Modulo Operations

Q. What is the time 15 hours before 11 p.m.? (3 marks)

Q. Find the least positive value of $x$ such that $67+x\equiv 1\left(mod4\right)$.

1. 2

Q. A man starts his journey from Bangalore to Delhi by train. He starts at 23.30 on Wednesday. If it takes 34 hours of travel time to reach Delhi and if the train is not late, when will he reach Delhi?

1. Saturday at 6.30 hours
2. Friday at 6.30 hours
3. Friday at 9.30 hours
4. Saturday at 9.30 hours

Q. $\text{If}17\equiv 4\left(mod13\right)\text{then}51\equiv x\left(mod13\right)$, then find the value of $x$.

1. 12

Q. When 70004 is divided by 7 , the remainder is _______.

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

Q. When 778 is divided by 7, the remainder is _________.

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

Q. $\text{If}{10}^4\equiv x\left(mod19\right),\text{then}x$ = ____.

1. 5
2. 2
3. 3
4. 6

Q.

The least positive remainder, when $123\times 125\times 127$ is divided by $124$ is

1. $4$

2. $120$

3. $121$

4. $130$

Q. $\text{If}17\equiv 4\left(mod13\right)\text{and}42\equiv 3\left(mod13\right),$ then ____.

1. $-25\equiv -1\left(mod13\right)$
2. $-35\equiv 1\left(mod13\right)$
3. $-25\equiv 1\left(mod13\right)$
4. $59\equiv 6\left(mod13\right)$

Q. The remainder when $7\times 19$ is divided by 6 is ________.

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

Q. $\text{If}17\equiv 4\left(mod13\right)\text{then}51\equiv x\left(mod13\right)$, find x.

1. 4
2. 15
3. 13
4. 12

Q. $\text{If}9\equiv 3\left(mod6\right)\text{and}14\equiv 2\left(mod6\right)$, then $126\equiv z\left(mod6\right)$. Find z.

1. z = 1
2. z = 3
3. z = 5
4. z = 6

Q. $\text{If}9\equiv 3\left(mod6\right)\text{and}14\equiv 2\left(mod6\right)$, then $-5\equiv y\left(mod6\right)$. Find y.

1. 6
2. 5
3. 1
4. -1

Q. $\mathrm{Determine}\mathrm{the}\mathrm{value}\mathrm{of}d\mathrm{such}\mathrm{that}21\equiv 3\left(\mathrm{mod}d\right)$

1. 6, 9, 18
2. 2, 3, 7
3. 3, 6, 8
4. 6, 9, 12

Q. $\text{If}9\equiv 3\left(mod6\right)\text{and}14\equiv 2\left(mod6\right)$, then $23\equiv x\left(mod6\right)$. Find x.

1. x = 6
2. x = 5
3. x = 3
4. x = 1

Q. Which of the following can not be the possible values of $a$ if $45\equiv 0\text{(mod a)}?$

1. 9
2. 5
3. 3
4. 14

Q. $\text{If}17\equiv 4\left(mod13\right)\text{and}42\equiv 3\left(mod13\right)$, then _____.

1. $59\equiv 5\left(mod13\right)$
2. $59\equiv 7\left(mod13\right)$
3. $24\equiv 7\left(mod13\right)$
4. $59\equiv 4\left(mod13\right)$

Q. $\text{If}17\equiv 4\left(mod13\right)\text{then}y\equiv 22\left(mod13\right)$, find y.

1. 18
2. 25
3. 35
4. 45

Q. What is the sum of the series $2.06+2.02+1.98+...+0.78?$

1. $-12.48$
2. $22.56$
3. $-34.89$
4. $46.86$

Q. The modal class is

1. $50-55$
2. $55-60$
3. $60-65$
4. none of these