A train left station X at A hour B minutes. It reached station Y at B hour C minutes on the same day, after travelling for C hours A minutes (Clock shows time from $0$hours to $24$hours). Number of possible value(s) of A is ............

In the following question, one statement is followed by three conclusion. Select the appropriate answer from the option given below.

$A_0, A_1, A_2 ,....$ is a sequence of numbers with   $A_0=0, A_1=3$, and $A_t=\left(t+1\right) A_{t-1}-t A_{t-2}=2, 3, 4,....$

Conclusion $1:$ $A_8=77$.

Conclusion $2: A_{10}=121$.

Conclusion $3: A_{12}=145$.

Directions : In these questions one statement is followed by three conclusions. Select the appropriate answer from the options given below

A, B, C be real numbers satisfying$\mathrm{A}<\mathrm{B}<\mathrm{C}, \mathrm{A}+\mathrm{B}+\mathrm{C}=6$ and$\mathrm{A} \mathrm{B}+\mathrm{B} \mathrm{C}+\mathrm{C} \mathrm{A}=9$

Conclusion I.$1<\mathrm{B}<3$

Conclusion II.$2<\mathrm{A}<3$

Conclusion III.$0<\mathrm{C}<1$

Directions: These questions are followed by two statements labelled as I and II. You have to decide, if these statements are sufficient to conclusively answer the questions. Choose the appropriate answer from options given below.

The base of a triangle is $60 \mathrm{cm}$ and one of the base angles is $60$. What is the length of the shortest side of the triangle?

I. The sum of lengths of other two sides is $80 \mathrm{cm}$

II. The other base angle is $45$

Directions: These questions are followed by two statements labelled as I and II. You have to decide, if these statements are sufficient to conclusively answer the questions. Choose the appropriate answer from options given below.

A, B, C, D, E and F are six integers such that $\mathrm{E}<\mathrm{F}, \mathrm{B}>\mathrm{A}, \mathrm{A}<\mathrm{D}<\mathrm{B} . \mathrm{C}$ is the greatest integer. Is A the smallest integer ?

$$\begin{gathered} \mathrm{I}. \mathrm{E}+\mathrm{B}<\mathrm{A}+\mathrm{D} \\ \mathrm{II}. \mathrm{D}<\mathrm{F} \end{gathered}$$