Download Mathematics Chapter 1

TEST PAPER (Std. X)
1. EUCLID’S ALGORITHM
AND REAL NUMBERS
_________________________________________________________________________________
TOTAL MARKS : 30
MAXIMUM TIME : 1 Hr.
PART – A
Fill in the blanks by selecting the proper alternative from those given below each question.
(1 mark each)
1. If l.c.m. of two numbers (greater than 1) is the product of them, then their g.c.d. is _____ .
(A) 1
(B) 2
(C) one of the numbers
(D) a prime
2. If p1 and p2 are distinct primes, their g.c.d. is _____ .
(A) p1
(B) p2
(C) p1p2
(D) 1
3 g.c.d. (15, 24, 40) = _____ .
(A) 40
(B) 1
4.
(C) 14
(D) 15 x 24 x 40
= _____
(A)
+
(B)
+1
(C)
(D) does not exist
(B) 136 x 221 x 391
(C) g.c.d. (136, 221, 391)
5. l.c.m. (136, 221, 391) = _____
(A) 40664
6.
(D) 136 x 221
has _____ digits after decimal point.
(A) 5
(B) 4
(C) 3
(D) 2
7. 2m5n (m, n  N) ends with _____ .
(A) 0 (B) 5 (C) 25 (D) 125
8. (5k + 1)2 leaves remainder _____ on dividing by 5.
(A) 2
(B) 0
(C) – 1 or 1
(D) 1
9. Product of any four consecutive positive integers is divisible by _____ .
(A) 16 (B) 48 (C) 24 (D) 32
10. If g.c.d. (a, b) = 18, l.c.m.  _____ .
(A) 36 (B) 72 (C) 48 (D) 108
11. Given positive integers a and b, there exist unique non-negative integers q and r such that ____ .
(A) 0  r < b (B) 0 < r < b (C) 0 < r  b (D) 0  r  b
12. Cube of an integer is of the form _____ .
(A) 9k or 9k + 1 (B) 9k or 9k  1 (C) 9k or 3k  1
13. g.c.d. (120, 23) = _____ .
(A) 120 (B) 1 (C) 23
(D) 9k or 3k + 1
(D) 120 x 23
14. If p is a natural number greater than 1 and p has only one factor other than 1 namely itself, then
p is called a _____ .
(A) prime (B) composite (C) factor (D) natural
15. 4n cannot end in _____ .
(A) 4 (B) n (C) 0
(D) 1
16. Which of the following does not have terminating decimal expansion ?
(A)
(B)
(C)
(D)
PART B
SECTION A
Solve the following showing calculations (2 marks each)
1. Prove that the square of an integer is of the form 9k or 3k + 1.
2. Prove that product of four consecutive positive integers is divisible by 24.
3. Find g.c.d. (24871, 3466)
4. Find g.c.d. (144, 610) using Euclid’s algorithm and find l.c.m. (144, 610) using the relation
ab = g.c.d. (a, b) x l.c.m. (a, b)
5. Prove
6. Simplify :
+
is irrational.
+
+
+ ... +
7. Find the largest number dividing 110, 62, 92 and leaving remainders 5, 6 and 1 respectively.