Ques 1 : Choose the correct answer. 
If the sum of two numbers is 55 and the H.C.F. and L.C.M of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to: 
Option 1 : 55/601 
Option 2 : 601/55 
Option 3 : 11/120 
Option 4 : 120/11 

Ques 2 : Choose the correct answer. 
Three different containers contain 496 litres, 403 litres and 713 litres of mixtures of milk and water respectively. What biggest measure can measure all the different quantities exactly ? 
Option 1 : 1 litre 
Option 2 : 7 litre 
Option 3 : 31 litre 
Option 4 : 41 litre 

Ques 3 : Choose the correct answer. 
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ? 
Option 1 : 4 
Option 2 : 10 
Option 3 : 15 
Option 4 : 16 

Ques 4 : Choose the correct answer. 
Four different electronic devices make a beep after every 30 minutes, 1 hour, 3/2 hour and 1 hour 45 minutes respectively. All the devices beeped together at 12 noon. They will again beep together at: 
Option 1 : 12 midnight 
Option 2 : 3 a.m. 
Option 3 : 6 a.m. 
Option 4 : 9 a.m. 

Ques 5 : Choose the correct answer. 
The number of prime factors of (3 x 5)^{12} (2 x 7)^{10} (10)^{25} is: 
Option 1 : 47 
Option 2 : 60 
Option 3 : 72 
Option 4 : None of these 

Ques 6 : Choose the correct answer. 
What least value must be assigned to * so that the number 63576*2 is divisible by 8? 
Option 1 : 1 
Option 2 : 2 
Option 3 : 3 
Option 4 : 4 

Ques 7 : Choose the correct answer. 
Which of the following numbers is exactly divisible by 24 ? 
Option 1 : 35718 
Option 2 : 63810 
Option 3 : 537804 
Option 4 : 3125736 

Ques 8 : Choose the correct answer. 
The number nearest to 15207, which is divisible by 467, is: 
Option 1 : 14342 
Option 2 : 15211 
Option 3 : 14944 
Option 4 : 15411 
Option 5 : None of these 

Ques 9 : Choose the correct answer. 
The smallest number, which is a perfect square and contains 7936 as a factor is: 
Option 1 : 251664 
Option 2 : 231564 
Option 3 : 246016 
Option 4 : 346016 
Option 5 : None of these 

Ques 10 : Choose the correct answer. 
In a division problem, the divisor is twenty times the quotient and five times the remainder. If remainder is 16, the number will be: 
Option 1 : 3360 
Option 2 : 336 
Option 3 : 1616 
Option 4 : 20516 
Option 5 : None of these 

Ques 11 : Choose the correct answer. 
The L.C.M. of two numbers is 4800 and their G.C.M. is 160. If one of the numbers is 480, then the other number is: 
Option 1 : 1600 
Option 2 : 1800 
Option 3 : 2200 
Option 4 : 2600 
Option 5 : None of these 

Ques 12 : Choose the correct answer. 
The L.C.M. of two numbers is 140. If their ratio is 2:5, then the numbers are: 
Option 1 : 28,70 
Option 2 : 28,7 
Option 3 : 8,70 
Option 4 : 8,40 
Option 5 : None of these 

Ques 13 : Choose the correct answer. 
If a number is exactly divisible by 85, then what will be the remainder when the same number is divided by 17? 
Option 1 : 3 
Option 2 : 1 
Option 3 : 4 
Option 4 : 0 

Ques 14 : Choose the correct answer. 
The least perfect square number which is exactly divisible by 3, 4, 7, 10 and 12 is: 
Option 1 : 8100 
Option 2 : 17600 
Option 3 : 44100 
Option 4 : None of these 

Ques 15 : Choose the correct answer. 
(x^{n}+y^{n}) is divisible by (xy): 
Option 1 : for all values of n 
Option 2 : only for even values of n 
Option 3 : only for odd values of n 
Option 4 : for no values of n 

Ques 16 : Choose the correct answer. 
The greatest number that will divide 63, 138 and 228 so as to leave the same remainder in each case: 
Option 1 : 15 
Option 2 : 20 
Option 3 : 35 
Option 4 : 40 

Ques 17 : Choose the correct answer. 
Find the largest number, smaller than the smallest fourdigit number, which when divided by 4,5,6 and 7 leaves a remainder 2 in each case. 
Option 1 : 422 
Option 2 : 842 
Option 3 : 12723 
Option 4 : None of these 

