Kavya \\\\\\\\ go to work yesterday as she \\\\\\\\ feeling well. Select the most appropriate option to complete the above sentence.

What is the value of $\left(\frac{3^{81}}{27^4}\right)^{\frac{1}{3}}$ ?

Identify the option that has the most appropriate sequence such that a coherent paragraph is formed: P. It is because deer, like most of the animals that tigers normally prey on, run much faster! It simply means, another day of empty stomach for the big cats. Q. Tigers spend most of their life searching for food. R. If they trace the scent of deer, tigers follow the trail, chase the deer for a mile or two in the dark, and yet may not catch them. S. For several nights, they relentlessly prowl through the forest, hunting for a trail that may lead to their prey.

Spheres of unit diameter are centered at $(l, m, n)$ where $l$, $m$, and $n$ take every possible integer values. The distance between two spheres is computed from the center of one sphere to the center of the other sphere. For a given sphere, $x$ is the distance to its nearest sphere and $y$ is the distance to its next nearest sphere. The value of $\frac{y}{x}$ is:

The relationship between two variables $x$ and $y$ is given by $x + py + q = 0$ and is shown in the figure. Find the values of $p$ and $q$. Note: The figure shown is representative. !image(https://firebasestorage.googleapis.com/v0/b/gexam-717fd.firebasestorage.app/o/public%2F1781884085939image.png?alt=media&token=5d57c46f-20bf-4ec3-bc65-edea2a03d8e9)

Each row of Column-I has three items and each item is represented by a circle in Column-II. The arrangement of circles in Column-II represents the relationship among the items in Column-I. Identify the option that has the most appropriate match between Column-I and Column-II. Note: The figures shown are representative. !image(https://firebasestorage.googleapis.com/v0/b/gexam-717fd.firebasestorage.app/o/public%2F1781884200744image.png?alt=media&token=638d1172-7dac-40f0-bb2c-177ff6463344)

In the given figure, $EF$ and $HJ$ are coded as $30$ and $80$, respectively. Which one among the given options is most appropriate for the entries marked (i) and (ii) ? !image(https://firebasestorage.googleapis.com/v0/b/gexam-717fd.firebasestorage.app/o/public%2F1781884307566image.png?alt=media&token=5a51ccef-6507-42b6-b316-01d74b682a0c)

Scores obtained by two students $P$ and $Q$ in seven courses are given in the table below. Based on the information given in the table, which one of the following statements is INCORRECT? !image(https://firebasestorage.googleapis.com/v0/b/gexam-717fd.firebasestorage.app/o/public%2F1781884469059image.png?alt=media&token=618336d1-1d24-4409-a7e6-ffe0814969a8)

In the triangle $PQR$, the lengths of $PT$ and $TR$ are in the ratio of $3:2$. $ST$ is parallel to $QR$. Two semicircles are drawn with $PS$ and $PQ$ as diameters, as shown in the figure. Which one of the following statements is true about the shaded area $PQS$? Note: The figure shown is representative. !image(https://firebasestorage.googleapis.com/v0/b/gexam-717fd.firebasestorage.app/o/public%2F1781884559531image.png?alt=media&token=6025b608-afec-4e57-b22f-9a893f470886)

The decimal number system uses the characters $0, 1, 2, \dots, 8, 9$, and the octal number system uses the characters $0, 1, 2, \dots, 6, 7$. For example, the decimal number $12$ ($= 1 \times 10^1 + 2 \times 10^0$) is expressed as $14$ ($= 1 \times 8^1 + 4 \times 8^0$) in the octal number system. The decimal number $108$ in the octal number system is

A shopkeeper buys shirts from a producer and sells them at $20\%$ profit. A customer has to pay $₹3,186.00$ including $18\%$ taxes, per shirt. At what price did the shopkeeper buy each shirt from the producer?

If, for non-zero real variables $x, y$, and real parameter $a > 1$, $$x : y = (a + 1) : (a - 1),$$ then, the ratio $(x^2 - y^2) : (x^2 + y^2)$ is

In the given text, the blanks are numbered (i)–(iv). Select the best match for all the blanks. Following a row (i) the shopkeeper (ii) the price of a frying pan, the cook stood (iii) a row to withdraw cash (iv) the ATM booth.

In the following figure, $$CD = 5\text{ cm}, BE = 10\text{ cm}, AE = 12\text{ cm},$$ $$\angle DAB = \angle DCB, \text{ and } \angle DAE = \angle DBC = 90^\circ$$ Points AFCD create a rhombus. !image(https://uadmin.udsfgecw.tech/file/download/public/public:699d19c5-1ac9-4ee3-8ff2-d038098f6217.png) The length of BF (in cm) is