Placement Written test paper for MNC  Math questions and answers Part –2
Ques 51 : Choose the correct answer.  
If antilog _{x} 5 = 30, what can you infer about x?  
Option 1 : x is a number between 1 and 2  Option 2 : x is 30^{5}  Option 3 : x is a number between 2 and 3  Option 4 : None of these  


Ques 52 : Choose the correct answer.  
Every time x is increased by a given constant number, y doubles and z becomes three times. How will log(y) and log(z) behave as x is increased by the same constant number?  
Option 1 : Both will grow linearly with different slopes  Option 2 : Both will grow linearly with same slopes  Option 3 : y will grow linearly, while z will not  Option 4 : z will grow linearly, while y will not  


Ques 53 : Choose the correct answer.  
x triples every second. How will log_{2}x change every second?  
Option 1 : It will double every second  Option 2 : It will triple every second  Option 3 : It increases by a constant amount every second.  Option 4 : None of these  


Ques 54 : Choose the correct answer.  
f(x) grows exponentially with x, how will f(log(x)) grow?  
Option 1 : Exponentially  Option 2 : Linearly  Option 3 : Quadratically  Option 4 : None of these  


Ques 55 : Choose the correct answer.  
What is the value of log_{512 }8?  
Option 1 : 3  Option 2 : 1/3  Option 3 : 3  Option 4 : 1/3  


Ques 56 : Choose the correct answer.  
What is the value of log_{7} (1/49)?  
Option 1 : 2  Option 2 : 1/2  Option 3 : 1/2  Option 4 : 2  


Ques 57 : Choose the correct answer.  
Given that log_{64} x = 2/6, what is the value of x?  
Option 1 : 2  Option 2 : 4  Option 3 : 6  Option 4 : 8  


Ques 58 : Choose the correct answer.  
If 7^{x} = 85, what is the value of x?  
Option 1 : log_{7}85  Option 2 : log_{85}7  Option 3 : log_{10}7  Option 4 : log_{10}85  


Ques 59 : Choose the correct answer.  
If log_{10}2 = 0.3010, what is the number of digits in 2^{64}  
Option 1 : 19  Option 2 : 20  Option 3 : 18  Option 4 : None of these  


Ques 60 : Choose the correct answer.  
What is log_{1}10?  
Option 1 : 1  Option 2 : 10  Option 3 : 0  Option 4 : Tends to infinity  


Ques 61 : Choose the correct answer.  
What is log_{10}0 ?  
Option 1 : 0  Option 2 : 10  Option 3 : 1  Option 4 : Not defined  


Ques 62 : Choose the correct answer.  
What is the value of log_{3} (9)?  
Option 1 : 3  Option 2 : 1/3  Option 3 : 3  Option 4 : Not defined  


Ques 63 : Choose the correct answer.  
Rajeev multiplies a number by 10, the log (to base 10) of this number will change in what way?  
Option 1 : Increase by 10  Option 2 : Increase by 1  Option 3 : Multiplied by 10  Option 4 : None of these  


Ques 64 : Choose the correct answer.  
The logarithm of a very small positive number will tend to which of the following?  
Option 1 : 0  Option 2 : negative infinity  Option 3 : positive infinity  Option 4 : 1  


Ques 65 : Choose the correct answer.  
If n numbers are in geometric progression, the logarithm of the number will be in which of the following?  
Option 1 : Geometric Progression  Option 2 : Arithmetic Progression  Option 3 : Harmonic Progression  Option 4 : None of these  


Ques 66 : Choose the correct answer.  
Which of the following is equivalent to log(a + b) ?  
Option 1 : log a + log b  Option 2 : log a * log b  Option 3 : log a – log b  Option 4 : None of these  


Ques 67 : Choose the correct answer.  
What is the value of log_{3} (1/9) + log _{9} 81 ?  
Option 1 : 2  Option 2 : 2  Option 3 : 0  Option 4 : 4  


Ques 68 : Choose the correct answer.  
What is the value of log_{3} 1.5 + log_{3} 6 ?  
Option 1 : 2  Option 2 : 2.7  Option 3 : 1.8  Option 4 : None of these  


Ques 69 : Choose the correct answer.  
Which of the following is log_{8} x equivalent to?  
Option 1 : log_{2} (x/3)  Option 2 : log_{2} (3x)  Option 3 : (log_{2}x)/ 3  Option 4 : None of these  


Ques 70 : Choose the correct answer.  
If n numbers are in arithmetic progression, the logarithm of the number will be in which of the following?  
Option 1 : Exponentially  Option 2 : Linearly  Option 3 : Quadratically  Option 4 : None of these  


Ques 71 : Choose the correct answer.  
What is the value of log_{20} 1 ?  
Option 1 : 0  Option 2 : 1  Option 3 : 20  Option 4 : None of these  


Ques 72 : Choose the correct answer.  
The unit’s digit in the product (7^{71} x 6^{59} x 3^{65}) is  
Option 1 : 1  Option 2 : 2  Option 3 : 4  Option 4 : 6  


Ques 73 : Choose the correct answer.  
1.5^{2 }* 0.0225^{1/2} = ?  
Option 1 : 0.0375  Option 2 : 0.3375  Option 3 : 3.275  Option 4 : 32.75  


Ques 74 : Choose the correct answer.  
If x^{1/2} / 441^{1/2} = 0.02, the value of x is:  
Option 1 : 0.1764  Option 2 : 1.764  Option 3 : 1.64  Option 4 : 2.64  


Ques 75 : Choose the correct answer.  
The value of 2^{1/2} upto three places of decimal is  
Option 1 : 1.41  Option 2 : 1.412  Option 3 : 1.413  Option 4 : 1.414  


