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21. P ( x ) = ( x999 + x998 + x997 + . . . . + x + 1)2 - x999Q ( x ) = x998 + x 997 + . . . . + x + 1The reminder when P ( x ) is divided by Q ( x ) is
Answer: Option B
Explanation:Solution: ((x^999 x^998 ... x 1)^2-x^999)/(x^998 x^997 ... x 1)
=> ((x^999 x^998 ... x 1)^2-x^999)/(x^999 x^998 ... x 1)-x^999 or,
=>(x^998 ... x 2)^2-1/(x^998 ... x 2)-1 [taking x^999 as common and cancelling it]
we can now use the identity a^2-b^2=(a b)*(a-b)
using this we can see that p(x) is clearly divisible by q(x)
i.e. p(x)/q(x)= (x^999 x^998 ... x 1) x^999
so the remainder will be 0
Workspace
Tags: TCS
22. In this question, A^B means A raised to power B. If x^2*y*z < 0, then which one of the following statements must also be true?
I. yz < 0
II. z < 0
III. x < 0
Answer: Option A
Explanation:Solution: x^2 will always be positive no matter whatever be the value of x
So to satisfy this condition x^2*y*z < 0 => yz<0 because x^2 will always be positive.
Workspace
Tags: TCS
23. What is the value of (222224*444445*222221+666668)/222222^2
Answer: Option B
Explanation:Let 222222 =x now the expression becomes
(((x+2)*(2x+1)*(x-1)) (3x+2))/x^2
Now solve it by algebra multiplication,addition and division.
we will get 2x+3 i.e 444447
Workspace
Tags: TCS
24. What is the unit's digit of 21^3 *21^2*34^7*46^8*77^8 ?
25. What is the value of ( (x^2012 + x^2011 +.........+ x+1)^2 - x^2012) / (x^2011 +x^2010..........+x+1)
26. If pq=28 where p and q are whole numbers then which of the following will be (p2 - q2)?
Answer: Option C
Explanation:Solution: pq=28
So possible factors of 28 are (1,28) (7,4) (14,2)
Now going for option verification with the factors we get 28^2-1^2 = 783 hence option c is the answer.
Workspace
Tags: IBM
27. what is vale of a if a is integer?
1. a^4=1
2. a^3+1=0
Answer: Option A
Explanation:a^3+1=0=> a^3=-1
if a^3 is -1 then a must be (-1)^3=-1
(-1)^4 = 1
=> a=-1.
Workspace
Tags: Wipro
28. If the operation,^ is defined by the equation x ^ y = 2x + y,what is the value of 'a' in 2 ^ a = a ^ 3 ?
Answer: Option D
Explanation:2^a = 2*2 + a ......(i)
=> a^3 = 2*a + 3 .....(ii)
=> 4 + a = 2a + 3
=> a=1.
Workspace
Tags: Wipro
29. Company A rented a truck $1000 per month. company B purchased the same type of truck for $35000.in addition company B paid $120 monthly maintenance charges. What is relative cost to the competing company for this type of truck after 6 years of operation.
Answer: Option A
Explanation:A's total cost to be spent for 6 years= 6*12*1000 = Rs 72,000
B's total cost + monthly maintenance = 35000+(6*12*120) = Rs 43,640
Relative cost= 72000-43640
= Rs. 28,360
Workspace
Tags: IBM
30. As a mean encouraging company employee to use public transportation,employee is offer a $0.60 per side discount bus fare. John has spend $30000 per week from monday to friday.How much cost pay after the discount?
Answer: Option B
Explanation:Employee is offered discount per side = $0.60.
So both side total disccount = $0.60*2 = $1.20
So, for 5 days = 1.20*5= $6
Total amout = (30000-6) = $29994
Workspace
Tags: IBM