [+1, -0.25] Mathematics
What is the least number divisible by all numbers from 1 to 10?
A. 2520
B. 5040
C. 1260
D. 756
Show Answer Correct Answer: ALCM of 1 to 10 = 2^3×3^2×5×7 = 8×9×5×7 = 2520.
Q4. [+1, -0.25] Mathematics
How many three-digit numbers are divisible by 7?
Show Answer Correct Answer: BSmallest 3-digit multiple of 7 = 105, largest = 994. Count = (994-105)/7 + 1 = 889/7 + 1 = 127 + 1 = 128.
Q5. [+1, -0.25] Mathematics
What is the unit digit of 7^105?
Show Answer Correct Answer: ACyclicity of 7 is 4: 7^1=7, 7^2=49, 7^3=343, 7^4=2401. 105 mod 4 = 1, so unit digit = 7.
Q6. [+1, -0.25] Mathematics
Which of the following is an irrational number?
A. 22/7
B. 3.14
C. √3
D. 0.333...
Show Answer Correct Answer: C√3 is irrational as it cannot be expressed as p/q. 22/7, 3.14, and 0.333... are rational.
Q7. [+1, -0.25] Mathematics
What is the value of 2^10?
A. 512
B. 1024
C. 2048
D. 256
Show Answer Correct Answer: B2^10 = 1024. 2^1=2, 2^2=4, 2^3=8, 2^4=16, 2^5=32, 2^6=64, 2^7=128, 2^8=256, 2^9=512, 2^10=1024.
Q8. [+1, -0.25] Mathematics
The sum of two numbers is 45 and their difference is 15. What is the larger number?
Show Answer Correct Answer: ALet numbers be x and y. x+y=45, x-y=15. Adding: 2x=60, x=30. So larger = 30.
Q9. [+1, -0.25] Mathematics
How many factors does the number 36 have?
Show Answer Correct Answer: C36 = 2^2 x 3^2. Number of factors = (2+1)(2+1) = 9. Factors: 1,2,3,4,6,9,12,18,36.
Q10. [+1, -0.25] Mathematics
What is the value of 0.1 + 0.01 + 0.001 + 0.0001?
A. 0.1111
B. 0.111
C. 0.1011
D. 0.1101
Show Answer Correct Answer: A0.1 + 0.01 = 0.11. 0.11 + 0.001 = 0.111. 0.111 + 0.0001 = 0.1111.
Q11. [+1, -0.25] Mathematics
What is the HCF of 48 and 72?
Show Answer Correct Answer: B48 = 2^4 x 3, 72 = 2^3 x 3^2. HCF = 2^3 x 3 = 8 x 3 = 24.
Q12. [+1, -0.25] Mathematics
Find the LCM of 12, 18, and 24.
Show Answer Correct Answer: C12=2^2x3, 18=2x3^2, 24=2^3x3. LCM = 2^3x3^2 = 8x9 = 72.
Q13. [+1, -0.25] Mathematics
Two numbers are in the ratio 3:5 and their LCM is 225. What is the smaller number?
Show Answer Correct Answer: ALet numbers be 3x and 5x. LCM = 15x = 225, so x = 15. Smaller = 3x = 45.
Q14. [+1, -0.25] Mathematics
The HCF of two numbers is 12 and their LCM is 240. If one number is 48, find the other.
Show Answer Correct Answer: BProduct = HCF x LCM. Other = (12 x 240)/48 = 2880/48 = 60.
Q15. [+1, -0.25] Mathematics
What is the greatest number that divides 101 and 75 leaving remainders 3 and 5 respectively?
Show Answer Correct Answer: C101-3=98, 75-5=70. Required number = HCF(98,70). 98=2x7^2, 70=2x5x7. HCF = 2x7 = 14.
Q16. [+1, -0.25] Mathematics
Three bells ring at intervals of 4, 6, and 10 seconds. They start ringing together. After how many seconds will they ring together again?
Show Answer Correct Answer: DLCM of 4, 6, and 10 = 60. They will ring together every 60 seconds.
Q17. [+1, -0.25] Mathematics
If A:B = 2:3 and B:C = 4:5, find A:C.
A. 2:5
B. 8:15
C. 7:15
D. 3:5
Show Answer Correct Answer: BA:B = 2:3 = 8:12, B:C = 4:5 = 12:15. So A:C = 8:15.
