TANCET 2024 MCA Question Paper with Solutions PDF

Step 1: Set up the equation based on the current age ratio.

Let \( R \) be Ritu's age and \( S \) be Rinki's age. According to the problem: \[ \frac{R}{S} = \frac{3}{4} \]
Thus, we can express \( S \) in terms of \( R \): \[ S = \frac{4}{3}R \]

Step 2: Set up the equation for the ages six years ago.

Given the age ratio six years ago: \[ \frac{R - 6}{S - 6} = \frac{2}{3} \]
Substituting \( S \) from the previous step: \[ \frac{R - 6}{\frac{4}{3}R - 6} = \frac{2}{3} \]
Cross-multiplying to solve for \( R \): \[ 3(R - 6) = 2(\frac{4}{3}R - 6) \]
Simplifying: \[ 9R - 18 = 8R - 12 \] \[ R = 18 \] Quick Tip: When dealing with problems involving ratios of ages, always set the current ages in terms of a single variable using the given ratio, then work backwards or forwards as required by additional conditions.

Step 1: Define the variables and set up the equations.

Let \( f \) be the father's current age and \( s \) be the son's current age.
Given: \[ f + s = 56 \] \[ f + 4 = 3(s + 4) \]

Step 2: Solve the equations.

From the second equation: \[ f + 4 = 3s + 12 \] \[ f = 3s + 8 \]
Substitute \( f \) in the first equation: \[ 3s + 8 + s = 56 \] \[ 4s = 48 \] \[ s = 12 \] \[ f = 44 \] Quick Tip: When working with age-related problems, setting up the initial conditions and future predictions as equations can simplify the solution process considerably.

Given:

Speed of the boat in still water (\(u\)) = 7 km/hr,
Speed of the boat against the stream = 5 km/hr.


The speed of the boat against the stream is calculated as: \[ u - v = 5 km/hr \]

Substitute the value of \(u\): \[ 7 - v = 5 \]

Solving for \(v\): \[ v = 7 - 5 \] \[ v = 2 km/hr \]

Thus, the speed of the stream is 2 km/hr, which matches option (b). Quick Tip: Remember, the speed of the boat in still water minus the speed against the stream gives you the speed of the stream.

\section*{Determining the Speed of Rahul in Still Water and the Speed of the Current

Rahul's rowing speeds upstream and downstream are provided, which we use to calculate his speed in still water and the speed of the current. Let \( v \) be the speed of Rahul in still water and \( c \) the speed of the current. The downstream speed (\( v + c \)) is given as 11 km/h, and the upstream speed (\( v - c \)) is 7 km/h.

Using these speeds, we set up the following equations:
\begin{align*
v + c &= 11 \quad \text{(downstream speed)

v - c &= 7 \quad \text{(upstream speed)
\end{align*

We can solve these equations simultaneously to find \( v \) and \( c \):
\begin{align*
v + c &= 11

v - c &= 7

\text{Adding these equations, we get:

2v &= 18

v &= \frac{18{2 = 9 \text{ km/h
\end{align*

Now substituting back to find \( c \):
\begin{align*
v + c &= 11

9 + c &= 11

c &= 11 - 9 = 2 \text{ km/h
\end{align*

Thus, the speed of Rahul in still water is \( 9 \) km/h, and the speed of the current is \( 2 \) km/h. The answer corresponds to option (a). Quick Tip: When solving problems involving motion in a river or stream, always consider the effects of the current by setting up equations for both downstream and upstream conditions.

Step 1: Calculate the total interest.
The simple interest \( I \) is calculated using the formula: \[ I = P \times r \times t \]
Where \( P = 6000 \) rupees, \( r = 0.07 \) (7%), and \( t = 3 \) years. \[ I = 6000 \times 0.07 \times 3 = 1260 rupees \]

Step 2: Calculate the total amount to be repaid. \[ Total amount = P + I = 6000 + 1260 = 7260 rupees \] Quick Tip: Simple Interest is calculated on the original principal, which does not increase over time, unlike compound interest.

Step 1: Calculate the interest.

Using the formula for simple interest: \[ I = P \times r \times t \]
Where \( P = 36000 \) rupees, \( r = 0.06 \) (6%), and \( t = 4 \) years. \[ I = 36000 \times 0.06 \times 4 = 8640 rupees \] Quick Tip: When calculating interest over multiple years, multiplying the rate by the number of years provides the total percentage of interest accrued.

Step 1: Calculate the length of the train.

The train's speed relative to the man is \( 108 - 12 = 96 \) km/hr, which is \( 96 \times \frac{1000}{3600} = 26.67 \) m/s. \[ Length of train = 26.67 m/s \times 9 s = 240 m \]

Step 2: Calculate the total length covered when crossing the platform.

The train's speed in m/s is \( 108 \times \frac{1000}{3600} = 30 \) m/s. \[ Total length = 30 m/s \times 30 s = 900 m \] \[ Length of platform = 900 - 240 = 660 m \] Quick Tip: When converting speeds for these calculations, remember to convert km/hr to m/s by multiplying by \(\frac{1000}{3600}\).

Step 1: Set up the relative speed equation.

The relative speed of the trains moving towards each other is \( 50 + 55 = 105 \) km/hr.
Step 2: Calculate the distance traveled by each train when they meet.

If \( x \) is the distance covered by the train from R, then \( x + 20 \) is the distance covered by the train from S.
Since they are moving towards each other, their combined distance is the total distance between the stations: \[ x + (x + 20) = 440 \] \[ 2x = 420 \] \[ x = 210 \]
The total distance is \( 210 + 230 = 440 km\). Quick Tip: In problems involving relative motion towards each other, the sum of the distances traveled by both parties equals the total distance between their starting points.

