**Find solutions for all the questions at the end of each set:**

### Set A

1. Which among 2^(1/2),3^(1/3),4^(1/4),6^(1/6) and 12^(1/12) is the largest?

(a) 2^(1/2)

(b) 3^(1/3)

(c) 4^(1/4)

(d) 6^(1/6)

2. Consider a sequence where the nth term, tn=n/(n+2),n=1,2,……. . The value of t3×t4×t5×……..×t53 equals-

(a) 2/495

(b) 2/477

(c) 12/55

(d) 1/1485

3. If 1/b=1/3,b/c=2,c/d=1/2,d/e=3 and e/f=1/4, then what is the value of abc/def ?

(a) 3/8

(b) 27/8

(c) 3/4

(d) 27/4

4. If x=-0.5, then which of the following has the smallest value?

(a) 2^(1/x)

(b) 1/x

(c) 1/x^2

(d) 2^x

5. The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?

(a) 21

(b) 25

(c) 41

(d) 67

6. When you reverse the digits of the number 13, the number increases by 18. How many other two digit numbers increase by 18 when their digits are reversed?

(a) 5

(b) 6

(c) 7

(d) 8

7. The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be

(a) 101 : 88

(b) 87 : 100

(c) 110 : 111

(d)97 : 84

8. The rightmost non-zero digit of the number 30^2720 is

(a) 1

(b) 3

(c) 7

(d) 9

9. Let x=√(4+√(4-√(4+√(4-(……..) ∞)) ) ) . Then, x equals

(a) 3

(b) ((√13-1)/2)

(c) ((√13+1)/2)

(d) √13

10. A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is

(a) 10

(b) 12

(c) 14

(d) 16

Answers:

1. (b); LCM of 2, 3, 4, 6, 12=12

(2^1/2)^12, (3^1/3)^12, (4^1/4)^12, (6^1/6)^12, (12^1/12)^12

=(2)^6, (3)^4, (4)^3, (6)^2, (12)^1

=64, 81, 64, 36, 12

Hence, 3^(1/3) is the largest.

2. Given t_n=n/(n+2), n=1,2,….

Therefore, t_3=3/5, t_4=4/6, t_5=5/7, …., t^53=53/55

Therefore t_3 × t_4 × t_5 ×….×t_53

=3/5 × 4/6 × 5/7 × 6/8 ×…..×51/53 × 52/54 × 53/55

=(3×4)/(54×55) = 2/495

3. (a); Given that a/b=1/3, b/c=2, c/d=1/2, d/e=3 and e/f=1/4

Therefore a/b × b/c × c/d = 1/3 × 2 × 1/2= 1/3

a/d=a/3 and c/d × d/e=1/2 × 3 = 3/2

c/e=3/2

and e/f × d/e × b/c × c/d=1/4 × 3 × 2 × 1/2 = 3/4

b/f= 3/4

therefore, abc/ def= a/d × c/e × b/f = 1/3 × 3/2 × ¾ = 3/8

4. (b); Using options, we can solve the question easily.

Put x=- ½

(a) 2^(-2)= ¼

(b) 1/(- ½) = -2

(c) 1/(- a/2)^2 = 4

(d) 2^(-1/2)=1/√2

(e) 1/√-(1/2) = √2

5. (c); Using options, we find that four consecutive odd numbers are 37, 39, 41 and 43. The sum of these 4 numbers is 160, when divided by 10, we get 16 which is a perfect square.

Therefore, 41 is one of the odd numbers.

6. (b); Let the number be (10x+y), so when the digits of number are reversed the number becomes (10y+x). According the question, (10y+x)-(10x+y)=18

9(y-x)=18 y-x=12

So, the possible pairs of (x, y) are

(1, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 8) and (7, 9).

But we want the number other than 13. Thus, there are 6 possible numbers ie, 24, 35, 46, 57, 68, 79.

So, total number of possible numbers are 6.

7. (d); Using options, we find that sum of numerator and denominator of 97 : 84 is (97+84)=181 which is a prime number. Hence, it is the appropriate answer.

8. (a) [(30^4]^680 hence, the rightmost non-zero digit is 1.

9. (c); x=(√(4+√(4-x))

(x^2-4)=4+√(4-x)

Now, put the values from option only option (c) satisfies the condition.

10. (b); Let the rectangle has m and n tiles along its length and breadth respectively.