Q18. [+1, -0.25] Mathematics
If 3x = 5y = 7z, find the ratio x:y:z.
A. 35:21:15
B. 15:21:35
C. 21:35:15
D. 35:15:21
Show Answer Correct Answer: ALet 3x=5y=7z=k. Then x=k/3, y=k/5, z=k/7. Multiplying by LCM 105: x:y:z = 35:21:15.
Q19. [+1, -0.25] Mathematics
Rs. 750 is divided among A, B, C in the ratio 2:3:5. What is C's share?
A. Rs. 150
B. Rs. 225
C. Rs. 375
D. Rs. 300
Show Answer Correct Answer: CTotal parts = 2+3+5 = 10. C's share = (5/10) x 750 = 375.
Q20. [+1, -0.25] Mathematics
The ratio of the ages of Ram and Shyam is 7:5. If Ram is 8 years older than Shyam, find Shyam's age.
Show Answer Correct Answer: CLet ages be 7x and 5x. 7x-5x=2x=8, so x=4. Shyam = 5x = 20.
Q21. [+1, -0.25] Mathematics
If 6 men can do a work in 12 days, how many men are needed to do the same work in 9 days?
Show Answer Correct Answer: CM1D1 = M2D2. 6x12 = M2x9. M2 = 72/9 = 8 men.
Q22. [+1, -0.25] Mathematics
If 15 workers earn Rs. 4500 in 10 days, what will 10 workers earn in 12 days?
A. Rs. 3000
B. Rs. 3200
C. Rs. 3600
D. Rs. 4000
Show Answer Correct Answer: CEarnings = k x workers x days. k = 4500/(15x10) = 30. For 10 workers in 12 days: 30x10x12 = 3600.
Q23. [+1, -0.25] Mathematics
The ratio of incomes of A and B is 4:5 and their expenditures are in ratio 2:3. If each saves Rs. 2000, find B's income.
A. Rs. 4000
B. Rs. 5000
C. Rs. 6000
D. Rs. 8000
Show Answer Correct Answer: BLet incomes be 4x,5x and expenditures be 2y,3y. Savings: 4x-2y=2000, 5x-3y=2000. Solving: x=1000, so B=5x=5000.
Q24. [+1, -0.25] Mathematics
Two numbers are in ratio 5:7. If 6 is added to each, the ratio becomes 3:4. Find the smaller number.
Show Answer Correct Answer: ALet numbers be 5x,7x. (5x+6)/(7x+6)=3/4. Cross multiply: 20x+24=21x+18. x=6. Smaller=5x=30.
Q25. [+1, -0.25] Mathematics
What is 15% of 300?
Show Answer Correct Answer: C15% of 300 = (15/100) x 300 = 45.
Q26. [+1, -0.25] Mathematics
If 40% of a number is 120, what is the number?
Show Answer Correct Answer: BLet number be x. 0.4x = 120, x = 120/0.4 = 300.
Q27. [+1, -0.25] Mathematics
A number increased by 25% gives 300. Find the original number.
Show Answer Correct Answer: CLet number = x. x + 0.25x = 1.25x = 300, x = 300/1.25 = 240.
Q28. [+1, -0.25] Mathematics
What is 0.5% of 5000?
Show Answer Correct Answer: C0.5% = 0.5/100 = 0.005. 0.005 x 5000 = 25.
Q29. [+1, -0.25] Mathematics
In an exam, a student scores 56% marks and gets 112 marks. What are the maximum marks?
Show Answer Correct Answer: C56% of max = 112, so max = 112/0.56 = 200.
Q30. [+1, -0.25] Mathematics
If the price of sugar decreases by 20%, by how much percent must consumption increase to keep expenditure same?
Show Answer Correct Answer: CLet original price = P, consumption = C. New price = 0.8P. For same expenditure PC = 0.8P x Cnew. Cnew = C/0.8 = 1.25C. Increase = 25%.
Q31. [+1, -0.25] Mathematics
A candidate scores 35% and fails by 45 marks. The passing marks are 40% of the total. Find total marks.
Show Answer Correct Answer: CLet total = x. Passing = 0.4x. Scored = 0.35x. 0.4x - 0.35x = 45. 0.05x = 45, x = 900.
Q32. [+1, -0.25] Mathematics
A shopkeeper buys an article for Rs. 500 and sells it for Rs. 600. What is the profit percentage?