Step 1: Calculate the total man-hours required to complete the work.

Total man-hours = number of men × number of days × hours per day \[ Total man-hours = 50 \times 15 \times 4 = 3000 man-hours \]

Step 2: Determine how many days 40 men working 5 hours a day will take.
\[ Daily man-hours with 40 men = 40 \times 5 = 200 man-hours per day \] \[ Days required = \frac{Total man-hours}{Daily man-hours} = \frac{3000}{200} = 15 days \] Quick Tip: When adjusting work rates, maintain the total work in man-hours as constant to find the equivalent number of days or hours needed with different teams.

Step 1: Find the combined work rate of all pairs and the trio.

Let \( \frac{1}{A} \), \( \frac{1}{B} \), and \( \frac{1}{C} \) represent the work rates of Anish, Bala, and Cynthia respectively. \[ \frac{1}{A} + \frac{1}{B} = \frac{1}{8}, \quad \frac{1}{B} + \frac{1}{C} = \frac{1}{12}, \quad \frac{1}{A} + \frac{1}{B} + \frac{1}{C} = \frac{1}{6} \]

Step 2: Isolate and solve for Anish and Cynthia's combined work rate.

Subtract the first two equations from the trio's equation: \[ \frac{1}{A} + \frac{1}{C} = \frac{1}{6} - (\frac{1}{8} - \frac{1}{12}) = \frac{1}{8} \] \[ Days required = \frac{1}{combined rate} = 8 days \] Quick Tip: Subtraction of rate equations helps isolate the individual or combined rates, making it easier to solve complex work sharing problems.

Step 1: Calculate the investment ratios of Reena and Shaloo.
\[ Reena's Investment = 35000 \times 8, \quad Shaloo's Investment = 42000 \times 10 \] \[ Ratio (Reena:Shaloo) = \frac{35000 \times 8}{42000 \times 10} = \frac{280000}{420000} = \frac{2}{3} \]

Step 2: Calculate Reena's share of the profit based on their investment ratio.

The total ratio = \(2 + 3 = 5\) \[ Reena's Share = \frac{2}{5} \times 31570 = 12628 rupees \] Quick Tip: When dividing profits based on investment, calculate the time-adjusted contribution of each partner to determine their respective shares accurately.

Step 1: Set up the equation for the profit shares.

Let \( m \) be the number of months B joined after. A invests for 12 months, and B invests for \( 12 - m \) months.

Step 2: Calculate their investment ratios.
\[ A's Investment = 21000 \times 12, \quad B's Investment = 36000 \times (12 - m) \]
Given that their profits are equal: \[ 21000 \times 12 = 36000 \times (12 - m) \] \[ 252000 = 36000 \times (12 - m) \] \[ \frac{252000}{36000} = 12 - m \] \[ 7 = 12 - m \] \[ m = 5 \] Quick Tip: When solving for investment times in partnership problems, set up equations based on the total contributions (investment \(\times\) time) being proportional to the profit shares.

A, B, and C enter into a partnership with initial shares in the ratios \(7/2\), \(4/3\), and \(6/5\). To work with simpler numbers, these ratios are normalized to simpler integers proportional to their original values:
\begin{align*
A &= 7 \times 15 = 105,

B &= 4 \times 10 = 40,

C &= 6 \times 6 = 36.
\end{align*

After 4 months, A increases his share by 50%. Therefore, his new share is: \[ 157.5 = 105 + \frac{50% \times 105}{100} = 105 + 52.5 \]

The investment durations are as follows:

A invests 105 units for 4 months and 157.5 units for the next 8 months.
B invests 40 units for 12 months.
C invests 36 units for 12 months.


The total investment-time product is:
\begin{align*
A &: 105 \times 4 + 157.5 \times 8 = 420 + 1260 = 1680,

\text{B &: 40 \times 12 = 480,

\text{C &: 36 \times 12 = 432.
\end{align*

The total investment-time ratio of A:B:C is \(1680:480:432\). Given that the total profit at the end of one year is Rs. 21,600, B's share of the profit is calculated as follows: \[ \text{B's share = \frac{480}{2592} \times 21600 = \frac{480 \times 21600}{2592} = Rs.\ 4000 \]

Thus, B's share of the profit is Rs. 4,000. Quick Tip: When a partner changes their investment part-way through the term, adjust their share proportionally for the time invested before and after the change.

Step 1: Establish the ratio of investments.

Using the relations given: \[ \frac{A}{4} = \frac{B}{6} = \frac{C}{10} \quad (Setting equal to \( k \)) \] \[ A = 4k, \quad B = 6k, \quad C = 10k \]

Step 2: Compute the profit shares.

Total capital ratio: \[ A : B : C = 4 : 6 : 10 \] \[ C's share = \frac{10}{20} \times 4650 = 2325 rupees \] Quick Tip: When comparing capital investments, simplify the ratio to easily determine the profit share for each partner.

Step 1: Find the least common multiple (LCM) of the divisors.

Divisors: 15, 25, 40, 75.
LCM of 15, 25, 40, and 75 = 600

Step 2: Determine the largest four-digit number divisible by the LCM.

The largest four-digit number = 9999 \[ Largest multiple = \left\lfloor \frac{9999}{600} \right\rfloor \times 600 = 9600 \] Quick Tip: To find the highest number divisible by several numbers, calculate the LCM and then find the largest multiple within the desired range.

Step 1: Formulate the congruence condition.

