# Answers by Lakshman Patel RJIT

0 votes
1
Consider the binary tree in the figure below: Outline a procedure in Pseudo-code to delete an arbitrary node from such a binary tree with $n$ nodes that preserves the structures. What is the worst-case time complexity of your procedure?
0 votes
2
Consider the binary tree in the figure below: Give different steps for deleting the node with key $5$ so that the structure is preserved.
1 vote
3
Five persons $\text{P, Q, R, S and T}$ are sitting in a row not necessarily in the same order. $Q$ and $R$ are separated by one person, and $S$ should not be seated adjacent to $Q.$ The number of distinct seating arrangements possible is: $4$ $8$ $10$ $16$
1 vote
4
The ratio of the area of the inscribed circle to the area of the circumscribed circle of an equilateral triangle is ___________ $\frac{1}{8}$ $\frac{1}{6}$ $\frac{1}{4}$ $\frac{1}{2}$
1 vote
5
In the figure shown above, $\text{PQRS}$ is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at $S$ and $Q$. The probability that any point picked randomly within the square falls in the shaded area is ____________ $4-\frac{\pi }{2}$ $\frac{1}{2}$ $\frac{\pi }{2}-1$ $\frac{\pi }{4}$
1 vote
6
A superadditive function $f(\cdot)$ satisfies the following property $f\left ( x_{1} +x_{2}\right )\geq f\left ( x_{1} \right ) + f\left ( x_{2} \right )$ Which of the following functions is a superadditive function for $x > 1$? $e^{x}$ $\sqrt{x}$ $1/x$ $e^{-x}$
1 vote
7
An engineer measures THREE quantities, $X, Y$ and $Z$ in an experiment. She finds that they follow a relationship that is represented in the figure below$: ($the product of $X$ and $Y$ linearly varies with $Z)$ Then, which of the following statements is FALSE? For fixed $Z$; $X$ is ... to $Y$ For fixed $Y$; $X$ is proportional to $Z$ For fixed $X$; $Z$ is proportional to $Y$ $XY/Z$ is constant
1 vote
8
Select the graph that schematically represents BOTH $y=x^{m}\:\text{and}\:y=x^{1/m}$ properly in the interval $0\leq x \leq 1$, for integer values of $m,$ where $m > 1.$
1 vote
9
Five friends $P,Q,R,S$ and $T$ went camping. At night, they had to sleep in a row inside the tent. $P,Q$ and $T$ refused to sleep next to $R$ since he snored loudly. $P$ and $S$ wanted to avoid $Q$ as he usually hugged people in sleep. Assuming everyone was satisfied with the sleeping arrangements, what is the order in which they slept? $RSPTQ$ $SPRTQ$ $QRSPT$ $QTSPR$
1 vote
10
The revenue and expenditure of four different companies $\text{P, Q, R and S}$ in $2015$ are shown in the figure. If the revenue of company $\text{Q}$ in $2015$ was $20$% more than that in $2014$, and company $\text{Q}$ had earned a profit of $10$% on expenditure in $2014$, then its expenditure (in million rupees) in $2014$ was _______. $32.7$ $33.7$ $34.1$ $35.1$
1 vote
11
The distance between Delhi and Agra is $233$ km. A car $P$ started travelling from Delhi to Agra and another car $Q$ started from Agra to Delhi along the same road $1$ hour after the car $P$ started. The two cars crossed each other $75$ minutes after the car $Q$ started. Both ... car $Q$. How many kilometers the car $Q$ had travelled when the cars crossed each other? $66.6$ $75.2$ $88.2$ $116.5$
1 vote
12
The following figure shows the data of students enrolled in $5$ years $(2014\;\text{to}\; 2018)$ for two schools $P$ and $Q$. During this period, the ratio of the average number of the students enrolled in school $P$ to the average of the difference of the number of students enrolled in schools $P$ and $Q$ is _______. $8 : 23$ $23 : 8$ $23 : 31$ $31 : 23$
1 vote
13
The profit shares of two companies $P$ and $Q$ are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company $P$ to the revenue of company $Q$, during $2013-2018$ is ________. $15 : 17$ $16 : 17$ $17 : 15$ $17 : 16$
1 vote
14
Consider a square sheet of side $1$ unit. The sheet is first folded along the main diagonal. This is followed by a fold along its line of symmetry. The resulting folded shape is again folded along its line of symmetry. The area of each face of the final folded shape, in square units, equal to _________ $\frac{1}{4}$ $\frac{1}{8}$ $\frac{1}{16}$ $\frac{1}{32}$
1 vote
15
Five persons $\text{P, Q, R, S}$ and $\text{T}$ are to be seated in a row, all facing the same direction, but not necessarily in the same order. $\text{P}$ and $\text{T}$ cannot be seated at either end of the row. $\text{P}$ should not be seated adjacent ... is to be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is: $2$ $3$ $4$ $5$