Show Answer Correct Answer: CProfit = 600-500 = 100. Profit% = (100/500)x100 = 20%.
Q33. [+1, -0.25] Mathematics
If a person sells an article at a loss of 10%, he gets Rs. 50. What is the cost price?
A. Rs. 500
B. Rs. 52
C. Rs. 55.55
D. Rs. 60
Show Answer Correct Answer: CSP = CP x (1 - 0.10) = 0.9CP = 50. CP = 50/0.9 = Rs. 55.55.
Q34. [+1, -0.25] Mathematics
A man sold two items each for Rs. 120. On one he gains 20% and on the other he loses 20%. Find his overall gain or loss percentage.
A. No profit no loss
B. Loss 4%
C. Profit 4%
D. Loss 2%
Show Answer Correct Answer: BCP1 = 120/1.2 = 100, CP2 = 120/0.8 = 150. Total CP = 250, Total SP = 240. Loss% = (10/250)x100 = 4%.
Q35. [+1, -0.25] Mathematics
A trader marks his goods 30% above CP and gives a discount of 10%. Find his profit percentage.
Show Answer Correct Answer: CLet CP=100. MP=130. Discount 10% => SP=130x0.9=117. Profit=17%.
Q36. [+1, -0.25] Mathematics
By selling 15 articles, a person gains the cost price of 3 articles. Find gain%.
Show Answer Correct Answer: CLet CP of 1 article = Re 1. CP of 15 = Rs 15. Gain = CP of 3 = Rs 3. SP = 18. Gain% = (3/15)x100 = 20%.
Q37. [+1, -0.25] Mathematics
If CP of 12 articles is equal to SP of 9 articles, find gain%.
A. 25%
B. 30%
C. 33.33%
D. 40%
Show Answer Correct Answer: CLet CP of 1 = Re 1. CP of 12 = 12 = SP of 9. SP of 1 = 12/9 = 4/3. Gain = 4/3-1 = 1/3. Gain% = (1/3)x100 = 33.33%.
Q38. [+1, -0.25] Mathematics
A shopkeeper sells an item at Rs. 360 after a discount of 10%. What is the marked price?
A. Rs. 380
B. Rs. 390
C. Rs. 400
D. Rs. 420
Show Answer Correct Answer: CSP = MP x (100-d)/100. 360 = MP x 0.9. MP = 360/0.9 = 400.
Q39. [+1, -0.25] Mathematics
Find simple interest on Rs. 2000 at 5% per annum for 3 years.
A. Rs. 200
B. Rs. 300
C. Rs. 400
D. Rs. 500
Show Answer Correct Answer: BSI = PxRxT/100 = 2000x5x3/100 = 300.
Q40. [+1, -0.25] Mathematics
At what rate of simple interest will Rs. 600 amount to Rs. 720 in 4 years?
Show Answer Correct Answer: CSI = 720-600 = 120. R = 100xSI/(PxT) = 100x120/(600x4) = 12000/2400 = 5%.
Q41. [+1, -0.25] Mathematics
Find the compound interest on Rs. 5000 at 10% per annum for 2 years.
A. Rs. 1000
B. Rs. 1025
C. Rs. 1050
D. Rs. 1100
Show Answer Correct Answer: CA = 5000(1+0.1)^2 = 5000x1.21 = 6050. CI = 6050-5000 = 1050.
Q42. [+1, -0.25] Mathematics
In how many years will Rs. 8000 become Rs. 9261 at 5% p.a. compounded annually?
Show Answer Correct Answer: C8000(1.05)^n = 9261. (1.05)^n = 9261/8000 = 1.157625. 1.05^3 = 1.157625. So n = 3.
Q43. [+1, -0.25] Mathematics
The difference between CI and SI for 2 years at 10% per annum on a certain sum is Rs. 50. Find the sum.
A. Rs. 4000
B. Rs. 4500
C. Rs. 5000
D. Rs. 5500
Show Answer Correct Answer: CCI - SI = P(r/100)^2. 50 = P(10/100)^2 = P(0.01). P = 5000.
Q44. [+1, -0.25] Mathematics
A sum doubles itself in 8 years at simple interest. Find the rate of interest.
A. 10%
B. 11%
C. 12.5%
D. 15%
Show Answer Correct Answer: CSI = P. So P = PxRx8/100, R = 100/8 = 12.5%.
Q45. [+1, -0.25] Mathematics
A car covers a distance of 240 km in 4 hours. Find its speed in m/s.
