The figure shows two $4$-tile patterns. !image(https://firebasestorage.googleapis.com/v0/b/gexam-717fd.firebasestorage.app/o/public%2F1779777549359image.png?alt=media&token=c9e9dde3-929d-4416-9692-78041854593a) Either one or both of the patterns can be used any number of times and in any orientation to construct a new pattern. Which one of the options below cannot be constructed by using only these two $4$-tile patterns assuming there are no overlaps among them?

Consider a knock-out women's badminton singles tournament where there are no ties. The loser in each game is eliminated from the tournament. Every player plays until she is defeated or remains the last undefeated player. The last undefeated player is declared the winner of the tournament. If there are $64$ players in the beginning of the tournament, how many games should be played in total to declare the winner of the tournament?

A student needs to enroll for a minimum of $60$ credits. A student cannot enroll for more than $70$ credits. The credits are divided amongst project and three distinct sets of courses namely, core courses, specialization courses, and elective courses. It is compulsory for a student to enroll for exactly $15$ credits of core courses and exactly $20$ credits of project. In addition, a student has to enroll for a minimum of $10$ credits of specialization courses. The maximum credits of elective courses that a student can enroll for is

'When the teacher is in the room, all students stand silently.' If the above statement is true, which one of the following statements is not necessarily true?

Combinatorics deals with problems involving counting. For example, “How many distinct arrangements of $N$ distinct objects in $M$ spaces on a circle are possible?” is a typical problem in combinatorics. This kind of counting is sometimes used in the modeling of several physical phenomena. Often, in such models, the different combinatorial possibilities are assigned probability values. Assigning probabilities enables the computation of the average values of physical quantities. Consider the following statements: P: Combinatorics is always invoked in the modeling of physical phenomena. Q: Modeling some physical phenomena involves assigning probabilities to combinatorial possibilities in order to compute average values of physical quantities. Based on the passage above, what can be inferred about statements P and Q?

Ravi had \\\\\\ younger brother who taught at \\\\\\ university. He was widely regarded as \\\\\\ honorable man. Select the option with the correct sequence of articles to fill in the blanks.

If '$\to$' denotes increasing order of intensity, then the meaning of the words dry $\to$ arid $\to$ parched is analogous to diet $\to$ fast $\to$ \\\\\\\\. Which one of the given options is appropriate to fill the blank?

If two distinct non-zero real variables $x$ and $y$ are such that $(x + y)$ is proportional to $(x - y)$ then the value of $\frac{x}{y}$

Ravi had \\\\\\\ younger brother who taught at \\\\\\\ university. He was widely regarded as \\\\\\\ honorable man. Select the option with the correct sequence of articles to fill in the blanks.

The CEO’s decision to downsize the workforce was considered \underline{myopic} because it sacrificed long-term stability to accommodate short-term gains. Select the most appropriate option that can replace the word “myopic” without changing the meaning of the sentence.

The average marks obtained by a class in an examination were calculated as $30.8$. However, while checking the marks entered, the teacher found that the marks of one student were entered incorrectly as $24$ instead of $42$. After correcting the marks, the average becomes $31.4$. How many students does the class have?

Consider the relationships among $P$, $Q$, $R$, $S$, and $T$: $P$ is the brother of $Q$. $S$ is the daughter of $Q$. $T$ is the sister of $S$. $R$ is the mother of $Q$. The following statements are made based on the relationships given above. (1) $R$ is the grandmother of $S$. (2) $P$ is the uncle of $S$ and $T$. (3) $R$ has only one son. (4) $Q$ has only one daughter. Which one of the following options is correct?

According to the map shown in the figure, which one of the following statements is correct? Note: The figure shown is representative. image needed to be inserted here

“I put the brown paper in my pocket along with the chalks, and possibly other things. I suppose every one must have reflected how primeval and how poetical are the things that one carries in one’s pocket: the pocket-knife, for instance the type of all human tools, the infant of the sword. Once I planned to write a book of poems entirely about the things in my pocket. But I found it would be too long: and the age of the great epics is past.” (From G.K. Chesterton’s “A Piece of Chalk”) Based only on the information provided in the above passage, which one of the following statements is true?