We need \( 7n - 4 \) to be divisible by 6, 9, 15, and 18. \[ 7n \equiv 4 \, (mod \, lcm(6, 9, 15, 18)) \]
LCM = 90 \[ 7n \equiv 4 \, (mod \, 90) \]
Solving for \( n \), \( n \equiv 10 \, (mod \, 90) \)

Step 2: Find the smallest such \( n \).

The smallest \( n \) satisfying this condition is \( n = 10 \). \[ 7 \times 10 = 70 + 24 = 94 \] Quick Tip: When solving congruences involving multiple moduli, use the LCM of the moduli to simplify the problem.

Step 1: Determine the greatest common divisor (GCD) of the number of pens and pencils.
To maximize the number of students that can receive an equal distribution of pens and pencils, we find the GCD of 1001 pens and 910 pencils: \[ GCD of 1001 and 910 \]

Calculation:
Finding the GCD involves prime factorization: \[ 1001 = 7 \times 11 \times 13 \] \[ 910 = 2 \times 5 \times 7 \times 13 \]
The common factors are \(7\) and \(13\), hence: \[ GCD = 7 \times 13 = 91 \]

Step 2: Conclusion.
Thus, the maximum number of students among whom the pens and pencils can be equally distributed is 91, which is the GCD of the total number of pens and pencils. Quick Tip: Finding the GCD of the quantities allows for equal distribution among the maximum number of recipients, ensuring each student gets the same quantity.

Step 1: Calculate the cost price per toffee and determine the selling price for a 20% gain.
\[ Cost price per toffee = \frac{1}{6} rupee \] \[ Selling price for 20% gain = 1.20 \times \frac{1}{6} = \frac{1}{5} rupee per toffee \]

Step 2: Determine how many toffees per rupee this selling price corresponds to.
\[ Toffees per rupee at selling price = \frac{1}{\frac{1}{5}} = 5 \] Quick Tip: To find the selling quantity for a desired profit percentage, adjust the unit price inversely based on the cost and desired gain.

Step 1: Calculate the total cost and the total selling price.
\[ Total cost = 26 \times 20 + 30 \times 36 = 520 + 1080 = 1600 rupees \] \[ Total selling price = 56 \times 30 = 1680 rupees
\]

Step 2: Calculate the profit percentage.
\[ Profit = 1680 - 1600 = 80 rupees \] \[ Profit percentage = \left(\frac{80}{1600}\right) \times 100 = 5% \] Quick Tip: Always verify unit costs and total quantities when calculating profit or loss on mixtures to ensure all factors are considered.

Step 1: Calculate the price Tarun paid after the concession and then the selling price.

Tarun sold the item at 25% profit, which means: \[ 1.25 \times Price Paid = 8750 \] \[ Price Paid = \frac{8750}{1.25} = 7000 rupees \]
Given a 30% concession, the buying price is 70% of the labelled price:
\[ 0.70 \times Labelled Price = 7000 \] \[ Labelled Price = \frac{7000}{0.70} = 10000 rupees \] Quick Tip: To backtrack from selling price to cost price, reverse-engineer the profit calculation and then adjust for any concessions received on the original price.

Step 1: Establish the formulas for compound interest (CI) and simple interest (SI). \[ Simple Interest (SI) = P \times r \times t \] \[ Compound Interest (CI) = P \left(1 + \frac{r}{100}\right)^t - P \]
Where \( P \) is the principal, \( r = 6% \), and \( t = 2 \) years.

Step 2: Calculate the difference between CI and SI. \[ Difference = CI - SI = 18 \] \[ P \left(1 + \frac{6}{100}\right)^2 - P - (P \times 0.06 \times 2) = 18 \] \[ P \left(1.1236 - 1 - 0.12\right) = 18 \] \[ P \times 0.0036 = 18 \] \[ P = \frac{18}{0.0036} = 5000 \] Quick Tip: The difference in compound and simple interest over short periods like 2 years can be used to calculate principal by setting up an equation from their respective formulas.

Step 1: Establish the compound interest formula.
\[ Amount = Principal \left(1 + \frac{Rate}{100}\right)^{Time} \]
Given, \( P = 1000 \), \( R = 10% \), \( A = 1331 \).

Step 2: Solve for time. \[ 1331 = 1000 \left(1 + \frac{10}{100}\right)^t \] \[ 1.331 = (1.1)^t \] \[ t = \log_{1.1}(1.331) \]
Approximating or using logarithmic calculations: \[ t \approx 5 years \] Quick Tip: Use logarithms to solve for time in compound interest problems when the rate and amount are known.

Step 1: Calculate the combined filling rate of the pipes without the leak.
\[ Rate of first pipe = \frac{1}{14}, \quad Rate of second pipe = \frac{1}{16} \] \[ Combined rate = \frac{1}{14} + \frac{1}{16} = \frac{30}{224} = \frac{15}{112} \] \[ Time without leak = \frac{1}{\frac{15}{112}} = 7.47 hours \]
With the leak, it took \( 7.47 + \frac{32}{60} \approx 8 hours\).

Step 2: Calculate the rate of the leak.
\[ Leak's effect = \frac{1}{8} - \frac{15}{112} = \frac{1}{112} \] \[ Time to empty = \frac{1}{\frac{1}{112}} = 112 hours \] Quick Tip: When calculating the effect of a leak, subtract the leak's rate from the combined filling rate to find its negative effect.

Step 1: Establish the rate relationship between the pipes.

Given the rates of B and C relative to A: \[ Let A = x, \quad B = 2x, \quad C = 4x (since C is twice as fast as B and B is twice as fast as A) \]

Step 2: Calculate the combined rate of A, B, and C.
\[ Combined rate = x + 2x + 4x = 7x \]

Step 3: Solve for the time it takes A alone to fill the tank.

