December 30, 2019
Placement Written test paper for MNC  Math questions and answers Part –6
Ques 251 : Choose the correct answer.  
If a, b, c, d, e are five consecutive odd numbers, their average is:  
Option 1 : 5 (a + 4)  Option 2 : (abcde/5)  Option 3 : 5 (a + b + c + d + e)  Option 4 : None of these  


Ques 252 : Choose the correct answer.  
(x % of 932) + 30 = 309.6 Find x. 

Option 1 : 25  Option 2 : 30  Option 3 : 35  Option 4 : 40  


Ques 253 : Choose the correct answer.  
Which of the following multipliers will cause a number to be increased by 29.7% ?  
Option 1 : 1.297  Option 2 : 12.97  Option 3 : 129.7  Option 4 : 1297  


Ques 254 : Choose the correct answer.  
If 2A = 3B and 4B = 5C, then A: C is:  
Option 1 : 4 : 3  Option 2 : 8 : 15  Option 3 : 15 : 8  Option 4 : 3 : 4  


Ques 255 : Choose the correct answer.  
0.4777 . . . is the recurring decimal for the fraction:  
Option 1 : 4777/100000  Option 2 : 477/100  Option 3 : 437/1000  Option 4 : 43/90  


Ques 256 : Choose the correct answer.  
0.8888 ÷ 0.011 is equal to:  
Option 1 : 8.08  Option 2 : 80.8  Option 3 : 0.808  Option 4 : None of these  


Ques 257 : Choose the correct answer.  
The ascending order of rational numbers 7/10, 5/8, 2/3 is:  
Option 1 : 7/10, 2/3, 5/8  Option 2 : 7/10, 5/8, 2/3  Option 3 : 5/8, 7/10, 2/3  Option 4 : 2/3, 5/8, 7/10  


Ques 258 : Choose the correct answer.  
If A is real and 1 + A + A^{2} + A^{3} = 40, then A is equal to:  
Option 1 : 3  Option 2 : 1  Option 3 : 1  Option 4 : 3  


Ques 259 : Choose the correct answer.  
(1 + 3 + 5 + … + 3983) / 1992 = ?  
Option 1 : 1988  Option 2 : 1992  Option 3 : 1990  Option 4 : None of these  


Ques 260 : Choose the correct answer.  
Which one of the following should be added to 25p^{2} + 16q^{2}, so that the resulting sum becomes a perfect square?  
Option 1 : 20pq  Option 2 : 30pq  Option 3 : 40pq  Option 4 : 50p^{2}q^{2}  


Ques 261 : Choose the correct answer.  
(1.0816) ^{1/2}= ?  
Option 1 : 0.14  Option 2 : 1.4  Option 3 : 1.004  Option 4 : 1.04  


Ques 262 : Choose the correct answer.  
If the digit in the units place of a square natural number is 6, then the digit in the tens place will be:  
Option 1 : 1  Option 2 : 3  Option 3 : Even  Option 4 : Odd  


Ques 263 : Choose the correct answer.  
(a+b)^{3}(ab)^{3} can be factorized as:  
Option 1 : 2b(3a^{2}+b^{2})  Option 2 : 2a(3a^{2}+b^{2})  Option 3 : 2b(3b^{2}+a^{2})  Option 4 : 2a(a^{2}+3b^{2})  


Ques 264 : Choose the correct answer.  
If 9x^{2}+3px+6q when divide by 3x+1 leaves a remainder 3/4 and qx^{2}+4px+7 is exactly divisible by x+1, then the values of p and q respectively will be:  
Option 1 : 0, 7/4  Option 2 : 7/4, 0  Option 3 : Same  Option 4 : 7/4, 0  


Ques 265 : Choose the correct answer.  
The equations 2x+3y7=0 and 10x+15y35=0 are:  
Option 1 : Consistent and have unique solution  Option 2 : Consistent and have infinitely many solutions  Option 3 : inconsistent  Option 4 : none of these  


Ques 266 : Choose the correct answer.  
The solution of the simultaneous equations (1/2)x + (1/3)y = 2 and x+y=1 is:  
Option 1 : x = 0, y = 1  Option 2 : x = 1, y = 0  Option 3 : x = 2/3, y = 3/2  Option 4 : x = 10, y = 9  


Ques 267 : Choose the correct answer.  
If the equation x^{2}2(k+1)x+(9/2)k=0 has two identical roots then the values of k are:  
Option 1 : k=1, 2  Option 2 : k=2 or 1/2  Option 3 : k=3, 1/2  Option 4 : none of these  


Ques 268 : Choose the correct answer.  
The number which should be subtracted from 5a^{2}3ab+7b^{2} to make it equal to a^{2}+ab+b^{2}, is:  
Option 1 : 4a^{2}4ab+6b^{2}  Option 2 : 4a^{2}4ab+5b^{2}  Option 3 : 4a^{2}+4ab+6b^{2}  Option 4 : 4a^{2}3ab+6b^{2}  Option 5 : None of these 