Ques 76 : Choose the correct answer.  
The value of (8^{25}– 8^{26}) is:  
Option 1 : 7 x 8^{25}  Option 2 : 7 x 8^{26}  Option 3 : 8 x 8^{26}  Option 4 : None of these  


Ques 77 : Choose the correct answer.  
If 2^{2n1} = (1 / 8^{n3}) then the value of n is:  
Option 1 : 3  Option 2 : 2  Option 3 : 0  Option 4 : 2  


Ques 78 : Choose the correct answer.  
If 2^{x} = 3^{y} = 6^{z}, then (1/x + 1/y + 1/z) is equal to: 

Option 1 : 0  Option 2 : 1  Option 3 : 3/2  Option 4 : 0.5  


Ques 79 : Choose the correct answer.  
What is the remainder when 17^{23} is divided by 16?  
Option 1 : 0  Option 2 : 1  Option 3 : 2  Option 4 : 3  


Ques 80 : Choose the correct answer.  
What will be the remainder when 13^{36} is divided by 2196?  
Option 1 : 0  Option 2 : 1  Option 3 : 12  Option 4 : 2195  


Ques 81 : Choose the correct answer.  
The roots of the equation 4^{x}3*2^{x+2}+32=0 would include  
Option 1 : 2, 3  Option 2 : 1, 2, 3  Option 3 : 1, 2  Option 4 : 4, 8  


Ques 82 : Choose the correct answer.  
If a^{x} =b, b^{y}=c and c^{z} =a, then the value of xyz is:  
Option 1 : 0  Option 2 : 1  Option 3 : 2  Option 4 : 3  


Ques 83 : Choose the correct answer.  
If x = 1+2^{1/2} and y=12^{1/2}, then x^{2}+y^{2} is –  
Option 1 : 2  Option 2 : 3  Option 3 : 6  Option 4 : 0  


Ques 84 : Choose the correct answer.  
If 4^{x+3} = 2^{x+7}, then the value of x is:  
Option 1 : 3  Option 2 : 2  Option 3 : 1  Option 4 : None of these  


Ques 85 : Choose the correct answer.  
2^{x+y} = 2*(2)^{1/2} and 2^{xy} = 2^{1/2},the value of x is:  
Option 1 : 1  Option 2 : 2  Option 3 : 3  Option 4 : 4  Option 5 : None of these 


Ques 86 : Choose the correct answer.  
If x = 8, y = 27, the value of (x^{4/3}+y^{2/3})^{1/2} is:  
Option 1 : 5  Option 2 : 6  Option 3 : 7  Option 4 : 8  Option 5 : None of these 


Ques 87 : Choose the correct answer.  
If x^{y} = y^{x} and x = 2y, the value of y is:  
Option 1 : 1  Option 2 : 2  Option 3 : 3  Option 4 : 4  Option 5 : None of these 


Ques 88 : Choose the correct answer.  
If 2^{x} * 3^{y} = 18 and 2^{2x} * 3^{y}= 36, the value of x is:  
Option 1 : 0  Option 2 : 1  Option 3 : 2  Option 4 : 3  Option 5 : None of these 


Ques 89 : Choose the correct answer.  
What is the value of 50^{0} ?  
Option 1 : 0  Option 2 : 1  Option 3 : 50  Option 4 : None of these  


Ques 90 : Choose the correct answer.  
What is the value of 6^{2} ?  
Option 1 : 1/36  Option 2 : 36  Option 3 : 36  Option 4 : None of these  


Ques 91 : Choose the correct answer.  
What is the value of 0^{10} ?  
Option 1 : 0  Option 2 : 1  Option 3 : 10  Option 4 : None of these  


Ques 92 : Choose the correct answer.  
What is the value of 25^{1.5} ?  
Option 1 : 325  Option 2 : 32.5  Option 3 : 125  Option 4 : None of these  


Ques 93 : Choose the correct answer.  
What is the value of (0.027)^{1/3}?  
Option 1 : 0.3  Option 2 : 0.03  Option 3 : 0.003  Option 4 : None of these  


Ques 94 : Choose the correct answer.  
What is the value of (0.016)^{1/4}?  
Option 1 : 0.2  Option 2 : 0.02  Option 3 : 0.002  Option 4 : None of these  


Ques 95 : Choose the correct answer.  
Walking 6/7th of his usual speed, a man is 12 minutes too late. The usual time taken by him to cover that distance is:  
Option 1 : 1 hour  Option 2 : 1 hr 12min  Option 3 : 1 hr 15 min  Option 4 : 1 hr 20 min  


Ques 96 : Choose the correct answer.  
A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively ?  
Option 1 : 2 : 1  Option 2 : 3 : 2  Option 3 : 8 : 3  Option 4 : Cannot be determined  Option 5 : None of these 


Ques 97 : Choose the correct answer.  
In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:  
Option 1 : 21 m  Option 2 : 26 m  Option 3 : 28 m  Option 4 : 29 m  


Ques 98 : Choose the correct answer.  
In a family, the father took 1/5 of the cake and he had 4 times as much as others had, then the family members are:  
Option 1 : 16  Option 2 : 17  Option 3 : 18  Option 4 : None of these  


Ques 99 : Choose the correct answer.  
The price of sugar is increased by 25%. In order not to increase the expenditure a lady must reduce her consumption by:  
Option 1 : 25%  Option 2 : 20%  Option 3 : 30%  Option 4 : None of these  


Ques 100 : Choose the correct answer.  
I read 3/8 of a book on one day, and 4/5 of the remainder on another day. If now there were 30 pages unread, the book contains:  
Option 1 : 240 pages  Option 2 : 230 pages  Option 3 : 340 pages  Option 4 : 140 pages  Option 5 : None of these 