A. 15 m/s
B. 16.33 m/s
C. 16.67 m/s
D. 17 m/s
Show Answer Correct Answer: CSpeed = 240/4 = 60 km/h. In m/s = 60 x 5/18 = 300/18 = 16.67 m/s.
Q46. [+1, -0.25] Mathematics
A train 200 m long crosses a pole in 10 seconds. Find the speed of the train in km/h.
Show Answer Correct Answer: CSpeed = Distance/Time = 200/10 = 20 m/s. In km/h = 20 x 18/5 = 72 km/h.
Q47. [+1, -0.25] Mathematics
A man walks at 5 km/h from home and reaches office 3 minutes late. If he walks at 6 km/h, he reaches 7 minutes early. Find the distance.
A. 4 km
B. 4.5 km
C. 5 km
D. 6 km
Show Answer Correct Answer: CLet distance = d km. d/5 - d/6 = (7+3)/60 = 10/60 = 1/6. (6d-5d)/30 = 1/6. d/30 = 1/6. d = 5 km.
Q48. [+1, -0.25] Mathematics
Two trains 150 m and 200 m long run at 60 km/h and 40 km/h respectively opposite directions. Find time to cross each other.
A. 10.2 s
B. 11.5 s
C. 12.6 s
D. 13.5 s
Show Answer Correct Answer: CRelative speed = 60+40=100 km/h = 100x5/18 = 250/9 m/s. Total length = 350 m. Time = 350/(250/9) = 350x9/250 = 12.6 s.
Q49. [+1, -0.25] Mathematics
A boat travels downstream 30 km in 2 hours and upstream 24 km in 3 hours. Find the speed of the boat in still water.
A. 8.5 km/h
B. 11.5 km/h
C. 12 km/h
D. 10 km/h
Show Answer Correct Answer: BDownstream speed = 30/2=15 km/h. Upstream speed = 24/3=8 km/h. Boat speed = (15+8)/2 = 11.5 km/h.
Q50. [+1, -0.25] Mathematics
Ravi takes 3 hours to row 12 km downstream and 4 hours to row 8 km upstream. Find the speed of the stream.
A. 0.5 km/h
B. 1 km/h
C. 1.5 km/h
D. 2 km/h
Show Answer Correct Answer: BDownstream speed = 12/3 = 4 km/h. Upstream speed = 8/4 = 2 km/h. Stream speed = (4-2)/2 = 1 km/h.
Q51. [+1, -0.25] Mathematics
A man cycles at 12 km/h for 30 minutes and then at 8 km/h for next 45 minutes. Find average speed.
A. 9 km/h
B. 9.2 km/h
C. 9.6 km/h
D. 10 km/h
Show Answer Correct Answer: CD1 = 12 x 0.5 = 6 km. D2 = 8 x 0.75 = 6 km. Total D = 12 km. Total T = 1.25 h. Avg speed = 12/1.25 = 9.6 km/h.
Q52. [+1, -0.25] Mathematics
A and B together can do a work in 12 days. B alone can do it in 20 days. In how many days can A alone do it?
Show Answer Correct Answer: CA+B 1-day work = 1/12. B's 1-day = 1/20. A's 1-day = 1/12-1/20 = 5/60-3/60 = 2/60 = 1/30. A takes 30 days.
Q53. [+1, -0.25] Mathematics
A can do a work in 10 days, B in 15 days. They work together for 4 days, then A leaves. In how many days will B finish the remaining work?
Show Answer Correct Answer: C4-day work of A+B = 4(1/10+1/15) = 4(5/30) = 20/30 = 2/3. Remaining = 1/3. B's time = (1/3)/(1/15) = 5 days.
Q54. [+1, -0.25] Mathematics
A pipe can fill a tank in 6 hours and another can empty it in 8 hours. If both are opened together, how long to fill the tank?
A. 20 h
B. 22 h
C. 24 h
D. 26 h
Show Answer Correct Answer: CIn 1 hour, fill = 1/6 - 1/8 = 4/24-3/24 = 1/24. Time = 24 hours.
Q55. [+1, -0.25] Mathematics
A is twice as good as B and together they finish work in 14 days. In how many days can A alone do it?
Show Answer Correct Answer: CLet B's 1-day work = x, A's = 2x. 2x+x=1/14. 3x=1/14, x=1/42. A's 1-day = 2/42 = 1/21. A takes 21 days.