Ques 269 : Choose the correct answer.  
If x = (1/2) (2p+2qr), y = (1/3) (p2q+3r) and z=(1/5) (3p4r+5q), then the value of 2x3y5z is:  
Option 1 : 0  Option 2 : q  Option 3 : 2  Option 4 : None of these  


Ques 270 : Choose the correct answer.  
The roots of the quadratic equation 6x^{2}5x+1=0 are:  
Option 1 : 2,3  Option 2 : 1/2,1/3  Option 3 : 3,4  Option 4 : 1/3,1/4  Option 5 : None of these 


Ques 271 : Choose the correct answer.  
If a = 16, b=25, the value of 1/(a^{1/2} – b^{1/2}) is:  
Option 1 : 10  Option 2 : 15  Option 3 : 20  Option 4 : 25  Option 5 : 30 


Ques 272 : Choose the correct answer.  
3a^{2} (ab+bc+ca) =  
Option 1 : 3a^{2}+3a^{2}bc+3a^{3}c  Option 2 : 3a^{3}b+3a^{2}bc+3c  Option 3 : 3a^{3}b+3a^{2}bc+3a^{3}c  Option 4 : a^{3}b+abc+a^{2}c  Option 5 : None of these 


Ques 273 : Choose the correct answer.  
x^{4}yxy^{4} =  
Option 1 : xy(xy)(x^{2 }+ xy + y^{2})  Option 2 : xy(x+y)(x^{2}xy+y^{4})  Option 3 : x(xy1)(x^{2}xy+y)  Option 4 : (x^{3}+y^{2})xy  Option 5 : None of these 


Ques 274 : Choose the correct answer.  
Factors of 6a^{2}25a+4 are:  
Option 1 : (a+4) (a6)  Option 2 : (a4) (6a+1)  Option 3 : (a4)(6a1)  Option 4 : (a6) (a4)  Option 5 : None of these 


Ques 275 : Choose the correct answer.  
The correct relationship after eliminating x, y and z from x+y = a, y+z=b and z+x = c and x+y+z = m, is:  
Option 1 : m=x+y+z  Option 2 : 2m=a+b+c  Option 3 : m=xyz  Option 4 : 2m=xyz  Option 5 : None of these 


Ques 276 : Choose the correct answer.  
If r = at^{2} and s = 2at, the relation among s, r and a is:  
Option 1 : s^{2}=4ar  Option 2 : s=ar  Option 3 : s=2ar  Option 4 : s^{2}=ar  Option 5 : None of these 


Ques 277 : Choose the correct answer.  
If a+b=6, ab=5, the value of ab is:  
Option 1 : 4  Option 2 : 5  Option 3 : 6  Option 4 : 7  Option 5 : 9 


Ques 278 : Choose the correct answer.  
X – 5 + 4 > 0 and X^{2} < 4. Then x can be:  
Option 1 : 4  Option 2 : 2  Option 3 : 0.5  Option 4 : All of these  


Ques 279 : Choose the correct answer.  
If f(x) = sum of all the digits of x, where x is a natural number, then what is the value of f(101)+f(102)+f(103)+ .. +f(200)?  
Option 1 : 1000  Option 2 : 784  Option 3 : 999  Option 4 : 1001  


Ques 280 : Choose the correct answer.  
Pawan is a very confused person. Once he wrote 1+2+3+4+5+6+7+8+9+10 = 100. In how many places you need to change ‘+’ with ‘ * ‘ to make the equality hold good ?  
Option 1 : 2  Option 2 : 4  Option 3 : 3  Option 4 : None of these  


Ques 281 : Choose the correct answer.  
What is the highest power of 82 contained in 83!82! ?  
Option 1 : 3  Option 2 : 2  Option 3 : 164  Option 4 : None of these  


Ques 282 : Choose the correct answer.  
If x = 0.75, then what is the value of the expression (1+x+x^{2}) + x^{3}/(1x) ?  
Option 1 : 0.25  Option 2 : 4  Option 3 : 1.75  Option 4 : 1  


Ques 283 : Choose the correct answer.  
If a lies between 2 and 3, both included, and b lies between 4 and 6, both included, then what is the ratio of minimum and maximum limits of a^{2}b^{2}?  
Option 1 : 4  Option 2 : 4  Option 3 : 32/7  Option 4 : – 28/6  


Ques 284 : Choose the correct answer.  
If a, b, c are roots of the equation 1x^{3}4x^{2}+6.5x + 3.5 = 0, then what is the value of a^{2} + b^{2} + c^{2}?  
Option 1 : 1  Option 2 : 64  Option 3 : 169  Option 4 : 3  


