Modular Arithmetic and Congruence Modulo

Q.

Question 113

A sugar factory has annual sales of 3 billion 720 million kilograms sugar. Express this number in the standard form.

Q. Rational numbers are written in the form of $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne$

1. 1
2. \N
3. -1

Q. Question 2(v)
Express the following numbers in usual form:
$5.8\times {10}^{12}$

Q. Whch of the following could be the value of d such that $15\equiv 3\left(modd\right)$.

1. 2
2. 1
3. 4
4. 3

Q. Find the number of integer solutions of $3x\equiv 1\left(mod15\right)$.

1. 0
2. 1
3. 2
4. 3

Q. The least positive value of $x$ such that $98\equiv (x+4)\left(mod5\right)$ is ___.

1. 4
2. 5
3. 1
4. 2

Q. Two integers a and b are congruence modulo n if _____ for some integer k.

1. b - a = kn
2. b + a = kn
3. b - a = 0
4. b + a = 0

Q. Find -5 (mod 3).

1. $-5\equiv \left(2\right)\left(mod3\right)$
2. $-5\equiv \left(1\right)\left(mod3\right)$
3. $-5\equiv \left(0\right)\left(mod3\right)$
4. $-5\equiv \left(3\right)\left(mod1\right)$

Q. Find 8 (mod 4).

1. $8\equiv \left(8\right)\left(mod4\right)$
2. $8\equiv \left(4\right)\left(mod4\right)$
3. $8\equiv \left(0\right)\left(mod4\right)$
4. $8\equiv \left(4\right)\left(mod8\right)$

Q. If a positive integer is divided by $n,$ then the possible remainders are .

1. 0, 1, 2, ......, n-1
2. 0, 1, 2, ......, n
3. 0, 1, 2, ......, n+1
4. 0, 1, 2, ......, n+2

Q. The least positive value of $x$ such that $126\equiv (x+4)\left(mod6\right)$ is _________.

1. 2
2. 4
3. 6
4. 8

Q.

Question 133

An inch is approximately equal to 0.02543 metres. Write this distance in standard form.

Q. $a\equiv b\left(modn\right)$ means .

1. a+b divisible by n
2. a-b divisible by n
3. a divisible by n

Q. $\mathrm{Find}\mathrm{the}\mathrm{remainder}\mathrm{when}{2}^{34}\mathrm{is}\mathrm{divided}\mathrm{by}7.$$\left[3\right]$

Q. The number $0.0000000000085$ in standard form is $=8.5\times {10}^m$. Value of $\mathrm{mod}\left(m\right)$ is

Q.

Numbers that can be expressed as a ratio of p and q where p and q are integers and $q\ne 0$ are called __numbers.

Q.

Find the value of each of the following.

$\left|-27\right|$

Q. Total number of ways of selecting two numbers from the set {1, 2, 3, ....., 90} so that their sum is divisible by 3, is

1. $885$
2. $1335$
3. $1770$
4. $3670$

Q. Find the least positive value of \(x\) such that \(126 \equiv (x + 4)(mod ~6)\).

Q.

$\left|\frac{-5}{6}\right|=\frac{5}{6}$

1. True
2. False

Q. The digit in the units place of ${6789}^5$ is

1. $6$
2. $8$
3. $7$
4. $9$

Q. A value of x satisfying $150x\equiv 35$ (Mod 31) is ____.

1. 22
2. 24
3. 14
4. 12

Q. Find the mean of the following frequency distribution by the assumed mean method :

No. of apples	$50-53$	$53-56$	$56-59$	$59-62$	$62-65$
No of boxes	$20$	$150$	$115$	$95$	$20$