1. What is the remainder obtained when 2^156 is divided by 13???
1) 1 2) 6 3)11 4)none of these
2. what is 7^85/2402 ???
3. For
a company X the turnover (Rs. lakh) & profatiability (in %) are given
for the
year 2001 for its 5 diff. products.(profitability refers to returns
on investement
as a %) turnover
of co. X(productwise) profitability
C 15%
E 20%
the turnover of c increases by x%. if the profit generated at the same profitability is equal to the profit of E, find x.
a. 400%
b. 300%
c. 500%
d. none of these
3) A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 35 7/17(35 + 7/17) . What was the number erased?
(a) 7
(b)8
(c) 9
(d) None of these
Ans: 7,
4) Raju has 128 boxes with him. He has to put atleast 120 oranges in one box and 144 at the most. Find the least number of boxes which will have the same number of oranges.
(a) 5
(b) 103
(c) 6
(d) Cannot be determined
Ans: 104
C 15%
E 20%
the turnover of c increases by x%. if the profit generated at the same profitability is equal to the profit of E, find x.
a. 400%
b. 300%
c. 500%
d. none of these
3) A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 35 7/17(35 + 7/17) . What was the number erased?
(a) 7
(b)8
(c) 9
(d) None of these
Ans: 7,
4) Raju has 128 boxes with him. He has to put atleast 120 oranges in one box and 144 at the most. Find the least number of boxes which will have the same number of oranges.
(a) 5
(b) 103
(c) 6
(d) Cannot be determined
Ans: 104
5)
An urn contains a number of colored balls, with equal numbers of
each
color. Adding 20 balls of a new color to the urn would not change
the probability of drawing (without replacement) two balls of the
same color. How
many balls are in the urn? (Before the extra balls are added.)
a) 210
b) 95
c) 190
d) Data Insufficient
a) 210
b) 95
c) 190
d) Data Insufficient
6) A hexagon with consecutive sides of lengths 2, 2, 7, 7, 11, and 11 is inscribed in a circle. Find the radius of the circle.
a)
2
b) 7
c) 11
d) None of these
b) 7
c) 11
d) None of these
7. what is 1^2 - 2^2 + 3^2 - 4^2.......................+199^2
-200^2?
Ans. this can be written as ( E stands for Sigma )
n=0 n=0
E (2n+1)^2 - E (2n)^2,
99 100
Now, (2n+1)^2 = 4n^2 + 4n + 1 and 2n^2 = 4n^2, so, we will have
= -(2*100)^2 + E (4n + 1)
= -(2*100)^2 + 4*E (n + 1)
= -40000 + 99 + 4*99*100/2
= -40000 + 99 + 19800
= -20101
8. What is the sum of the series till 3n
Series...1 + 3 - 5 + 7 + 9 -11+ 13 + 15 - 17
Ans. take 3 terms at once, and we will have,
(1+3-5) + (7+9-11) + (13+15-17) + .....
= -1 + 5 + 11 + ....
this is clearly in 3x-1 form, where x is varying from 0 to n ( as we have 3n
terms ) thus,
= E (3x-1)
= 3*(E x) - E 1
= 3*n(n+1)/2 - n
= (3n^2 + 3n - 2n )/2
= (3n^2 + n)/2
Ans. this can be written as ( E stands for Sigma )
n=0 n=0
E (2n+1)^2 - E (2n)^2,
99 100
Now, (2n+1)^2 = 4n^2 + 4n + 1 and 2n^2 = 4n^2, so, we will have
= -(2*100)^2 + E (4n + 1)
= -(2*100)^2 + 4*E (n + 1)
= -40000 + 99 + 4*99*100/2
= -40000 + 99 + 19800
= -20101
8. What is the sum of the series till 3n
Series...1 + 3 - 5 + 7 + 9 -11+ 13 + 15 - 17
Ans. take 3 terms at once, and we will have,
(1+3-5) + (7+9-11) + (13+15-17) + .....
= -1 + 5 + 11 + ....
this is clearly in 3x-1 form, where x is varying from 0 to n ( as we have 3n
terms ) thus,
= E (3x-1)
= 3*(E x) - E 1
= 3*n(n+1)/2 - n
= (3n^2 + 3n - 2n )/2
= (3n^2 + n)/2
9)
A rectangle is such that it can be perfectly cut into
smaller squares of a maximum possible side of
length
12 units. It is also known that the perimeter of
such a rectangle is 384 units.
