
1 
What are last two digits of 7^{2008} 

A. 
21 

B. 
61 

C. 
01 

D. 
41 
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Correct answer is : C
Explanation 2008 is divisible by 2.. but doesn't have repeated last digits for multiples of 2
7^2=49
7^4=2401
let's check for multiples of 4
(7^4)^2=5764801
in the same way (7^4)^3 will also have last digit 01 because 01X01=01.
So the result of(7^4)^k will have last digit 01 for any +ve integer k because
01X01X01X............k times= 01
2008 is multiple of 4 so the answer is 01.
2 
How many integers greater than 999 but not greater than 4000 can be formed with digits 0, 1, 2, 3 and 4 if repetition of digit is allowed? 

A. 
499 

B. 
500 

C. 
375 

D. 
376 
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Correct answer is : D
Explanation in between 999 and 4000 means start from 1000 end with 4000
let consider numbers are wxyz
w contain 1,2,3 and 4, but 4 happens only at once the number is 4000
remaining xyz may have numbers 0 or 1 or 2 or 3 or 4
totally 5 chances for each digit
for xyz is 5*5*5=125
now wxyz, w have 3 chances mainly are 1 , 2 ,3
so 3*125=375
and another single condition is 4000
so finally 375+1=376 is answer
3 
The area of the circumscribing three circles of unit radius toching each other is: 

A. 
(Π/3)(2 + √3)^{2}


B. 
6Π(2 + √3)^{2}


C. 
3Π(2 + √3)^{2}


D. 
(Π/6)(2 + √3)^{2}

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Correct answer is : A
Explanation By joining three unit circles,we get equilateral triangle of 2units length.
As we should find the outer circle joining three circles the center will be center of triangle so radius = (circum radius of equilateral triangle + radius of circle)
R=1+2/√ 3
area= ∏r^2
=∏(1+2/√ 3)^2
=∏/3(2+√ 3)^2
4 
If x, y, z are in GP, then 1/(1 + log_{10}x), 1/(1 + log_{10}y) and 1/(1 + log_{10}z) will be in: 

A. 
AP 

B. 
GP 

C. 
HP 

D. 
Cannot be determined 
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Correct answer is : C
Explanation let x=a y=ar z=ar^2
log10 x + log10 z =2 log10 x + 2 log10r = 2log10 y
Therefore 1+log10x,1+log10y,1+log10z will be in A.P.
So ans is HP
5 
If p, q, r are three consecutive distinct natural numbers then the expressions (q + r  p)(p + r  q)(p + q  r) is 

A. 
Positive 

B. 
Negative 

C. 
Nonpositive 

D. 
Nonnegative 
