1). Eight students appear in an examination. In how many ways can the result be announced. Each student can either pass or fail in the exam?
a) 128
b) 64
c) 32
d) 256
e) None of these
2). 12 delegates are seated at a round table conference. What is the probability that two particular delegates sit together?
a) 2/9
b) 1/11
c) 1/9
d) 2/11
e) None of these
3). Ram invests a certain sum of money in Bank A for a period of 5 years and gets Rs. 3800 as simple interest. After that he withdraws the amount and invests it in Bank B for 10 years which provides double the rate of interest as provided by Bank A. From Bank B he gets Rs. 30,400 as simple interest. Find the sum of money invested in Bank A.
a) Rs. 3800
b) Rs. 38000
c) Rs. 7600
d) Can’t be determined
e) None of these
4). An amount of money grows up to Rs. 4000 in 2 years and up to Rs. 8000 in 3 years on compound interest. What is the sum?
a) Rs. 1200
b) Rs. 1000
c) Rs. 1600
d) Rs. 2400
e) None of these
5). What is the sum of 5, 7, 9, 11, 13, …., up to 15th odd number?
a) 285
b) 302
c) 955
d) 289
e) None of these
6). The difference between a two digit number and the number obtained by interchanging the digits is 45. What is the difference of the two digits of the number?
a) 6
b) 5
c) 4
d) 3
e) None of these
7). What is the five digit smallest number when divided by 24, 30, 36 and 48 leaves no remainder?
a) 10040
b) 10020
c) 10060
d) 10080
e) None of these
8). The sum of the three numbers is 152. If the ratio between the first and second be 3:5 and that between the second and third be 5:11, what is the third number?
a) 111
b) 55
c) 88
d) 66
e) None of these
9). Three persons A, B and C invested capitals in the ratio 2:3:4. At the end of the business term, they received the profits in the ratio 10:7:5. What is the ratio of time for which they contributed their capital?
a) 4:3:1
b) 12:10:9
c) 12:14:15
d) 5:4:1
e) None of these
10). If the annual decrease in the population of a city is 15% and the present population is 8 lakhs, what will be the population after 3 years?
a) 3.7 lakhs
b) 6.725 lakhs
c) 4.913 lakhs
d) 5.185 lakhs
e) None of these
Solutions -
1. There are two possibility for each students either fail or pass.
Number of ways for the result = (2)8 = 256
Answer: d
2. n(S) = Number of ways of sitting 12 person at round table = (12-1)! = 11!
If we consider 2 particular person as one unit then number of person = 12-2+1 =11
So 11 persons can sit on round table in (11-1)!=10! Ways. The two persons can sit in 2! Ways among themselves.
n(E) = 10!×2!
n(S)=11!
P(E)=(10!×2!/11!) = (2!/11!) = (2/11)
Answer: d
3. Let the invest Rs. x at a rate of r% pa in Bank A.
(xr5/100)=3800
=xr = 76000 ….(i)
In Bank B he invests Rs. (x+3800) at a rate of 2r% pa.
[(x+3800)(2r×10)/100] = 30400
xr+3800r = [(30400×100)/(2×10)]
Using value from (i)
76000+3800r = 1520000
r=20% pa.
=> x × 20 = 76000
X = 3800
Answer: a
4. Required sum = 4000(4000/8000)2 = 4000×(1/4) = 1000
Answer: b
5. Required sum
=(1+3+5+7+ ….. +17th odd number)-(1+3)
= 172 – 4 = 289 – 4 = 285
Answer: a
6. Let the number is 10x + y.
10x+y-(10y+x) = 45
=> 9(x-y) = 45
x-y=5
Answer: b
7. LCM of 24, 30, 36, 48 =720
720)10000(13
9360
______
640
Required number = 10000+(720-640) = 10080
Answer: d
8. The ratio among the three number is
3 : 5
5 : 11
__________
15: 25: 55
Third number = [152/(15+25+55)]×55
= (152/95) × 55 = 88
Answer: c
9. Ratio of time = (10/2):(7/3):(5/4) = 5:(7/3):(5/4)
Ratio = 60:28:15
Answer: e
10. Required population = 800000[1-15/100]3
= 800000[17/20]3
= (800000×17×17×17)/8000
= 491300 = 4.913 lakhs
Answer: c
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