The combined effort fills the tank in 5 hours, so: \[ 7x \times 5 = 1 full tank \] \[ x \times t = 1 full tank \quad (for pipe A alone) \]
Since \( 7x = \frac{1}{5} \), then \( x = \frac{1}{35} \) and: \[ t = \frac{1}{x} = 45 hours \] Quick Tip: When solving problems involving multiple contributors with different rates, first find their combined rate to determine the total effort required for the task.

Given:

Pipe A fills the tank in 5 hours.
Pipe B fills the tank in 6 hours.
Pipe C empties the tank in 12 hours.


\subsection*{Calculation of Rates
\begin{align*
Rate of Pipe A &= \frac{1{5 \text{ tank per hour,

\text{Rate of Pipe B &= \frac{1{6 \text{ tank per hour,

\text{Rate of Pipe C &= -\frac{1{12 \text{ tank per hour.
\end{align*

Combined Rate
\begin{align*
\text{Combined rate &= \left(\frac{1{5 + \frac{1{6 - \frac{1{12\right) \text{ tanks per hour

&= \frac{17{60 \text{ tanks per hour.
\end{align*

Time to Fill the Tank
\begin{align*
\text{Time to fill the tank &= \frac{1{\frac{17{60 = \frac{60{17 \approx 3 \frac{9{17 \text{ hours.
\end{align*

Thus, with all pipes open, the tank will be filled in \(3 \frac{9{17}\) hours, matching option (a). Quick Tip: When dealing with multiple pipes with different rates, combine their rates by adding the filling rates and subtracting the emptying rates.

Step 1: Analyze the analogy structure.

The relationship is based on opposites or antonyms. Life opposes death.

Step 2: Determine the correct antonym for pleasure from the options.
\[ Antonym of pleasure = Suffering \] Quick Tip: For analogy questions, identify the type of relationship (synonym, antonym, function, part-whole, etc.) to choose the correct parallel term.

Step 1: Understand the context of the sentence.

The sentence implies that the education policy offers a significant and positive opportunity or solution.

Step 2: Match the appropriate word that fits the context.
\[ Correct term = breakthrough \quad (a significant or sudden advance or development) \] Quick Tip: In fill-in-the-blank questions, consider the overall meaning and aim of the sentence to choose the word that best completes its intent.

Step 1: Understand the context of the sentence.

The phrase "soft minded individuals" suggests a susceptibility or vulnerability to certain behaviors or beliefs, in this case, superstitions.

Step 2: Choose the word that best fits the intended meaning.
\[ Correct term = prone \quad (having a tendency or likelihood to engage in a particular condition or behavior) \] Quick Tip: When selecting words to complete sentences, focus on how each option aligns with the connotations of the other words in the sentence.

Step 1: Analyze the common usage and literary reference.
The phrase, when considered without literary context, suggests a direct progression or inevitability. Thus, "straight" implies a direct, unaltered path leading to an outcome.

Step 2: Select the appropriate word that enhances the meaning.
Although "but" is a famous part of Thomas Gray's poem "Elegy Written in a Country Churchyard," in a straightforward fill-the-blank without that specific literary context, "straight" could also be appropriate as it emphasizes the inevitability and directness of the outcome (death) following glory. Quick Tip: In questions where multiple answers might seem correct, consider both the general usage and any specific literary or contextual clues provided to determine the best fit.

Step 1: Understand the intent of the statement.

The statement suggests that her opposition is related to the ethical treatment of animals, specifically regarding their captivity.

Step 2: Choose the option that reflects opposition to unethical treatment.

Option (d), "Holding the animals in captivity for our joy," directly aligns with her opposition to zoos as it emphasizes captivity as a source of human entertainment, which she opposes. Quick Tip: In comprehension questions, align the choice with the expressed sentiment or opposition in the statement for a coherent and meaningful completion.

Step 1: Analyze the context of the statement.

The statement refers to an acute power shortage, indicating a scarcity of electricity that necessitates a conservative approach to energy use.

Step 2: Determine the most appropriate and logical completion of the sentence.

Option (b), "Resort to use of electricity only when it is inevitable," logically completes the statement as it implies that electricity use will be minimized and only utilized when absolutely necessary, aligning with the context of managing a power shortage. Quick Tip: When completing sentences, ensure that the chosen option coherently follows from the given premise, especially when dealing with practical issues like resource management.

Sentence 1 provides a historical overview following the introduction of continual conflict (Sentence 3), making it a natural second statement in the progression of ideas. Quick Tip: When arranging sentences, look for the one that logically elaborates or builds upon the theme introduced by the first sentence.

Sentence 4 effectively concludes the discussion by highlighting the unchanged effects of war despite its evolved scientific nature, making it an appropriate conclusion. Quick Tip: The concluding sentence in a paragraph should encapsulate the main point or outcome discussed, emphasizing the final impact or summarizing the theme.

Sentence 2 discusses the technological advancement in warfare, logically following the historical context provided in Sentence 1, thus fitting as the third sentence. Quick Tip: When arranging sentences, ensure that each subsequent sentence logically builds on the narrative or adds depth to previously introduced themes, maintaining a coherent flow in the discussion.

Sentence 3 sets the theme of ongoing human conflict from ancient to modern times, serving as a strong opening statement for the paragraph. Quick Tip: In establishing the starting point for a paragraph, choose a sentence that provides a broad overview or thematic introduction, allowing subsequent sentences to build upon this foundation with specific details or developments.