The maximum possible number of squares of side 5 units that can be cut out of any such rectangle is
1) 72 2) 361 3) 336 4) Cant say
10) Amar transport corporation has five trucks each of which can carry 10 tonnes. The schedule of the trucks
is such that the first truck leaves every day, the second leaves every alternate day; the third every third day & so on. Find out how many days in the year 2000 at least four trucks left on the same day (Assume that all the trucks left for the first time on the 1st of Jan 2000)
1)49 2)60 3)63 4)70
11) If in a mixture of Alchohal and Milk say A the ratio of alch to milk is 5:7 and in another mixture say B the ratio of alch to milk is 6:8 then what is the ratio in which these two must be taken to get a mixture with alch to milk ratio as 1:1
The maximum possible number of squares of side 5 units that can be cut out of any such rectangle is
1) 72 2) 361 3) 336 4) Cant say
10) Amar transport corporation has five trucks each of which can carry 10 tonnes. The schedule of the trucks
is such that the first truck leaves every day, the second leaves every alternate day; the third every third day & so on. Find out how many days in the year 2000 at least four trucks left on the same day (Assume that all the trucks left for the first time on the 1st of Jan 2000)
1)49 2)60 3)63 4)70
11) If in a mixture of Alchohal and Milk say A the ratio of alch to milk is 5:7 and in another mixture say B the ratio of alch to milk is 6:8 then what is the ratio in which these two must be taken to get a mixture with alch to milk ratio as 1:1
12) Compute
x if x = 1/1*2 + 1/2*3 + 1/3*4 + ....+ 1/(n-1)*n +
1/n*(n+1)
a) n/(n-1)
b) 2n/(n+1)
c) n/(n+1)
d) None of these
1/n*(n+1)
a) n/(n-1)
b) 2n/(n+1)
c) n/(n+1)
d) None of these
13) What is the Unit digit of 7^5^6^13 ?
Ans. 9
Ans. 9
14)There is a work to be done by three friends A,B,C. Three of them together take 5 hours less than A alone would have taken,one-third that B alone would have taken and two-ninths the time C alone would have taken. How long does the three them take to finish the work?
(a) 3 hrs
(b) 4 hrs
(c) 5 hrs
(d) None of these
15)
a seven digit number 6a5b4c8 is divisible by 72 and a+b <= 5. Then
what is
the maximum value of (a+b+c)^2 ?
16) a six digit number is formed by writing 3 consecutive two digit number side by side in ascending order. If the number so formed is divisible by 2,3,4,5,6,8, then what is the hundreds digit of the number?
17) A & B are running on a circular track with speeds in ratio of 5:3. If the distance covered in one round is 3/2 km, what is the distance covered by A when he corsses B for the 7th time?
18) General Elan Periasamy Thirumaran ( only to confuse you ;-) ) has decided to go for a trip from HYD to GOA and comeback in his CAR. The total distance covered is 2000 KM. Now if he uses all the five tires ( including stepney ) equally, what is the distance covered by each tire.
19) What is the max. no of equilateral triangles that can be formed from using 13 match sticks?
20) In a book there a 700 pages numbered from 1 to 700. How many 3's one will find if he starts from page 1 to page 700?
16) a six digit number is formed by writing 3 consecutive two digit number side by side in ascending order. If the number so formed is divisible by 2,3,4,5,6,8, then what is the hundreds digit of the number?
17) A & B are running on a circular track with speeds in ratio of 5:3. If the distance covered in one round is 3/2 km, what is the distance covered by A when he corsses B for the 7th time?
18) General Elan Periasamy Thirumaran ( only to confuse you ;-) ) has decided to go for a trip from HYD to GOA and comeback in his CAR. The total distance covered is 2000 KM. Now if he uses all the five tires ( including stepney ) equally, what is the distance covered by each tire.
19) What is the max. no of equilateral triangles that can be formed from using 13 match sticks?
20) In a book there a 700 pages numbered from 1 to 700. How many 3's one will find if he starts from page 1 to page 700?
21) A
person starts from the origin of the coordinate axis . He travels
in this
pattern . 1 unit to right , (1/2) units up , (1/4) units right,
(1/8) units
down , and continues the above pattern . At what point will
he ultimately
come to stop?