Q56. [+1, -0.25] Mathematics
Three taps A, B, C fill a tank in 6, 8, 12 hours respectively. If all taps are opened together, how long to fill the tank?
A. 2 h
B. 2 h 20 min
C. 2 h 40 min
D. 3 h
Show Answer Correct Answer: C1-hour work = 1/6+1/8+1/12 = 4/24+3/24+2/24 = 9/24 = 3/8. Time = 8/3 h = 2 h 40 min.
Q57. [+1, -0.25] Mathematics
10 men can complete a work in 20 days. They start work and after 5 days, 5 more men join. How many more days to finish?
Show Answer Correct Answer: CTotal work = 10x20 = 200 man-days. Work done in 5 days = 10x5 = 50. Remaining = 150. Men now = 15. Days = 150/15 = 10.
Q58. [+1, -0.25] Mathematics
Find the average of the first 10 prime numbers.
A. 12.5
B. 12.7
C. 12.9
D. 13.1
Show Answer Correct Answer: CFirst 10 primes: 2,3,5,7,11,13,17,19,23,29. Sum=129. Avg=129/10=12.9.
Q59. [+1, -0.25] Mathematics
The average of 5 numbers is 20. If one number is removed, the average becomes 16. Find the removed number.
Show Answer Correct Answer: CSum of 5 = 5x20 = 100. Sum of 4 = 4x16 = 64. Removed = 100-64 = 36.
Q60. [+1, -0.25] Mathematics
The average age of a family of 5 members is 30 years. If the age of the youngest is 10, find the average age of the remaining 4.
Show Answer Correct Answer: CTotal age = 5x30 = 150. Sum of 4 = 150-10 = 140. Avg of 4 = 140/4 = 35.
Q61. [+1, -0.25] Mathematics
The average of 10 numbers is 15. Each number is multiplied by 2. Find the new average.
Show Answer Correct Answer: CIf each number is multiplied by k, average also gets multiplied by k. New avg = 15x2 = 30.
Q62. [+1, -0.25] Mathematics
The average marks of 40 students is 60. If the top 5 students with average 90 are excluded, what is the average of remaining?
Show Answer Correct Answer: CTotal marks = 40x60 = 2400. Top 5 sum = 5x90 = 450. Remaining 35 sum = 2400-450 = 1950. Avg = 1950/35 = 55.7.
Q63. [+1, -0.25] Mathematics
The average of 20 numbers is 0. How many of them can be positive at most?
Show Answer Correct Answer: CSum = 0. If 19 are positive, the 20th must be negative to bring sum to 0. So at most 19 can be positive.
Q64. [+1, -0.25] Mathematics
If x + y = 12 and xy = 35, find x^2 + y^2.
Show Answer Correct Answer: Cx^2+y^2 = (x+y)^2 - 2xy = 144 - 70 = 74.
Q65. [+1, -0.25] Mathematics
If a + b + c = 0, find the value of a^3 + b^3 + c^3.
Show Answer Correct Answer: CIf a+b+c=0, then a^3+b^3+c^3 = 3abc. This is a standard algebraic identity.
Q66. [+1, -0.25] Mathematics
Factorise: x^2 - 7x + 12.
A. (x+3)(x+4)
B. (x-3)(x-4)
C. (x-2)(x-6)
D. (x+3)(x-4)
Show Answer Correct Answer: Bx^2-7x+12 = x^2-3x-4x+12 = x(x-3)-4(x-3) = (x-3)(x-4).
Q67. [+1, -0.25] Mathematics
If 2x - 3y = 5 and x + 2y = 6, find x.
Show Answer Correct Answer: CMultiply 2nd by 2: 2x+4y=12. Subtract 1st: 7y=7, y=1. Then x=6-2=4.
Q68. [+1, -0.25] Mathematics
Solve: (x-1)/(x+2) = 2/3.
Show Answer Correct Answer: C3(x-1) = 2(x+2). 3x-3 = 2x+4. x = 7.
Q69. [+1, -0.25] Mathematics
If x^2 + 1/x^2 = 34, find x + 1/x (positive values).
Show Answer Correct Answer: C(x+1/x)^2 = x^2+1/x^2+2 = 34+2 = 36. So x+1/x = 6.
Q70. [+1, -0.25] Mathematics
Find the value of k if x=2 is a root of x^2 + kx - 6 = 0.