Ques 285 : Choose the correct answer.  
If x + y = 7, then what is the sum of minimum and maximum values of x + y?  
Option 1 : 3/2  Option 2 : 7  Option 3 : 7  Option 4 : 0  


Ques 286 : Choose the correct answer.  
832.58242.31 =779.84 ?  
Option 1 : 179.57  Option 2 : 199.57  Option 3 : 295.05  Option 4 : None of these  


Ques 287 : Choose the correct answer.  
Which is the closest approximation to the product 0.3333 * 0.25 * 0.499 * 0.125 * 24 ?  
Option 1 : 1/8  Option 2 : 3/4  Option 3 : 3/8  Option 4 : 2/5  


Ques 288 : Choose the correct answer.  
The simplification of (0.2 * 0.2 + 0.02 * 0.02 – 0.4 * 0.02) / 0.36  
Option 1 : 0.009  Option 2 : 0.09  Option 3 : 0.9  Option 4 : 9  


Ques 289 : Choose the correct answer.  
If 1^{3} + 2^{3}+ 3^{3}+ ……….+ 9^{3} = 2025 ,then the value of (0.11)^{3} + (0.22)^{3} + ….+ (0.99^{)3} is close to:  
Option 1 : 0.2695  Option 2 : 0.3695  Option 3 : 2.695  Option 4 : 3.695  


Ques 290 : Choose the correct answer.  
In a purse there are 30 coins, twenty onerupee and remaining 50paise coins. Eleven coins are picked simultaneously at random and are placed in a box. If a coin is now picked from the box, find the probability of it being a rupee coin?  
Option 1 : 4/7  Option 2 : 1/2  Option 3 : 2/3  Option 4 : 5/6  


Ques 291 : Choose the correct answer.  
A, B and C are three students who attend the same tutorial classes. If the probability that on a particular day exactly one out of A and B attends the class is 7/10; exactly one out of B and C attends is 4/10; exactly one out of C and A attends is 7/10. I  
Option 1 : 46/100  Option 2 : 63/100  Option 3 : 74/100  Option 4 : 99/100  


Ques 292 : Choose the correct answer.  
A box contains 10 balls numbered 1 through 10. Anuj, Anisha and Amit pick a ball each, one after the other, each time replacing the ball. What is the probability that Anuj picks a ball numbered less than that picked by Anisha, who in turn picks a lesser n  
Option 1 : 3/25  Option 2 : 1/6  Option 3 : 4/25  Option 4 : 81/400  


Ques 293 : Choose the correct answer.  
A biased die has a probability of 1/4 of showing a 5, while the probability of any of 1, 2, 3, 4, or 6 turning up is the same . If three such dice are rolled, what is the probability of getting a sum of atleast 14 without getting a 6 on any die ?  
Option 1 : 5/24  Option 2 : 9/160  Option 3 : 1/30  Option 4 : 7/160  


Ques 294 : Choose the correct answer.  
A, B, C, D and E play the following game. Each person picks one card from cards numbered 1 through 10. The person who picks the greatest numbered card loses and is out of the game. Now the remaining four return their cards to the pack and draw again, and  
Option 1 : 3/14  Option 2 : 4/17  Option 3 : 1/5  Option 4 : 5/24  


Ques 295 : Choose the correct answer.  
Which among the following is greatest: 5^{1/2}, 11^{1/3}, 123^{1/6} ?  
Option 1 : 5^{1/2}  Option 2 : 11^{1/3}  Option 3 : 123^{1/6}  Option 4 : All are equal  


Ques 296 : Choose the correct answer.  
What are the unit’s digits of 3^{69}, 6^{864}, 4^{725} respectively ?  
Option 1 : 9,6 and 6  Option 2 : 6, 6 and 6  Option 3 : 3,6 and 4  Option 4 : None of these  


Ques 297 : Choose the correct answer.  
A = 1^{1} * 2^{2} * 3^{3} * 4^{4 }* 5^{5} * ……..10^{10}. How many zeroes will be there at the end of A ?  
Option 1 : 6  Option 2 : 15  Option 3 : 10  Option 4 : None of these  


Ques 298 : Choose the correct answer.  
If x = 3 + 3^{1/2}, then what is the value of x^{2 }+ 9/x^{2} ?  
Option 1 : 15 + 3 * 3^{1/2}  Option 2 : 18 + 3 * 3^{1/2}  Option 3 : 27 + 3 * 3^{1/2}  Option 4 : None of these  


Ques 299 : Choose the correct answer.  
If x^{4} + 1/x^{4} = 47, then find the value of x^{3} + 1/x^{3}  
Option 1 : 18  Option 2 : 27  Option 3 : 9  Option 4 : 12  


Ques 300 : Choose the correct answer.  
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:  
Option 1 : 1  Option 2 : 2  Option 3 : 3  Option 4 : 4 