(a) (4/3,2/5) (b) (3/2,4/3) (c) (2/5,4/3) (d) (4/5,4/3)
ANS: (a)
22) Given that 'a' and 'b' are positive integers and 'a' is not equal to 'b' and (4^a+1 (4^b+1)=3^c+1 find the value of a^b+b^a
(a)-1 (b) 0 (c) 1 (d) indeterminate
ANS: (d) inderminate
23) A set S consists of 12 distinct elements a1,a2,...,a12. How many subsets can be made of S with the restriction that the subscripts of elements in any subset starting from the second element is an integral multiple of the subscript of the first element.
eg: if the 1st element is a1, we could have the set as {a1, a2 , a3..} if the 1st element is a2, we could have the set as {a4 , a6..}
(a) 1221 (b) 2112 (c) 2101 (d) 2102
ANS:the total is, 2048 + 32 + 8 + 4 + 2 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 2102
24) Pagal-guy and the Don play roulette. Each has his own roulette. Pagal-guy's roulette is a circle divided into 3 equal sectors with the values 0 , 1 , 2 . He plays thrice and X is the sum of these values. The Don's roulette is a circle divided into 6 equal sectors with the values 1, 2, 3 , 4 , 5 , 6 . He plays only once and this value is Y. Given that Probability(Y>X)=0.5 find probability(Y<X)
(a) 75/73 (b) 55/162 (c) 67/128 (d) 1/2
ANS: 55/162
25. Ramu is given Rs 382 in one-rupee coins. He has been asked to allocate them into a number of bags such that any amount required between Re 1 and Rs 382 can be given by just handling out a certain number of bags without opening any of them. What is the minimum number of bags possible?
(a) (4/3,2/5) (b) (3/2,4/3) (c) (2/5,4/3) (d) (4/5,4/3)
ANS: (a)
22) Given that 'a' and 'b' are positive integers and 'a' is not equal to 'b' and (4^a+1 (4^b+1)=3^c+1 find the value of a^b+b^a
(a)-1 (b) 0 (c) 1 (d) indeterminate
ANS: (d) inderminate
23) A set S consists of 12 distinct elements a1,a2,...,a12. How many subsets can be made of S with the restriction that the subscripts of elements in any subset starting from the second element is an integral multiple of the subscript of the first element.
eg: if the 1st element is a1, we could have the set as {a1, a2 , a3..} if the 1st element is a2, we could have the set as {a4 , a6..}
(a) 1221 (b) 2112 (c) 2101 (d) 2102
ANS:the total is, 2048 + 32 + 8 + 4 + 2 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 2102
24) Pagal-guy and the Don play roulette. Each has his own roulette. Pagal-guy's roulette is a circle divided into 3 equal sectors with the values 0 , 1 , 2 . He plays thrice and X is the sum of these values. The Don's roulette is a circle divided into 6 equal sectors with the values 1, 2, 3 , 4 , 5 , 6 . He plays only once and this value is Y. Given that Probability(Y>X)=0.5 find probability(Y<X)
(a) 75/73 (b) 55/162 (c) 67/128 (d) 1/2
ANS: 55/162
25. Ramu is given Rs 382 in one-rupee coins. He has been asked to allocate them into a number of bags such that any amount required between Re 1 and Rs 382 can be given by just handling out a certain number of bags without opening any of them. What is the minimum number of bags possible?
a) 15
b) 13
c) 11
d) 17
Answer : (A)
26) What is the remainder when (2222)^5555 + (5555)^2222 is divided by 7?
a) 3
b) 5
c) 6
d) 0
Answer: (D)
b) 13
c) 11
d) 17
Answer : (A)
26) What is the remainder when (2222)^5555 + (5555)^2222 is divided by 7?
a) 3
b) 5
c) 6
d) 0
Answer: (D)
27) ABC is a
triangle. AD is perpendicular to BC. AM bisects angle
BAC. What is the measure of angle DAM ?
28) if x = 777...777 ( 101 7 are there ) then what is x mod 440 ?
Ans
: 332,
29) if x^2
+ y^2 - 4x - 6y + 13 = 0, then what is x:y?
30)
The first term of an AP is 10 and its 11th term is 40, then what is
the sum of squares of the first 20 terms of the series?
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