Tüm alıştırma soruları

The following table provides the annual expenditure (in ₹ Crores) of four administrative departments in a state over three fiscal years, with some values missing (indicated by dashes '—').

Based on the data provided, what is the difference (in ₹ Crores) between the average department expenditure in 2022-23 and the average department expenditure in 2021-22?

A positive integer $N$ when successively divided by $4$, $5$, and $6$ leaves remainders of $2$, $3$, and $4$, respectively. What is the sum of the remainders obtained when the smallest such number $N$ is successively divided by $6$, $5$, and $4$, in that order?

Find the unit digit of the numerical expression $N = (567^{63} \times 234^{45}) - 343^{37}$.

Three automatic signaling beacons in a traffic control system flash at regular time intervals of $\frac{4}{15}$ hours, $\frac{9}{20}$ hours, and $\frac{14}{35}$ hours, respectively. If all three beacons flash simultaneously at 12:00 noon, after how many hours will they all flash together again for the first time?

The table below presents the quarterly renewable energy generation (in Megawatts, MW) of four geographical zones of a state in 2025:

Based on the table, what is the average quarterly renewable energy generation (in MW) for the South Zone in 2025?

In an agricultural extension survey conducted among $250$ farmers in an administrative block, awareness of three welfare schemes was evaluated: Crop Insurance ($C$), Soil Health Card ($S$), and Kisan Credit Card ($K$). The survey revealed that $120$ farmers are aware of $C$, $110$ are aware of $S$, and $130$ are aware of $K$. Additionally, $45$ farmers are aware of both $C$ and $S$, $50$ are aware of both $S$ and $K$, and $40$ are aware of both $C$ and $K$. If $15$ farmers are aware of all three schemes, how many farmers are aware of exactly two of these schemes?

In a state public infrastructure development scheme for the fiscal year 2025–26, a total budget of ₹$9,000$ crore was allocated across four major sectors: Agriculture Irrigation, Highway Expansion, Solar Infrastructure, and Rural Electrification.

Agriculture Irrigation received $28\%$ of the total allocated budget. The budget allocated to Highway Expansion was $37.5\%$ more than the budget allocated to Agriculture Irrigation. The remaining allocated budget was divided between Solar Infrastructure and Rural Electrification in the ratio $5 : 4$.

Regarding the actual expenditures recorded at the end of the fiscal year:
- Agriculture Irrigation utilized $85\%$ of its allocated funds.
- Highway Expansion utilized $92\%$ of its allocated funds.
- Solar Infrastructure had an unspent budget of ₹$315$ crore.
- Rural Electrification spent an amount equal to $1.25$ times the unspent budget of Agriculture Irrigation.

Based on the information provided, what is the total unspent budget across all four sectors combined, expressed in crore rupees?

If $x = \frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}$ and $y = \frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}$, what is the value of $x^2 + y^2$?

A decentralized network consists of $13$ primary verification nodes. A smart contract generates a total of $37^{105}$ encrypted tokens that must be distributed equally among these $13$ nodes. The leftover tokens that cannot be distributed equally are sent to a burn address. How many tokens will be sent to the burn address?

A water storage tank is currently filled to $0.65$ of its total capacity. If the tank currently contains $130$ liters of water, what is the total capacity of the tank in liters?

An event organizer needs to pack $144$ apples, $180$ oranges, and $216$ bananas into identical fruit baskets. Each basket must contain only one type of fruit, and all baskets must contain exactly the same number of fruits. What is the minimum total number of fruit baskets the organizer must prepare?

In a digital encryption protocol, a security key is generated based on a master integer $N$. When $N$ is successively divided by $6$, $8$, and $9$, the resulting remainders are $4$, $3$, and $7$, respectively. If $N$ is the smallest possible positive integer that satisfies these conditions, what is the remainder when $N$ is divided by $19$?

Compute the exact Highest Common Factor (HCF) for the fractions $\frac{6}{25}$ and $\frac{9}{10}$. Express your final result as a decimal.

In a single row of books on a library shelf, an Encyclopedia is $28^{\text{th}}$ from the left end and a Dictionary is $35^{\text{th}}$ from the right end. If there are exactly 12 books placed strictly between them, what is the minimum possible total number of books in this row?

A secure digital vault requires a 2-digit numerical access code. The code is determined by calculating the value of the expression $(P + Q) - (R \times S)$, where the variables are defined based on the mathematical classification of numbers:

* $P$: The sum of all single-digit prime numbers.
* $Q$: The product of the smallest positive composite number and the smallest odd prime number.
* $R$: The total count of whole numbers strictly less than $10$ that are classified as neither prime nor composite.
* $S$: The smallest positive integer $n$ for which the expression $\sqrt{12n}$ results in a rational number.

What is the final numerical access code?

A mechanical watch, which gains time at a continuous and uniform rate, is observed to be exactly 5 minutes slow at 8:00 AM on a Sunday. By 8:00 AM on the immediately following Tuesday, the same watch is exactly 7 minutes fast. How many hours after 8:00 AM on that Sunday did the watch display the true, correct time?