Ques 18 : Choose the correct answer. 
What is the highest power of 5 that divides 90 x 80 x 70 x 60 x 50 x 40 x 30 x 20 x 10? 
Option 1 : 10 
Option 2 : 12 
Option 3 : 14 
Option 4 : None of these 

Ques 19 : Choose the correct answer. 
If a and b are natural numbers and ab is divisible by 3, then a^{3}b^{3} is divisible by: 
Option 1 : 3 but not by 9 
Option 2 : 9 
Option 3 : 6 
Option 4 : 27 

Ques 20 : Choose the correct answer. 
What is the greatest positive power of 5 that divides 30! exactly? 
Option 1 : 5 
Option 2 : 6 
Option 3 : 7 
Option 4 : 8 

Ques 21 : Choose the correct answer. 
In how many ways can a number 6084 be written as a product of two different factors ? 
Option 1 : 27 
Option 2 : 26 
Option 3 : 13 
Option 4 : 14 

Ques 22 : Choose the correct answer. 
What is the smallest fourdigit number which when divided by 6, leaves a remainder of 5 and when divided by 5 leaves a remainder of 3? 
Option 1 : 1043 
Option 2 : 1073 
Option 3 : 1103 
Option 4 : None of these 

Ques 23 : Choose the correct answer. 
P is an integer. P>883. If P7 is a multiple of 11, then the largest number that will always divide (P+4) (P+15) is: 
Option 1 : 11 
Option 2 : 121 
Option 3 : 242 
Option 4 : None of these 

Ques 24 : Choose the correct answer. 
Let C be a positive integer such that C + 7 is divisible by 5. The smallest positive integer n (>2) such that C + n^{2} is divisible by 5 is: 
Option 1 : 4 
Option 2 : 5 
Option 3 : 3 
Option 4 : Does not exist 

Ques 25 : Choose the correct answer. 
Four bells begin to toll together and then each one at intervals of 6 s, 7 s, 8 s and 9 s respectively. The number of times they will toll together in the next 2 hr is: 
Option 1 : 14 times 
Option 2 : 15 times 
Option 3 : 13 times 
Option 4 : 11 times 

Ques 26 : Choose the correct answer. 
The product of two numbers is 16200. If their LCM is 216, find their HCF. 
Option 1 : 75 
Option 2 : 70 
Option 3 : 80 
Option 4 : Data inconsistent 

Ques 27 : Choose the correct answer. 
There are four prime numbers written in ascending order of magnitude. The product of first three is 385 and that of last three is 1001. Find the first number. 
Option 1 : 5 
Option 2 : 7 
Option 3 : 11 
Option 4 : 17 

Ques 28 : Choose the correct answer. 
M and N are two distinct natural numbers. HCF and LCM of M and N are K and L respectively. A is also a natural number, which of the following relations is not possible? 
Option 1 : K*L=A 
Option 2 : K*A=L 
Option 3 : L*A=K 
Option 4 : None of these 

Ques 29 : Choose the correct answer. 
On dividing a number by 999,the quotient is 366 and the remainder is 103.The number is: 
Option 1 : 364724 
Option 2 : 365387 
Option 3 : 365737 
Option 4 : 366757 

Ques 30 : Choose the correct answer. 
The difference between two numbers is 1365.When the larger number is divided by the smaller one ,the quotient is 6 and the remainder is 15.The smaller number is: 
Option 1 : 240 
Option 2 : 270 
Option 3 : 295 
Option 4 : 360 

Ques 31 : Choose the correct answer. 
The ratio of two numbers is 3:4 and their HCF is 4.Their LCM is: 
Option 1 : 12 
Option 2 : 16 
Option 3 : 24 
Option 4 : 48 

Ques 32 : Choose the correct answer. 
A rectangular courtyard 3.78 meters long and 5.25 meters wide is to be paved exactly with square tiles ,all of the same size. What is the largest size of the tile which could be used for the purpose? 
Option 1 : 14 cm 
Option 2 : 21 cm 
Option 3 : 42 cm 
Option 4 : None of these 

Ques 33 : Choose the correct answer. 
The least perfect square which is divisible by 3, 4, 5, 6, 8 is: 
Option 1 : 900 
Option 2 : 1200 
Option 3 : 2500 
Option 4 : 3600 

