**Q.1 ) Raju drives slowly along the perimeter of a rectangular park at 24 kmph and completes one full round in 4 minutes. If the ratio of the length to the breadth of the park is 3:2, what are its dimensions?**

**a) 480m x 320m**

**b) 150m x 100m**

**c) 450m x 300m**

**d) 100m x 100m**

**Q.2 )What is the reminder when 6 ^ 17 + 17 ^ 6 is divided by 7?**

**a) 0**

**b) 1**

**c) 3**

**d) 6**

**Q.3) 22. How many divisors (including 1, but excluding 1000) are there for the number 1000?**

**a) 15**

**b) 16**

**c) 31**

**d) 10**

**Q. 4 ) In the polynomial f(x) =2*x^4 – 49*x^2 +54, what is the product of the roots, and what is the**

**sum of the roots (Note that x^n denotes the x raised to the power n, or x multiplied by itself n**

**times)?**

**a) 27,0**

**b) 54,2**

**c) 49/2, 54**

**d) 49,27**

**Q.5) Let f(m,n) =36*m + 24*n, where m and n are integers (positive or negative) What is the minimum positive value for f(m,n) for all values of m,n (this may be achieved for various values of m and n)?**

**a)9**

**b)6**

**c)5**

**d)12**

**Q.6) What is the maximum value of x3y3 + 3 x*y when x+y = 8?**

**a)4144**

**b)256**

**c)8192**

**d)102**

**Q.7) If f(x) = 2x+2 what is f(f(f(3)))?**

**a)18**

**b)8**

**c)38**

**d)16**

**Q.8 ) What are the total number of divisors of 1728(including 1 and 1728)?**

**a)24**

**b)25**

**c)26**

**d)28**

**Q.9 )What is the sum of the cube of the first 20 natural numbers (1 to 20)?**

**a)2870**

**b)2000**

**c)5650**

**d)44100**

**Q.10) If the price of an Petrol is decreased by 32% and then increased by 38%, the net effect on the price of the item is**

**a) A decrease of 1.66%**

**b) No change**

**c) A increment of 1%**

**d) An increase of 82.16%**

**Q.11) Find the number of trailing zeros in 120!**

**Q.12) In a rectangular coordinate system, what is the area of a triangle whose vertices whose vertices have the coordinates (4,0), (6, 3) adn (6 , -3)**

**a) 6**

**b) 7**

**c) 7.5**

**d) 6.5**

**Q.13) If the sum of factors of a number P is 60 , and the sum of reciprocal of factors is 5/2 .Find the number.**

**Q.14) Find the highest power of 2 in 10!**

**Q.15) Find the reminder when 3^75 is divided by 5.**

**Q.16 ) How many prime numbers between 1 and 100 are factors of 7150?**

** a)5**

**b)6**

** c)4**

**d)24**

**Q.17) If N= 70P, where P is a prime number greater than 2, how many different positive divisors does n have including n?**

**Q.18) a, b, c are non negitive integers such that 28a+30b+31c = 365. a + b + c = ?**

**a) Greater than 14**

**b) less than or equal to 11**

**c) 13**

**d) 12**

**Q.19 )Find the last digit of 847187569^12345678**

**Q.20 ) If a number is divided by a divisor , it leaves a remainder of 9 .When twice the same number is divided by same divisor , the remainder is 5 . Find the divisor**

** a) 23**

**b) 13**

**c)14**

**d) 17**

**Q.21) Two consecutive numbers are removed from the progression 1, 2, 3, …n. The arithmetic mean of the remaining numbers is 26 1/4. The value of n is**

a. 60 |
b.81 |

c. 50 |
d. Cannot be determined |

**Q.22) If 41895A8 is divisible by 44 . Find the value of A.**