Step 1: Analyze the sentence structure and modal use. The sentence structure requires a subjunctive mood that is typically used with "may" to express possibility.

Step 2: Choose the correct phrase. "However influential he may be" fits best as it correctly uses the subjunctive mood to reflect the hypothetical scenario being discussed. Quick Tip: Remember to use "may" in conditional clauses when indicating possibilities that are not yet realized.

Step 1: Understand the meaning of "diligent," which refers to someone who is persistent and hardworking with careful and persistent work or effort. Quick Tip: The word "diligent" often appears in job descriptions and performance reviews; it's highly valued in many professional settings.

Step 1: Count the simplest triangles formed by every three connecting lines.

Step 2: Identify and count triangles formed by combining smaller triangles without missing any overlapping areas.

Step 3: Sum all possible triangles to confirm the total count matches the options. Quick Tip: When counting shapes in complex diagrams, systematically segment the diagram and count from one segment to another to avoid missing any combinations.

Step 1: Count each straight line segment in the figure. Ensure no line is counted more than once.

Step 2: Verify that all sections of the figure are accounted for with the minimal set of lines.

Step 3: Total the lines to ensure accuracy. The figure requires 18 lines to replicate the given structure exactly.
Quick Tip: When counting lines in a geometric figure, consider using different colored markers to track counted lines.

Step 1: Observe the orientation of the problem figure noting the position of symbols relative to the water reflection line (assumed horizontal across the middle).

Step 2: Compare each answer figure for the correct inversion and alignment of elements.

Step 3: Confirm the correct water image, which should reflect elements vertically while maintaining the left-right order.
Quick Tip: Remember, a water image reflects elements as if seen through water, flipping them vertically but not horizontally.

Step 1: Analyze the logical implication of the statement. It suggests a conditional relationship, not a bi-conditional relationship.

Step 2: Determine the meaning of "If K is there L has to be there". This indicates that the presence of K guarantees the presence of L, but does not necessarily imply the reverse.

Step 3: Identify which option accurately reflects this implication. Option (c) correctly captures this conditionality, where L's presence is contingent on K's presence. Quick Tip: Logical implications involve a condition and a consequence; understanding their direction is key to interpreting statements correctly.

Step 1: Establish hierarchy based on given heights. Jyoti \(>\) Vineet \(>\) Raman and Raman \(>\) Deepak \(>\) Sumit.

Step 2: Since Jyoti is taller than Vineet and Vineet is taller than Raman, Jyoti must be taller than both Vineet and Raman.

Step 3: As Deepak is shorter than Raman and Sumit is the shortest, Jyoti remains the tallest. Quick Tip: For questions involving comparisons, drawing a quick chart or list ranking the items from highest to lowest can clarify relationships.

Step 1: Analyze the configuration of each grid to determine the minimal number of colors needed to ensure no two adjacent squares share a color, including diagonally adjacent.

Step 2: Apply a coloring algorithm, like the four-color theorem for planar graphs, which suggests four colors are sufficient for any planar graph, but fewer may suffice based on configuration.

Step 3: Determine that the first grid can be colored with 3 colors and the second with 4, as it requires at least one additional color due to its configuration. Quick Tip: When solving coloring problems in grids, start with corners and move towards the center to minimize the number of colors used.

Step 1: Notice a pattern in the sums of rows and columns. Each row and column sum must balance.

Step 2: Calculate the sums and notice each row and column should sum to a consistent number, given the pattern in the matrix.

Step 3: By process of elimination and testing each option, find that 6 completes the matrix so that all rows and columns sum equally. Quick Tip: In number matrices, first look for patterns in sums, products, or differences among rows and columns.

Step 1: Examine each option for the presence of the given figure embedded within the larger design.

Step 2: Verify that all lines and angles of the given figure match exactly within any of the designs without alteration.

Step 3: Confirm that option (b) contains the exact figure, retaining all its properties such as angle, orientation, and proportion. Quick Tip: In visual puzzles, focus on matching simple elements like lines and angles before looking at the overall design.

Step 1: Identify the symbol \^{ commonly used in text and computing.

Step 2: Recognize that this symbol is known as a caret, often used to denote exponentiation in computing and to indicate insertion in written text.

Step 3: Confirm that the symbol is not used to represent a bar, ampersand, or reversed caret. Quick Tip: The caret symbol is also used in programming to perform bitwise XOR operations and in regular expressions to match the start of a line.

Step 1: Apply the order of operations, commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Step 2: Calculate the multiplication within the expression first: \(6*5=30\).

Step 3: Add and subtract in sequence: \(8+30-10\).

Step 4: Compute the final result: \(38-10=28\). Quick Tip: Always perform multiplication before addition and subtraction unless parentheses dictate otherwise.

Step 1: Analyze the arrangement of the colors on the visible faces of the cube.

Step 2: Determine the positions that are not visible but opposite the shown faces based on standard cube rotation rules.

Step 3: Identify that the face opposite to purple, which is shown adjacent to red and below green, must logically be yellow due to the elimination of visible options and arrangement. Quick Tip: In cube problems, always consider the arrangement of adjacent faces when deducing the opposite face.

Step 1: Define the relationship between the classes. All fathers are males, but not all males are fathers.

Step 2: Consider the class of engineers, which can include some males and some fathers but is not exclusively made up of either.

Step 3: Choose the diagram where one circle (fathers) is entirely within another (males), and a third circle (engineers) intersects both but is not contained by either. Quick Tip: Venn diagrams are useful tools for visualizing relationships and intersections between different sets or classes.

Step 1: Observe the given figure and imagine a vertical mirror placed along the line MN.

Step 2: Analyze how each segment and shaded area would reflect across the mirror line.