1 vote
16
Ms. $X$ came out of a building through its front door to find her shadow due to the morning sun failing to her right side with the building to her back. From this, it can be inferred that building is facing _________ North East West South
1 vote
17
Given below are two statements $1$ and $2$, and two conclusions $\text{I}$ and $\text{II}$. $\text{Statement 1}:$ All entrepreneurs are wealthy. $\text{Statement 2}:$ All wealthy are risk seekers. $\text{Conclusion I}:$ ... $\text{I}$ nor $\text{II}$ is correct Both conclusions $\text{I}$ and $\text{II}$ are correct
1 vote
18
$\begin{array}{|c|c|} \hline \textbf{Company} & \textbf{Ratio} \\\hline C1 & 3:2 \\\hline C2 & 1:4 \\\hline C3 & 5:3 \\\hline C4 & 2:3 \\\hline C5 & 9:1 \\\hline C6 & 3:4 \\\hline\end{array}$ The distribution of employees at the rank ... $\textsf{C2}$ and $\textsf{C5}$ together is ________. $225$ $600$ $1900$ $2500$
1 vote
19
Four persons $\text{P, Q, R}$ and $\text{S}$ are to be seated in a row, all facing the same direction, but not necessarily in the same order. $\text{P}$ and $\text{R}$ cannot sit adjacent to each other. $\text{S}$ should be seated to the right of $\text{Q}$. The number of distinct seating arrangements possible is: $2$ $4$ $6$ $8$
2 votes
20
Five line segments of equal lengths, $\text{PR, PS, QS, QT}$ and $\text{RT}$ are used to form a star as shown in the figure above. The value of $\theta$, in degrees, is _______________ $36$ $45$ $72$ $108$
1 vote
21
Consider two rectangular sheets, Sheet $\text{M}$ and Sheet $\text{N}$ of dimensions $6\:\text{cm} \times 4\: \text{cm}$ each. Folding operation $1:$ The sheet is folded into half by joining the short edges of the current shape. Folding operation $2:$ The sheet is folded into half by ... of Sheet $\text{N}$ to the final folded shape of Sheet $\text{M}$ is _____________. $13:7$ $3:2$ $7:5$ $5:13$
1 vote
22
Four persons $P, Q, R$ and $S$ are to be seated in a row. $R$ should not be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is: $6$ $9$ $18$ $24$
1 vote
23
In an equilateral triangle $\text{PQR}$, side $\text{PQ}$ is divided into four equal parts, side $\text{QR}$ is divided into six equal parts and side $\text{PR}$ is divided into eight equals parts. The length of each subdivided part in $\text{cm}$ is an integer. The minimum area of the triangle $\text{PQR}$ possible, in $\text{cm}^{2}$, is $18$ $24$ $48\sqrt{3}$ $144 \sqrt{3}$
1 vote
24
Some football players play cricket. All cricket players play hockey. Among the options given below, the statement that logically follows from the two statements $1$ and $2$ above, is : No football player plays hockey Some football players play hockey All football players play hockey All hockey players play football
1 vote
25
Seven cars $\text{P, Q. R, S, T, U and V}$ are parked in a row not necessarily in that order. The cars $T$ and $U$ should be parked next to each other. The cars $S$ and $V$ also should be parked next to each other, whereas $P$ and $Q$ cannot be parked next to each ... . $Q$ and $R$ are not parked together. $V$ is the only car parked in between $S$ and $R$. Car $P$ is parked at the extreme end.
1 vote
26
In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in $\text{cm}^{2}$ is: $12.50$ $6.25$ $3.125$ $1.5625$
1 vote
27
Which one of the following numbers is exactly divisible by $\left ( 11^{13} +1\right )$? $11^{26} +1$ $11^{33} +1$ $11^{39} -1$ $11^{52} -1$
1 vote
28
For a regular polygon having $10$ sides, the interior angle between the sides of the polygon, in degrees, is: $396$ $324$ $216$ $144$
1 vote
29
Let $X$ be a continuous random variable denoting the temperature measured. The range of temperature is $[0, 100]$ degree Celsius and let the probability density function of $X$ be $f\left ( x \right )=0.01$ for $0\leq X\leq 100$. The mean of $X$ is __________ $2.5$ $5.0$ $25.0$ $50.0$
1 vote
30
The number of students passing or failing in an exam for a particular subject is presented in the bar chart above. Students who pass the exam cannot appear for the exam again. Students who fail the exam in the first attempt must appear for the exam in the following year. Students always pass ... the year $3$ respectively, are ______________. $65$ and $53$ $60$ and $50$ $55$ and $53$ $55$ and $48$