Show Answer Correct Answer: ASubstitute x=2: 4+2k-6=0 => 2k-2=0 => k=1.
Q71. [+1, -0.25] Mathematics
What is the value of (a+b)^2 - (a-b)^2?
Show Answer Correct Answer: B(a+b)^2-(a-b)^2 = (a^2+2ab+b^2)-(a^2-2ab+b^2) = 4ab.
Q72. [+1, -0.25] Mathematics
How many diagonals does a hexagon have?
Show Answer Correct Answer: DNumber of diagonals in polygon = n(n-3)/2. For hexagon n=6: 6x3/2 = 9.
Q73. [+1, -0.25] Mathematics
In a triangle, the angles are in ratio 2:3:5. Find the largest angle.
Show Answer Correct Answer: DSum = 2x+3x+5x = 10x = 180, x=18. Largest = 5x18 = 90°.
Q74. [+1, -0.25] Mathematics
The sum of interior angles of a polygon with 8 sides is:
A. 900°
B. 1000°
C. 1040°
D. 1080°
Show Answer Correct Answer: DSum = (n-2)x180 = (8-2)x180 = 6x180 = 1080°.
Q75. [+1, -0.25] Mathematics
Two angles of a triangle are 45° and 65°. Find the third angle.
Show Answer Correct Answer: A180° - (45+65) = 180-110 = 70°.
Q76. [+1, -0.25] Mathematics
If two parallel lines are cut by a transversal, the sum of interior angles on the same side is:
A. 90°
B. 180°
C. 270°
D. 360°
Show Answer Correct Answer: BInterior angles on the same side of a transversal are supplementary, summing to 180°.
Q77. [+1, -0.25] Mathematics
What is the area of a circle with diameter 14 cm? (Take π = 22/7)
A. 144 cm²
B. 150 cm²
C. 152 cm²
D. 154 cm²
Show Answer Correct Answer: DRadius = 7 cm. Area = πr^2 = (22/7)x49 = 22x7 = 154 cm².
Q78. [+1, -0.25] Mathematics
Find the area of a triangle with base 12 cm and height 8 cm.
A. 40 cm²
B. 44 cm²
C. 48 cm²
D. 52 cm²
Show Answer Correct Answer: CArea = (1/2) x base x height = (1/2) x 12 x 8 = 48 cm².
Q79. [+1, -0.25] Mathematics
The sides of a right triangle are 6 cm, 8 cm, and 10 cm. Find its area.
A. 20 cm²
B. 22 cm²
C. 24 cm²
D. 30 cm²
Show Answer Correct Answer: CArea of right triangle = (1/2) x product of legs = (1/2) x 6 x 8 = 24 cm².
Q80. [+1, -0.25] Mathematics
Find the volume of a cube whose side is 5 cm.
A. 100 cm³
B. 115 cm³
C. 125 cm³
D. 150 cm³
Show Answer Correct Answer: CVolume = side^3 = 5^3 = 125 cm³.
Q81. [+1, -0.25] Mathematics
Find the curved surface area of a cylinder of radius 7 cm and height 10 cm. (Take π = 22/7)
A. 400 cm²
B. 420 cm²
C. 430 cm²
D. 440 cm²
Show Answer Correct Answer: DCSA = 2πrh = 2 x 22/7 x 7 x 10 = 2 x 22 x 10 = 440 cm².
Q82. [+1, -0.25] Mathematics
The volume of a sphere is 288π cm³. Find its radius.
A. 4 cm
B. 5 cm
C. 6 cm
D. 7 cm
Show Answer Correct Answer: CV = (4/3)πr^3 = 288π. r^3 = 288 x 3/4 = 216. r = 6 cm.
Q83. [+1, -0.25] Mathematics
Find the area of a rhombus whose diagonals are 10 cm and 12 cm.
A. 50 cm²
B. 55 cm²
C. 60 cm²
D. 65 cm²
Show Answer Correct Answer: CArea = (1/2) x d1 x d2 = (1/2) x 10 x 12 = 60 cm².
Q84. [+1, -0.25] Mathematics
Find the total surface area of a cuboid of dimensions 4 cm x 5 cm x 6 cm.
A. 120 cm²
B. 128 cm²
C. 136 cm²
D. 148 cm²
Show Answer Correct Answer: DTSA = 2(lb+bh+hl) = 2(20+30+24) = 2x74 = 148 cm².