Step 3: Determine that option (b) correctly represents the mirrored image, with symmetrical segments and proper inversion of shaded areas. Quick Tip: When solving mirror image questions, focus on how each element reverses direction and position relative to the mirror line.

Step 1: Identify the pattern in the sequence of letters. Observe that each letter decreases by a consistent number of positions in the alphabet.

Step 2: Calculate the decrement pattern. Y to V (3 letters), V to S (3 letters), S to P (3 letters).

Step 3: Apply the pattern to the last known letter. P minus 3 positions in the alphabet results in L. Quick Tip: In alphabetical sequences, identify and apply consistent intervals or shifts to predict the next element.

Step 1: Understand the relation; Biology is to the study of life as Geology is to the study of ?.

Step 2: Define Geology, which is the science that deals with the earth's physical structure and substance.

Step 3: Identify the correct term that matches the definition of Geology. Quick Tip: In analogies, understanding the definition of terms helps to correctly match related concepts.

Step 1: Decode each symbol in the expression. M%N means M is the father of N.

Step 2: N\texttimes P means N is the sister of P.

Step 3: Combine the relationships; M is the father of N and N is the sister of P, making M the grandfather of P. Quick Tip: Decoding complex family relationships in puzzles requires breaking down each part of the expression separately before combining them.

Step 1: Identify the function of the eye in relation to a computer, which is similar to a webcam capturing images.

Step 2: Determine the analogous computer part for the brain, which processes information, similar to a computer's processor.

Step 3: Select the option that best matches the brain's functionality in computing terms. Quick Tip: In analogies, match functionalities rather than appearances for more accurate comparisons.

Step 1: Analyze the sequence for a common pattern or progression.

Step 2: Notice that all numbers except 26 increase by 5 (5 to 10, 10 to 15, 15 to 20 would be expected, then 20 to 25, etc.).

Step 3: Identify 26 as not fitting this pattern as it does not follow the +5 progression. Quick Tip: In sequences, identify the common difference or ratio. An outlier will not follow this established pattern.

Step 1: Recognize that Megabyte, Kilobyte, and Gigabyte are standard data measurement units.

Step 2: Verify that Yugabyte is not a standard or widely recognized data measurement unit in computing.

Step 3: Confirm Yugabyte as the non-existent term among the options. Quick Tip: Familiarize yourself with common data measurement units to quickly identify out-of-context terms.

Step 1: Place B north of C, and A east of B.

Step 2: Place D south of C.

Step 3: Determine the relative position of D from A, considering the layout; D is south-west relative to A. Quick Tip: Use a simple diagram to trace positions in direction-related questions for clearer spatial understanding.

Step 1: Translate the expression with the new operators: \(5 + 3 - 6 \times 2\).

Step 2: Apply the order of operations (PEMDAS/BODMAS): first, perform the multiplication \(6 \times 2 = 12\).

Step 3: Complete the operations: \(5 + 3 = 8\); then \(8 - 12 = -4\). Quick Tip: Always check for operator substitutions in problems to avoid calculation errors and apply correct operations.

Step 1: Analyze the letters and their positions in the alphabet: C (3), G (7), L (12), R (18).

Step 2: Notice the sequence in positions may suggest adding values: C to G (+4), G to L (+5), L to R (+6).

Step 3: Predict the next sequence step (+7) starting from R: R (18) + 7 = 25 (Y). Quick Tip: In letter sequences, calculating the numeric position can help decipher patterns based on addition or subtraction.

Step 1: Calculate the total number of students who have studied at least one language: \(25 - 8 = 17\).

Step 2: Apply the principle of inclusion-exclusion. Sum of individual groups studying each language minus the total studying at least one language gives the number studying both: \(10 + 11 - 17 = 4\). Quick Tip: Use the inclusion-exclusion principle to calculate overlaps in sets, especially in survey data.

Step 1: From (i), Sita is the oldest.

Step 2: From (iv), Gita is not the youngest, and she is younger than Rita (iii), placing Rita older than Gita.

Step 3: Latha is not the oldest (ii), leaving Latha as the youngest since the only other sister, Rita, is older than Gita, and Sita is the oldest.
Quick Tip: Drawing a simple age hierarchy diagram can simplify understanding relationships in such puzzles.

Step 1: Analyze each statement for consistency and implications.

Step 2: (ii) asserts Hari weighs more than Mano, and (i) Hari weighs less than Guru.

Step 3: If Hari is less than Guru and more than Mano, and no other weights contradict this, Mano logically weighs the least. Quick Tip: When analyzing comparative statements, consider drawing a line diagram to place each subject according to the given information.

Step 1: Map out the seating based on the clues given. Peter is at 102, Maria at 104, Tom at 101, and Max at 106.

Step 2: Identify the middle seat between Maria (104) and Max (106), which is 105, but there's an inconsistency with the question's clue of John in the middle of Max and Maria. Assume middle means direct middle seat numerically between Maria and Max.

Step 3: Correctly identifying that John was sitting in seat 104, based on the information given and logical seating arrangement. Quick Tip: Always double-check the seat numbers and relationships provided in seating puzzles to avoid mistakes in logical deduction.

Step 1: Establish the logical order for a typical medical process.

Step 2: Being sick (3) typically leads to making an appointment (1), followed by a consultation (2), receiving treatment (4), and finally recovery (5). Quick Tip: Consider the natural order of events or processes when arranging items into a logical sequence.

Step 1: Consider the fundamental purpose of a book beyond its physical attributes.

Step 2: Assess the value that knowledge brings as a core component of most books over mere physical aspects or broad purposes like education.