Ques 34 : Choose the correct answer. 
What will be obtained if 8 is subtracted from the HCF of 168, 189, and 231? 
Option 1 : 15 
Option 2 : 10 
Option 3 : 21 
Option 4 : None of these 

Ques 35 : Choose the correct answer. 
The largest four digit number which is a multiple of 8, 10,12 and 15 is: 
Option 1 : 120 
Option 2 : 9600 
Option 3 : 9840 
Option 4 : 9960 

Ques 36 : Choose the correct answer. 
If log_{x} (0.1) = 1/3, then the value of x is: 
Option 1 : 10 
Option 2 : 100 
Option 3 : 1000 
Option 4 : 1/1000 

Ques 37 : Choose the correct answer. 
If a^{x} = b^{y}, then: 
Option 1 : log(a/b) = x/y 
Option 2 : log(a) / log(b) = x/y 
Option 3 : log(a) / log(b) = y/x 
Option 4 : None of these 

Ques 38 : Choose the correct answer. 
If log_{8} x + log_{8} (1/6) = 1/3 then the value of x is: 
Option 1 : 12 
Option 2 : 16 
Option 3 : 18 
Option 4 : 24 

Ques 39 : Choose the correct answer. 
If log x + log y = log (x + y), then: 
Option 1 : x = y 
Option 2 : xy=1 
Option 3 : y = (x1)/x 
Option 4 : y = x/(x1) 

Ques 40 : Choose the correct answer. 
If log_{10} 7 = a, then log_{10}(1/70) is equal to: 
Option 1 : (1 + a) 
Option 2 : (1 + a)^{1} 
Option 3 : a/10 
Option 4 : 1/10a 

Ques 41 : Choose the correct answer. 
If log{(a+b)/3} = 0.5(log a + log b), then the correct relation between a and b is: 
Option 1 : a^{2}+b^{2} = 7ab 
Option 2 : a^{2}b^{2} = 7ab 
Option 3 : (a+b)^{2} = 2 
Option 4 : (a+b)/3 = (1/2)(a+b) 
Option 5 : None of these 

Ques 42 : Choose the correct answer. 
If log x = log 3 + 2 log 2 (3/4) log 16. The value of x is: 
Option 1 : 1/2 
Option 2 : 1 
Option 3 : 3/2 
Option 4 : 2 
Option 5 : None of these 

Ques 43 : Choose the correct answer. 
If log x =(1/2) log y = (1/5) log z, the value of x^{4}y^{3}z^{2} is: 
Option 1 : 0 
Option 2 : 1 
Option 3 : 2 
Option 4 : 3 
Option 5 : None of these 

Ques 44 : Choose the correct answer. 
If log_{10000} x = 1/4, then x is given by: 
Option 1 : 1/100 
Option 2 : 1/10 
Option 3 : 1/20 
Option 4 : none of these 

Ques 45 : Choose the correct answer. 
The value of 3^{1/2 log3(9) is:} 
Option 1 : 3 
Option 2 : 1/3 
Option 3 : 2/3 
Option 4 : none of these 

Ques 46 : Choose the correct answer. 
log_{e} xy – log_{e} x equals to: 
Option 1 : log_{e} x 
Option 2 : log_{e} x 
Option 3 : – log_{e} x 
Option 4 : none of these 

Ques 47 : Choose the correct answer. 
The value of (log_{a} n) / (log_{ab} n) is given by: 
Option 1 : 1 + log_{a} b 
Option 2 : 1 + log_{b} a 
Option 3 : log_{a} b 
Option 4 : log_{b} a 

Ques 48 : Choose the correct answer. 
If (a^{4} – 2a^{2}b^{2} + b^{4})^{x1} = (ab)^{2x} (a+b)^{2}, then x equals to: 
Option 1 : (a – b) / (a + b) 
Option 2 : log (a^{2} – b^{2}) 
Option 3 : log (a + b) / log (a – b) 
Option 4 : log (a – b) / log (a + b) 

Ques 49 : Choose the correct answer. 
If a, b, and c are in geometric progression then log_{a} n, log_{b} n and log_{c} n are in: 
Option 1 : AP 
Option 2 : GP 
Option 3 : HP 
Option 4 : None of these 

Ques 50 : Choose the correct answer. 
What is the value of antilog_{10}100? 
Option 1 : 2 
Option 2 : 10^{100} 
Option 3 : 100 
Option 4 : 10 