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Instruction:
 Total number of questions : 20.
 Time alloted : 30 minutes.
 Each question carry 1 mark, no negative marks.
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1.  The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is: 

Your Answer: Option (Not Answered) Correct Answer: Option B Explanation: Let the numbers 13a and 13b. Then, 13a x 13b = 2028 ab = 12. Now, the coprimes with product 12 are (1, 12) and (3, 4). [Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ] So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4). Clearly, there are 2 such pairs. Learn more problems on : Problems on H.C.F and L.C.M Discuss about this problem : Discuss in Forum 
2.  What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ? 

Your Answer: Option (Not Answered) Correct Answer: Option B Explanation: L.C.M. of 12, 18, 21 30 2  12  18  21  30  = 2 x 3 x 2 x 3 x 7 x 5 = 1260. 3  6  9  21  15  Required number = (1260 ÷ 2)  2  3  7  5 = 630. Learn more problems on : Problems on H.C.F and L.C.M Discuss about this problem : Discuss in Forum 
3.  The difference between a twodigit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number? 

Your Answer: Option (Not Answered) Correct Answer: Option B Explanation: Let the ten's digit be x and unit's digit be y. Then, (10x + y)  (10y + x) = 36 9(x  y) = 36 x  y = 4. Video Explanation: https://youtu.be/7QOJjAmGVx0 Learn more problems on : Problems on Numbers Discuss about this problem : Discuss in Forum 
4.  The sum of the digits of a twodigit number is 15 and the difference between the digits is 3. What is the twodigit number? 

Your Answer: Option (Not Answered) Correct Answer: Option D Explanation: Let the ten's digit be x and unit's digit be y. Then, x + y = 15 and x  y = 3 or y  x = 3. Solving x + y = 15 and x  y = 3, we get: x = 9, y = 6. Solving x + y = 15 and y  x = 3, we get: x = 6, y = 9. So, the number is either 96 or 69. Hence, the number cannot be determined. Learn more problems on : Problems on Numbers Discuss about this problem : Discuss in Forum 
5.  A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by: 

Your Answer: Option (Not Answered) Correct Answer: Option D Explanation: Let the ten's digit be x and unit's digit be y. Then, number = 10x + y. Number obtained by interchanging the digits = 10y + x. (10x + y) + (10y + x) = 11(x + y), which is divisible by 11. Video Explanation: https://youtu.be/lytJE8GqRvM Learn more problems on : Problems on Numbers Discuss about this problem : Discuss in Forum 
6.  If m and n are whole numbers such that m^{n} = 121, the value of (m  1)^{n + 1} is: 

Your Answer: Option (Not Answered) Correct Answer: Option D Explanation: We know that 11^{2} = 121. Putting m = 11 and n = 2, we get: (m  1)^{n + 1} = (11  1)^{(2 + 1)} = 10^{3} = 1000. Learn more problems on : Surds and Indices Discuss about this problem : Discuss in Forum 
7. 


Your Answer: Option (Not Answered) Correct Answer: Option B Explanation: S.P. = Rs. 250 each. To find gain percent, we must know the C.P. of each. Correct answer is (B). Learn more problems on : Profit and Loss Discuss about this problem : Discuss in Forum 
8.  A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? 

Your Answer: Option (Not Answered) Correct Answer: Option A Explanation: Relative speed = (120 + 80) km/hr
Let the length of the other train be x metres.
x + 270 = 500 x = 230. Learn more problems on : Problems on Trains Discuss about this problem : Discuss in Forum 
9.  A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is: 

Your Answer: Option (Not Answered) Correct Answer: Option D Explanation: Let the speed of the second train be x km/hr.
Distance covered = (108 + 112) = 220 m.
250 + 5x = 660 x = 82 km/hr. Learn more problems on : Problems on Trains Discuss about this problem : Discuss in Forum 
Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and
 
10. 


Your Answer: Option (Not Answered) Correct Answer: Option E Explanation: Let the two trains of length a metres and b metres be moving in opposite directions at u m/s and v m/s.
a = (375  180) = 195 m. Learn more problems on : Problems on Trains Discuss about this problem : Discuss in Forum 
11.  Which of the following statements is not correct? 

Your Answer: Option (Not Answered) Correct Answer: Option B Explanation: (a) Since log_{a} a = 1, so log_{10} 10 = 1. (b) log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3 log (2 + 3) log (2 x 3) (c) Since log_{a} 1 = 0, so log_{10} 1 = 0. (d) log (1 + 2 + 3) = log 6 = log (1 x 2 x 3) = log 1 + log 2 + log 3. So, (b) is incorrect. Learn more problems on : Logarithm Discuss about this problem : Discuss in Forum 
12.  The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle? 

Your Answer: Option (Not Answered) Correct Answer: Option B Explanation:
2l + 2b = 5b 3b = 2l
Then, Area = 216 cm^{2} l x b = 216
l^{2} = 324 l = 18 cm. Learn more problems on : Area Discuss about this problem : Discuss in Forum 
13.  A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road? 

Your Answer: Option (Not Answered) Correct Answer: Option B Explanation: Area of the park = (60 x 40) m^{2} = 2400 m^{2}. Area of the lawn = 2109 m^{2}. Area of the crossroads = (2400  2109) m^{2} = 291 m^{2}. Let the width of the road be x metres. Then, 60x + 40x  x^{2} = 291 x^{2}  100x + 291 = 0 (x  97)(x  3) = 0 x = 3. Video Explanation: https://youtu.be/R3CtrAKGxkc Learn more problems on : Area Discuss about this problem : Discuss in Forum 
14.  A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is: 

Your Answer: Option (Not Answered) Correct Answer: Option B Explanation:
Learn more problems on : Volume and Surface Area Discuss about this problem : Discuss in Forum 
15.  A can run 22.5 m while B runs 25 m. In a kilometre race B beats A by: 

Your Answer: Option (Not Answered) Correct Answer: Option A Explanation:
B beats A by 100 m. Learn more problems on : Races and Games Discuss about this problem : Discuss in Forum 
16.  In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together? 

Your Answer: Option (Not Answered) Correct Answer: Option D Explanation: In the word 'CORPORATION', we treat the vowels OOAIO as one letter. Thus, we have CRPRTN (OOAIO). This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged
Required number of ways = (2520 x 20) = 50400. Video Explanation: https://youtu.be/o3fwMoB0duw Learn more problems on : Permutation and Combination Discuss about this problem : Discuss in Forum 
17.  In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green? 

Your Answer: Option (Not Answered) Correct Answer: Option A Explanation: Total number of balls = (8 + 7 + 6) = 21.
n(E) = 7.
Learn more problems on : Probability Discuss about this problem : Discuss in Forum 
Find the odd man out.  
18.  3, 5, 7, 12, 17, 19 

Your Answer: Option (Not Answered) Correct Answer: Option D Explanation: Each of the numbers is a prime number except 12.
Learn more problems on : Odd Man Out and Series Discuss about this problem : Discuss in Forum 
Find out the wrong number in the given sequence of numbers.  
19.  6, 13, 18, 25, 30, 37, 40 

Your Answer: Option (Not Answered) Correct Answer: Option D Explanation: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong. Learn more problems on : Odd Man Out and Series Discuss about this problem : Discuss in Forum 
Find out the wrong number in the series.  
20.  3, 7, 15, 39, 63, 127, 255, 511 

Your Answer: Option (Not Answered) Correct Answer: Option C Explanation: Go on multiplying 2 and adding 1 to get the next number. So, 39 is wrong. Learn more problems on : Odd Man Out and Series Discuss about this problem : Discuss in Forum 