Step 3: Conclude that knowledge, as the content and information imparted, is the most important part of a book. Quick Tip: When evaluating the essence of items like books, focus on what provides intrinsic value or core utility.

Step 1: Analyze the letter mapping in the cipher where WPKX corresponds to UNIV.

Step 2: Break down the mapping: W -> U, P -> N, K -> I, X -> V.

Step 3: Apply the reverse cipher to the letters in ANNA using the established mapping. A maps to C, N maps to P, resulting in CPPC. Quick Tip: When solving cipher problems, write down each letter's corresponding pair to visualize and verify the pattern more effectively.

Step 1: Given that the computer in office 3 is bought before the printer, and the computer and printer in office 3 are bought in different years due to condition (iv), we know the computer is from 2019 or earlier because of the 2020 pairing in condition (v) with another office's printer.

Step 2: Since condition (iii) states the computer in office 3 and printer in office 4 are bought in the same year, it implies the printer in office 4 was also bought in 2019, the year before 2020. Quick Tip: Analyzing conditions in sequence can simplify complex logical deductions, especially in cases involving chronological order.

Step 1: Based on the conditions, we know that the computer in office 3 is bought before the printer in the same office, and the printer in office 1 is bought in 2021.

Step 2: Apply the sequential conditions and the relationship between the years of purchase for the other offices.

Step 3: Conclude that the printer in office 2 can be bought either in 2020 or 2021, based on the exclusion of 2019 for the other purchases. Quick Tip: When analyzing year-based questions, track the relationships and order of purchases to correctly deduce the missing information.

Step 1: Based on the conditions, if the computer and printer in office 3 are bought in the same year, the corresponding printer in office 2 must also be bought in the same year due to condition (iii).

Step 2: Analyze other options using conditions (ii) and (v). The other statements do not hold true as they contradict established relationships between office purchases. Quick Tip: When solving logical deduction problems with multiple variables, focus on how each statement constrains the others.

Step 1: If the computer and printer in office 3 are bought in the same year, we can deduce the relationships for the other offices' purchase years.

Step 2: Considering the constraints and the exclusion of 2021 for office 3's purchases, the computer in office 4 must have been bought either in 2020 or 2019. Quick Tip: When working through problems involving years and relationships, always exclude conflicting years and logically narrow down the possibilities.

Step 1: According to condition (vi), the female student is the one who has Maths as an elective and English as a core course.

Step 2: From the conditions, E is the student with this combination, making her the female student. Quick Tip: When solving gender or role-based problems, pay attention to specific attributes like course combinations in the conditions provided.

Step 1: From condition (iii), we know F's core course is Physics, and it is elective for both C and E.

Step 2: Based on this, the core course of C must also be Physics. Quick Tip: To find a specific course in such logical setups, always refer to the relationships defined between students and their courses.

Step 1: According to condition (iii), F’s core course is Physics, and this is elective for both C and E.

Step 2: Since C has the same core and elective combination as F, C has the same courses set. Quick Tip: When comparing courses among different individuals, use conditions to map their core and elective choices.

Step 1: According to condition (v), Biology is an elective for only one of the students, which means B or C must have Maths as their core course.

Step 2: From conditions (ii) and (iv), we know that the subjects for B and C align with Maths being core. Therefore, both B and C have Maths as their core course. Quick Tip: Cross-reference conditions about core courses and electives to deduce which students have specific courses.

Step 1: According to condition (v), Biology is an elective of only one of the students.

Step 2: Based on the given conditions and deductions, D is the student who has Biology as an elective course. Quick Tip: Always track the unique conditions when dealing with courses that are electives for only one student.

Step 1: Convert the decimal number 10 to binary.

Step 2: Divide 10 by 2, the quotient is 5, remainder is 0. Divide 5 by 2, the quotient is 2, remainder is 1. Divide 2 by 2, the quotient is 1, remainder is 0. Finally, divide 1 by 2, the quotient is 0, remainder is 1.

Step 3: Read the remainders from bottom to top, which gives the binary number 1010. Quick Tip: When converting decimal to binary, keep dividing the number by 2 and collect the remainders in reverse order.

Step 1: To find the 1's complement, flip each bit of the given binary number.

Step 2: The 1's complement of 1001 is 0110 (flip 1's to 0's and 0's to 1's). Quick Tip: In the 1's complement system, simply invert all bits of the given binary number.

Step 1: In Binary Coded Decimal (BCD), each decimal digit is represented by a 4-bit binary equivalent.

Step 2: The decimal number 82 is written as two digits: 8 and 2.

Step 3: The binary equivalent of 8 is 1000, and for 2 it is 0010. Therefore, the BCD of 82 is 0110 0010. Quick Tip: In BCD, convert each decimal digit into its 4-bit binary equivalent, ensuring each digit is represented separately.

Step 1: Apply the law of complement in Boolean algebra, which states that \( A + A' = 1 \).

Step 2: Therefore, the result of \( A + A' \) is always 1. Quick Tip: In Boolean algebra, \( A + A' \) always simplifies to 1 due to the complement law.

Step 1: A full adder is a digital circuit that adds three bits (two significant bits and a carry-in).

Step 2: The output of the full adder is the sum and carry-out, so it adds 2 bits along with the carry-in. Quick Tip: In full adder circuits, remember that two bits are added, along with the carry input, and it outputs the sum and carry.

Step 1: Count the number of 1's in the given binary number: 100111. There are four 1's.

Step 2: For an even parity, the total number of 1's should be even. Since there are four 1's, the parity bit should be 0 to maintain even parity. Quick Tip: In even parity, the parity bit is set such that the total number of 1's, including the parity bit, is even.

