1) Balki has got a 7 digit phone number. It is like this, Digit 1 appears exactly once the other 6 digit are essentially 3 non zero digit each appearing twice. How many trails are required to find the number corretly by Balki?
2) If the price of essential commodities goes up by 30 % and spending by only 10% then what is the reduction in the quantities of essential commodieties bought by a household?
3) maximum power of 20 which will divide 100! is
a) 24, b)20 c)22 d) 30
4. Integer such that when one divides n and n^3 , the remainders are `a' and `b' respectively.
Then how many different values can b-a have?
5) A three digit number is of the form 1! + 2! +3! ..................n! and is also equal to the sum
of the cubes of all its digits. What is the minimum value of 'n'?
n = 5, 1 + 2 + 6 + 24 + 120 = 153
1^3 + 5^3 + 3^3 = 153
6) Find the number of digits in (15)321.
Ans. 377.
(lets assume x = 15^321 then, log x = 321 * log 15 and that is 377)
7) After division of a number by 3,4,7 the remainders are 2,1,4 respectively. What will be the remainder if 84 divides the same number? {Options}
a) 80 b) 53 c) 79 d) 81
8) 76n- 56n where n>0 is divisible by,
a) 13 b) 127 c) 559 d) None of the above
9) Find the square root of 3+4i.
ANS : 2+i
10) There is a cube in which one pair of opposite faces is painted red; a second pair of opposite faces is painted blue, the third pair painted green. This cube is now cut into 216 smaller but identical cubes.
a) How many small cubes are there with no red paint at all?
b) How many small cubes are there with at least two different colors on their faces?
c) How many small cubes are there without any face painted?
d) How many small cubes are there with only red and green on their faces?
e) How many small cubes are there showing only green or blue on their faces?
216 = 6^3, so each side is divided in to 6 equal parts.
now answers,
a) small cubes without no red paint at all : 144 on each side which has red paint on it we will have 36 cubelets, 216 - 36*2 = 144
b) small cubes with atleast 2 diff colors on theie faces : 56
exactly 2 colors = no.Of edges * (6-2) = 12 * 4 = 48
exactly 3 colors = no Of corners = 8 , so the answer is 56
c) small cubes without nay face painted : (6-2)^3 = 64
d) cubes with onl RED and GREEN on their faces : 8
e) small cubes showing only green OR blue on their faces : 64
only Green : 2 * (6-2)^2 = 32
only Blue : -do- = 32
so, the answer is 64
11) A watermelon weighs 5000gms .99% of its weight is water.It is kept in a drying room and after some time it turns out that it is only 98% by weight.What is its weight now???
a) 2500 2) 4500 3) 4950 4) none
ANS : 3) 4950
12) What are the least & greatest nos. which when divided by 5, 7, 9 leave remainders 1, 2 & 3 respectively?
13) A number is formed by writing first 24 natural numbers.what will be the remainder when this is divided by 9 ?
Ans: 3
14) What should be least value of n such that n! is divisible by 990 ?
Ans: 11
15) If 10 parallel lines intersect 9 parallel lines then what is the no of paralellograms thus formed?
16) In wht ratio one shd mix two sollutions of water & alchohol in respective ratios of 2:3 and 4:5 to get a sollution of w:a as 5:7
17) In the lone village called krathardhamandala of arthagrahamandala state there lies this smart school going kid, who has a pencil box of volume 100 cu. cm. What is the maximum length of the pencil that can fit in such a box.
18) If a^b + b^a = 145, and a,b are positive ints, then howmany such pairs are possible ?
19) What is the number of ending zeros in 1^1 * 2^2 * 3^3........ 99^99* 100^100.
a. 1050
b. 1300
c. 1250
d. None of these.
20) What is the number of numbers in between 100 and 400 divisible by 2,3,5 and 7.
Ans: 1.
21) A man can buy 10 kg more rice when the price of reduces by 10%. If the price increases by 12.5%, how much less can he buy for Rs. 1800. What was the original price?
a. 15kg, Rs. 12
b. 10kg, Rs. 20
c. 9kg,Rs.20
d.12 kg, rs.15
e. insufficent data
22) A cistern can be filled separately by two pipes A and B in 40 minutes and 30 minutes resp. A tap C at the bottom can empty the full cistern in 60 mins. Taps A and B are opened at 3.10pm and tap Cis opened 10 minutes later. find when the cistern will b full.
a. 4.00 pm
b. 3.40pm
c. 3.20pm
d. 3.30pm
e.none of these
23) the ratio of milk to water in a mixture is 9:1. some water is mixed in it and now the new mixture contains 80% milk. If the initial mixture was 2 litres, how much water is mixed?
a.250ml
b.300ml
c.400ml
d.500 ml
24) Karim wants to donate hens to 14 fakirs, cows among 11 Brahmins and some goats to 12 churches. At the market he finds with every cow he is getting the hen free and also a discount on the purchase of one goat. Hence he decides to buy equal number of cows and goat. what is the minimum number of cows or goats that he should buy so that he is left with enough to gift a cow,a hen, and a goat to each of his 5 sisters. How many cows does karim gift to each brahmin?
a. 924,12
b. 924,80
c. 929,12
d.929, 84
e. none of these
25) A Candle Burns in 6 Hrs..Another Candle of the same height and width burns in 8 Hrs. After How Many Hours the height of the first candle will be half of the second Candle.
Ans: height of candle1 after x hrs=(6-x)/6
height of candle2 after x hrs=(8-x)/8
2*(6-x)6=(8-x)/8
x=4.8
26) What is the number of scores possible in a 150 bit CAT paper, where 1/3 mark is deducted for every wrong answer and 1 mark is awarded for every correct answer?
Ans: maximum possible score = 150
min possible score = -50
total possible scores = 200 * 3 = 600 - 3 = 597
27) What does 100 stand for if 5 X 6 = 33
a. 90 b. 81 c. 100 d. 110
28) How many factors are there for the number equal to 40^3 - 17^3 - 23^3?
Ans: 48
29) what is the value of 2^256 mod 19 ?
Ans. *
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