The number of white tiles

W=2m+2(n-2)=2(m+n-2)

And the number of red tiles=R=mn-2(m+n-2)

Given W=R 4(m+n-2)=mn

mn-4m-4n=-8

(m-4) (n-4)=8

m-4=8 or 4

M=12 or 8

Therefore 12 suits the option.

**Find solutions for all the questions at the end of each set:**

### Set B

1. The sum of the squares of first ten natural numbers is

(a) 281

(b) 402

(c) 385

(d) 502

2. The sum of the first seventeen prime number is

(a) 440

(b) 329

(c) 498

(d) 382

3. The sum of the prime number below 100 is

(a) 1061

(b) 1058

(c) 1160

(d) None of these

4. The number of prime numbers upto the counting 100 is

(a) 26

(b) 24

(c) 25

(d) 23

5. The multiplication of seven first odd numbers divided by the sum of nine even numbers provides the answer as

(a) 1501.5

(b) 1877.2

(c) 2413.1

(d) None of these

6. The product of two odd prime numbers is

(a) even

(b) odd

(c) either even or odd

(d) It depends upon the numbers chosen

7. Zero is counted as

(a) Whole number

(b) Prime number

(c) Integer

(d) a and c both are correct

8. Search the prime numbers from the given list

2, 12, 21, 37, 53, 101, 72,

(a) 2, 21, 53

(b) 12, 37, 53, 101

(c) 2, 37, 53, 101

(d) 2, 72, 101

9. Two rational numbers lying between 4/5 and 6/7 are

(a) 71/35,5/6

(b) 29/21,5/6

(c) 29/35,57/70

(d) None of these

10. The square root of a number which is divisible by 2, 4, 5 and 8 is

(a) 900

(b) 800

(c) 1600

(d) 400

Answer Key:

1.c

2.a

3.d

4.c

5.a

6.b

7.d

8.c

9.c

10.c

**Find solutions for all the questions at the end of each set:**

### Set C

Q1. Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. If both pipes are opened together, the time taken to fill the tank is:

a) 50 minutes

b) 12 minutes

c) 25 minutes

d) 15 minutes

Q2. A swimming pool has 3 drain pipes. The first two pipes A and B, operating simultaneously, can empty the pool in half the time C, the 3rd pipe, alone takes to empty it. Pipe A working alone, takes half the time taken by pipe B. Together they take 6 hours 40 minutes to empty the pool. Time taken by pipe A to empty the pool, in hours is

a) 15

b) 10

c) 30

d) 7

Q3. The percentage of loss when an article is sold at rs 50 is the as that of the profit when it is sold at Rs 70. The above mentioned percentage of profit or loss on the article is

a) 10%

b) 50/3%

c) 20%

d) 68/3%

Q4. A man had 100 kgs of sugar part of which he sold at 7% profit and rest at 17% profit. He gained 10% on the whole. How much did he sell at 7% profit?

a) 65 kg

b) 35 kg

c) 30 kg

d) 70 kg

Q5. A shopkeeper lists the price of an article as Rs 500. But he gives a certain discount which allows a certain discount which allows the buyer to pay Rs 500 for the article including 10% sales tax. The rate of discount is

a) 10%

b) 111/115%

c) 100/11%

d) 11%

Q6. A trader allows a trade discount of 20% and a cash discount of 26/4% on the marked price of the goods and gets a net gain of 205 of the cost. By how much above the cost should the goods be marked for the sale?

a) 40%

b) 50%

c) 60%

d) 70%

Q7. A sum of money invested at compound interest amount to Rs 650 at the end of first year and Rs 676 at the end of second year. The sum of money is:

a) Rs 6000

b) RS 5400

c) Rs 6250

d) Rs 5600

Q8. A loan of Rs 12300 at 5% per annum compound interest, is to be repaid in two equal annual instalments at the end of every year. Find the amount of each instalment.

a) RS 6651

b) Rs 6615

c) Rs 6516

d) RS 6156

Q9. A shopkeeper bought 15 kg of rice at the rate of Rs 29 per kg and 25 kg of rice at the rate of rs 20 per kg. He sold the mixture of both types of rice at the rate of Rs 27 per kg. His profit in this transaction is

a) Rs 125

b) Rs 150

c) Rs 140

d) Rs 145

Q10. A container contains 60 kg of milk. From this container 6 kg of milk was taken out and replaced by water. This process was repeated further two times. The amount of milk left in the container is

a) 34.24 kg

b) 39.64 kg

c) 43.74 kg

d) 47.64 kg

Answer Key:

1.b

2.a

3.b

4.d

5.c

6.c

7.c

8.b

9.d

10.c

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