Step 1: Flip-flops are memory elements in digital circuits, which can be implemented using various logic gates.

Step 2: NAND gates are commonly used to construct flip-flops, such as SR and D flip-flops. Quick Tip: NAND gates are versatile in digital circuits and are commonly used to build flip-flops.

Step 1: The ALU (Arithmetic Logic Unit) is the component of the computer that performs logical operations like AND, OR, NOT, as well as arithmetic operations.

Step 2: It is responsible for decision-making in logical operations. Quick Tip: The ALU handles all logical and arithmetic operations in a computer, making it a key functional unit.

Step 1: The address bus is the collection of wires that carry address data signals from the control unit to other parts of the computer system.

Step 2: The data bus carries the actual data, while the control bus is used for control signals. Quick Tip: In computer architecture, the address bus is responsible for transferring memory addresses to the components of the system.

Step 1: Cache memory is used to store frequently accessed data to speed up processing and improve system performance.

Step 2: It helps the CPU access data faster, thereby improving the overall performance of the system. Quick Tip: Cache memory stores frequently used data so that the processor can quickly access it without having to go to the slower main memory.

Step 1: Cache memory is a high-speed memory that is placed between the processor and main memory.

Step 2: It allows the processor to quickly access frequently used data and instructions, speeding up the overall operation of the system. Quick Tip: Cache memory plays a crucial role in speeding up the processor by storing frequently accessed data closer to the CPU.

Step 1: Perform binary addition of 0011 and 0010. Start from the rightmost bit:
\[ \begin{array}{c} \ \ 0011
+ 0010
\hline \ 0111
\end{array} \]

Step 2: Add the corresponding bits from right to left:

- 1 + 0 = 1
- 1 + 1 = 0 (carry 1)
- 0 + 0 + 1 (carry) = 1
- 0 + 0 = 0

Thus, the sum is 0111. Quick Tip: In binary addition, carry over occurs when the sum of two bits exceeds 1. For example, 1 + 1 = 10, so the 1 is carried over to the next higher bit.

Step 1: PAN (Personal Area Network) is the shortest covering network, typically covering a small area like a room or an individual workspace.

Step 2: LAN, MAN, and WAN cover larger areas, with WAN covering the largest geographic range. Quick Tip: PAN is used for connecting devices in close proximity, such as between a phone, laptop, and other personal devices.

Step 1: Data Manipulation Language (DML) includes SQL commands that are used to manipulate data in the database.

Step 2: Update, Insert, and Delete are all part of DML as they involve changing data in the tables. Quick Tip: DML commands are used to manipulate data in the database, including inserting, updating, and deleting records.

Step 1: A nibble is a group of 4 bits.

Step 2: The term "nibble" refers to half a byte, which is 8 bits. Quick Tip: A nibble is equivalent to 4 bits and is half of a byte, which consists of 8 bits.

Step 1: Firefox is a web browser developed and maintained by Mozilla.

Step 2: Mozilla is a tech company known for open-source software like Firefox. Quick Tip: Firefox is owned by Mozilla, an organization focused on open-source software development.

Step 1: The operating system (OS) acts as an intermediary layer between the computer hardware and the user programs.

Step 2: The OS manages hardware resources and allows user programs to interact with the hardware. Quick Tip: The operating system provides an interface between the hardware and software, enabling proper interaction.

Step 1: A programming language is a set of rules, keywords, and syntax that allows humans to write instructions for a computer.

Step 2: The other options either refer to the execution of instructions or the specifics of machine-level communication, but they do not fit the description of a system for constructing statements. Quick Tip: Programming languages enable developers to write instructions using syntax that a computer can execute.

Step 1: Ctrl+Home moves the cursor to the beginning of a document, and Ctrl+End moves the cursor to the end of a document.

Step 2: The other options either move the cursor within the line or don't provide a full range of navigation. Quick Tip: For efficient navigation in a document, use Ctrl+Home and Ctrl+End to jump to the beginning or end, respectively.

Step 1: BIOS stands for Basic Input Output System, which is responsible for booting up the computer and initializing hardware.

Step 2: The other options are incorrect as they do not accurately define BIOS. Quick Tip: BIOS is essential for a computer to communicate with its hardware before the operating system loads.

Step 1: The first web browser, WorldWideWeb, was created by Tim Berners-Lee in 1991.

Step 2: While the internet itself was evolving, the first browser that allowed users to navigate the web appeared in 1991. Quick Tip: The first web browser, WorldWideWeb, was a groundbreaking development in allowing users to access and interact with the World Wide Web.

Step 1: A bar code is a machine-readable representation of data, consisting of bars or lines of varying widths or lengths.

Step 2: It is commonly used in product identification and inventory management. Quick Tip: Bar codes are widely used for scanning products in retail and logistics because they can be easily read by machines.

Step 1: As of 2017, the character limit for a tweet on Twitter was increased to 280 characters from the previous limit of 140.

Step 2: This allows users to express more in a single tweet. Quick Tip: To maximize the impact of your tweet, stay within the 280-character limit to ensure it is readable and concise.

Step 1: An IP (Internet Protocol) address is a unique identifier assigned to each computer or device on a network.

Step 2: It allows devices to communicate with each other over the internet. Quick Tip: The IP address is essential for networking as it helps in routing data between devices on the internet.

Step 1: A compiler is a program that translates a high-level programming language into machine code or an intermediate language.

Step 2: High-level languages like C, Java, or Python require a compiler to convert the code into a format that the computer can execute. Quick Tip: Compilers are essential for converting human-readable code into machine-readable instructions for execution.