SIMPLIFICATION1. A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? A. C. 2. There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is: A. C. 3. The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is: A. C. 4. Rs. 3500 Rs. 3840 B. D. Rs. 3750 Rs. 3900 20 100 B. D. 80 200 45 75 B. D. 60 90

If a - b = 3 and a2 + b2 = 29, find the value of ab. A. C. 10 15 B. D. 12 18

5. The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ? A. C. E. Rs. 1200 Rs. 4800 None of these B. D. Rs. 2400 Cannot be determined

NUMBERS1. The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number? A. C. E. 69 96 None of these B. D. 78 Cannot be determined

2. The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is: A. C. 20 40 B. D. 30 None of these

3. A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by: A. C. 3 9 B. D. 5 11

4. In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is: A. C. 24 42 B. D. 26 46

5.

Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number. A. C. 3 17 B. D. 10 20

6.If one-third of one-fourth of a number is 15, then three-tenth of that number is: A. C. 35 45 B. D. 36 54

7.The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ? A. C. 240 295 B. D. 270 360

8.

The largest 4 digit number exactly divisible by 88 is: A. C. 9944 9988 B. D. 9768 8888

E.

None of these

9.What is the unit digit in(795 - 358)? A. C. 0 6 B. D. 4 7

10. What is the unit digit in {(6374)1793 x (625)317 x (341491)}? A. C. 0 3 B. D. 2 5

Problems on H.C.F and L.C.M

1.

Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case. A. C. 4 9 B. D. 7 13

2.

The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is: A. C. 276 322 B. D. 299 345

3.

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ? A. C. 4 15 B. D. 10 16

4.

Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is: A. C. 4 6 B. D. 5 8

5.

The greatest number of four digits which is divisible by 15, 25, 40 and 75 is: A. C. 9000 9600 B. D. 9400 9800

6.

The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is: A. C. 101 111 B. D. 107 185

7.

Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is: A. C. 40 120 B. D. 80 200

8.

The G.C.D. of 1.08, 0.36 and 0.9 is: A. C. 0.03 0.18 B. D. 0.9 0.108

9.

The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is: A. C. 1 3 B. D. 2 4

10. The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is: A. C. 74 184 B. D. 94 364

Permutation and Combination1. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

A. C. E.

63 126 135

B. D.

90 45

2.

How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed? A. C. 40 5040 B. D. 400 2520

3.

In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together? A. C. 10080 120960 B. D. 4989600 None of these

4.

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there? A. C. E. 159 205 None of these B. D. 194 209

5.

In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women? A. C. E. 266 11760 None of these B. D. 5040 86400