111). Time taken by a boat in covering a certain distance upstream is 1.5 times to that of covering same distance downstream. What will be the ratio between the speed of boat in still water and that of current ?
| A). 4 : 3 |
| B). 5 : 2 |
| C). 5 : 1 |
| D). 3 : 2 |
|
112). A boat takes 2 hours to travel 28 km upstream. If the respective ratio between speed of the boat downstream and the speed of the boat upstream is 9 : 7, what is the speed of the current ?
| A). 1 km/h |
| B). 2.5 km/h |
| C). 3 km/h |
| D). 2 km/h |
|
113). A boat travels from A to B upstream and then from B to C downstream taking the same time. The respective ratio between the distance from A to B and the distance from B to C is 5 : 7. If the boat takes 2 hours 30 minutes to travel a distance of 35 km downstream, what is the speed of the stream? (in km/h)
| A). 2 kmph |
| B). 1.5 kmph |
| C). 2.5 kmph |
| D). 2.2 kmph |
|
114). A certain sum is divided among A, B and C in such a way that A gets Rs. 221 more than \( \Large \frac{1}{6} \) th of the sum, B gets Rs. 40 less than \( \Large \frac{2}{5} \)th of the sum and C gets Rs. 300. What is the total sum invested?
| A). Rs. 1110 |
| B). Rs. 1120 |
| C). Rs. 1220 |
| D). Rs. 1320 |
|
115). Let G be a group of matrices of the form \( \Large \begin{pmatrix}x&x\\x&x\end{pmatrix} \) where \(x\in R*\) with matrix multiplication. Theh the inverse of \( \Large \begin{pmatrix}x&x\\x&x\end{pmatrix} \) is
| A). \( \Large \begin{pmatrix}1/4x&1/4x\\1/4x&/1/4x\end{pmatrix} \) |
| B). \( \begin{pmatrix}-x&-x\\-x&-x\end{pmatrix} \) |
| C). \( \Large \begin{pmatrix}x&x\\x&x\end{pmatrix} \) |
| D). \( \Large \begin{pmatrix}x/4&x/4\\x/4&x/4\end{pmatrix} \) |
|
116). Let G be a group. Then \( \Large x^{2}=x \) if and only if
| A). \( \Large x = x^{-1} \) |
| B). \( \Large 0(x) = 0(G) \) |
| C). \( \Large x = e \) |
| D). None of these |
|
117). The incorrect statement from the following is
| A). Any cyclic group is abelian |
| B). Any abelian group is cyclic |
| C). Any abelian group satisfies the rule \( \Large (ab)^{2}=a^{2}b^{2} \) |
| D). Any subgroup of an aoelian group is normal |
|
118). The order of -i, in (C*, .) is
|
119). In (\(Z_{7}\)- {0},\(\odot \)) the Inverse of 3 is
|
120). Let G be a group with identity element e. Then the solution of the equation xab = c is
| A). \( \Large x=ca^{-1}b^{-1} \) |
| B). \( \Large x=cb^{-1}a^{-1} \) |
| C). \( \Large x=a^{-1}b^{-1}c \) |
| D). \( \Large x=b^{-1}a^{-1}c \) |
|