Q85. [+1, -0.25] Mathematics
The length of a rectangle is thrice its breadth. If the perimeter is 96 cm, find its area.
A. 360 cm²
B. 384 cm²
C. 396 cm²
D. 432 cm²
Show Answer Correct Answer: DLet breadth = b, length = 3b. P = 2(3b+b) = 8b = 96, b=12, l=36. Area = 36x12 = 432 cm².
Q86. [+1, -0.25] Mathematics
How many bricks of size 20 cm x 10 cm x 8 cm are needed to build a wall 8 m x 6 m x 0.4 m?
A. 10000
B. 11000
C. 12000
D. 13000
Show Answer Correct Answer: CWall volume = 800x600x40 = 19,200,000 cm³. Brick volume = 20x10x8 = 1600 cm³. Bricks = 19200000/1600 = 12000.
Q87. [+1, -0.25] Mathematics
What is the value of cos(0°)?
Show Answer Correct Answer: Ccos(0°) = 1. This is a standard trigonometric value.
Q88. [+1, -0.25] Mathematics
What is the value of tan(45°)?
Show Answer Correct Answer: Ctan(45°) = 1. sin(45°)/cos(45°) = (1/√2)/(1/√2) = 1.
Q89. [+1, -0.25] Mathematics
If sin θ = 3/5, find cos θ.
Show Answer Correct Answer: Bsin²θ+cos²θ=1. cos²θ=1-9/25=16/25, cosθ=4/5.
Q90. [+1, -0.25] Mathematics
A 15 m long ladder reaches a window 12 m above ground. Find the distance of the foot of the ladder from the wall.
Show Answer Correct Answer: DUsing Pythagoras: distance² = 15²-12² = 225-144 = 81, distance = 9 m.
Q91. [+1, -0.25] Mathematics
If sec θ = 13/5, find tan θ.
A. 7/5
B. 8/5
C. 12/5
D. 13/12
Show Answer Correct Answer: Csec²θ=1+tan²θ. tan²θ=(169/25)-1=144/25, tanθ=12/5.
Q92. [+1, -0.25] Mathematics
Find the median of: 5, 7, 9, 11, 13, 15, 17.
Show Answer Correct Answer: CNumbers are already sorted. 7 numbers, median is the 4th = 11.
Q93. [+1, -0.25] Mathematics
Find the mode of: 2, 3, 3, 5, 5, 5, 7, 7, 9.
Show Answer Correct Answer: B5 appears 3 times, more than any other number. Mode = 5.
Q94. [+1, -0.25] Mathematics
Find the range of: 12, 25, 18, 30, 42, 10, 35.
Show Answer Correct Answer: CRange = max - min = 42 - 10 = 32.
Q95. [+1, -0.25] Mathematics
The mean of 10 observations is 42. If each observation is increased by 5, find the new mean.
Show Answer Correct Answer: CIf each value increases by 5, the mean also increases by 5. New mean = 42+5 = 47.
Q96. [+1, -0.25] Mathematics
The probability of getting a head when a fair coin is tossed is:
Show Answer Correct Answer: CA fair coin has 2 equally likely outcomes. P(head) = 1/2.
Q97. [+1, -0.25] Mathematics
The mean of five numbers is 18. If one number is 24, what is the mean of the other four?
A. 14.5
B. 15.5
C. 16.5
D. 17.5
Show Answer Correct Answer: CSum = 5x18 = 90. Sum of other 4 = 90-24 = 66. Mean = 66/4 = 16.5.
Q98. [+1, -0.25] Mathematics
A bag contains 4 red, 3 blue, and 5 green balls. One ball is drawn at random. Find the probability it is blue.
Show Answer Correct Answer: BTotal balls = 4+3+5 = 12. P(blue) = 3/12 = 1/4.
Q99. [+1, -0.25] Mathematics
A data set has values 10, 20, 30, 40, 50. If each value is divided by 10, find the new mean.
Show Answer Correct Answer: BOriginal mean = (10+20+30+40+50)/5 = 150/5 = 30. Dividing each by 10, new mean = 30/10 = 3.
Q100. [+1, -0.25] Mathematics
In a bar graph, the bar for 2020 is 6 cm tall representing a value of 300. What value does a 10 cm bar represent?
Show Answer Correct Answer: DScale = 300/6 = 50 per cm. For 10 cm: 10 x 50 = 500.