CBSE Class 9 Mathematics Number System Worksheet Set 03

Question. A number being successively divided by 3, 5 and 8 leaves remainders 1, 4 and 7 respectively. Find the respective remainders if the order of divisiors be reversed.
(A) 6, 5, 1
(B) 6, 4, 2
(C) 2, 4, 6
(D) 1, 3, 3
Answer: B

Question. If the LCM of first 100 natural numbers is P then the LCM of first 105 natural numbers would be :
(A) P
(B) P + 105
(C) P(P + 101)(P + 103)
(D) 103 × 101 × P
Answer: D

Question. If (232 + 1) is divisible by a certain number then which of the following is also divisible by that number.
(A) (216 – 1)
(B) 216 + 1
(C) 296 + 1
(D) None of these
Answer: C

Question. There are four prime numbers written in ascending order. The product of the first three is 385 and that of the last three is 1001. The lest number is :
(A) 11
(B) 13
(C) 17
(D) 19
Answer: C

Question. How many three-digit numbers would you find, which when divided by 3, 4, 5, 6, 7 leave the remainders 1, 2, 3, 4 and 5 respectively ?
(A) 4
(B) 3
(C) 2
(D) 1
Answer: C

Question. An operation defined as the product of non zero digits of x. e.g. An operation x defined as the product of non zero digits of x. e.g. 
25 = 2 × 5 = 10, then the sum of all the possible n where n is a two digit number formed by the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 is :
(A) 2350
(B) 2007
(C) 2025
(D) 4014
Answer: C

Question. What will be the last digit of (73)⁷⁵⁶⁴⁷⁶ .
(A) 9
(B) 7
(C) 3
(D) 1
Answer: C

Question. A number when divided by 259 leaves a remainder 139. What will be the remainder when the same number is divided by 37 ?
(A) 21
(B) 23
(C) 27
(D) 28
Answer: D

Question. Three pieces of cakes of weights 4(1/2) lbs, 6(3/4) lbs and 7(1/5) lbs respectively are to be divided into parts of equal weights. Further, each must be as heavy as possible. If one such part is served to each guest, then what is the maximum number of guests that could be entertained ?
(A) 54
(B) 72
(C) 20
(D) 41
Answer: D

Question. How many zeros at the end of first 100 multiples of 10.
(A) 100
(B) 124
(C) 920
(D) 1225
Answer: B

1. Express the following numbers in the form of p : q

(a) -25.6875

(b) 0.621621621..

(c) 15.712121212..

2. Write one rational & one fractional number between 0.515115111…. and 0.535335333….

3. Write one example each of two irrational numbers whose:

(a) Sum is a rational number

(b) Product is an irrational number

(c) Difference is an irrational number

(d) Quotient is a rational number

4. Simplify : [ { (625) ^-1/2 } ^-1/4 ] ²

5. (a) Find the value of x if 2x-7 x 5x-4 =1250

(b) Find the value of x and y if:

3^x-1 = 9 & 4^y+2 = 64

6. Find the value of a & b if 5 + 2√3/7 + 4√3 = a + b√3

7. If x = 3 + √8, then find the value of x² + 1x²