Your Answer : (Not Answered)

Correct Answer : D

The remainder is 2.

The remainder on division by 10 is the units digit of the product, and only the units digits of the factors matter: 3, 7, 7, 8 and 2.

\[ \begin{aligned} 3 \times 7 &= 21 \to 1 \\ 1 \times 7 &= 7 \\ 7 \times 8 &= 56 \to 6 \\ 6 \times 2 &= 12 \to 2 \end{aligned} \]

So the product ends in 2. 6 is the units digit one step before the last factor, a sign of dropping the 52. 3 and 8 come from slips in the chain.

Your Answer : (Not Answered)

Correct Answer : D

The leak would empty the full cistern in 40 hours.

Without the leak the cistern fills in 8 hours; with it, in 10. The leak's rate is the difference between the two filling rates:

\[ \frac{1}{8} - \frac{1}{10} = \frac{5 - 4}{40} = \frac{1}{40} \]

The leak empties 1/40 of the cistern per hour, so 40 hours to empty it. 16, 20 and 25 hours do not satisfy this; for example, a 20-hour leak would give a net rate of 1/8 - 1/20 = 3/40 and a filling time of 13.3 hours.

Your Answer : (Not Answered)

Correct Answer : C

The sum of x and y is 29.

There are 15 values, so the median is the 8th value in order.

Original data in order: 8, 9, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17. The 8th value is 14, so x = 14.

Replacing 8 by 18: 9, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 18. The 8th value is now 15, so y = 15.

x + y = 14 + 15 = 29. 28 would follow if the median did not change, which forgets that removing the smallest value shifts every position by one.

Your Answer : (Not Answered)

Correct Answer : B

Reversing adds 18, so \( 9(b-a) = 18 \) and \( b - a = 2 \); the digits also multiply to 24.

\[ a(a+2) = 24 \quad\Longrightarrow\quad a = 4, \ b = 6 \]

\[ \text{number} = 46 \]

Your Answer : (Not Answered)

Correct Answer : B

To find the unit digit of \(7^{7^7}\), we need to find the remainder of the power \(7^7\) when divided by the cycle length of 7, which is 4. So we need to find \(7^7 \pmod 4\). We can write 7 as \(8-1\). So, \(7 \equiv -1 \pmod 4\). Then \(7^7 \equiv (-1)^7 = -1 \equiv 3 \pmod 4\). The remainder of the power is 3. We need the 3rd unit digit in the cycle of 7 (7, 9, 3, 1), which is 3.

Your Answer : (Not Answered)

Correct Answer : B

Let the ten's digit be x and the unit's digit be y.

The number is 10x + y. The reversed number is 10y + x.

Given, x + y = 8 (Equation 1).

Given, (10x + y) - (10y + x) = 36.

9x - 9y = 36, which simplifies to x - y = 4 (Equation 2).

Adding Equation 1 and Equation 2: 2x = 12, so x = 6.

From x + y = 8, we get 6 + y = 8, so y = 2.

The number is 10(6) + 2 = 62.

Your Answer : (Not Answered)

Correct Answer : A

Let the tower be \( h \) m and the observation point \( d \) m away. The bottom of the flagstaff is the top of the tower.

\[ \tan 30^{\circ} = \frac{h}{d} \quad\Longrightarrow\quad d = h\sqrt{3} \]

\[ \tan 45^{\circ} = \frac{h+7}{d} \quad\Longrightarrow\quad h + 7 = d = h\sqrt{3} \]

\[ h(\sqrt{3} - 1) = 7 \quad\Longrightarrow\quad h = \frac{7}{\sqrt{3}-1} = \frac{7(\sqrt{3}+1)}{2} \]

\[ h = 3.5 \times 2.732 = 9.562 \text{ m} \]

Both sightings share the same \( d \), which is what allows one to be substituted into the other.

Your Answer : (Not Answered)

Correct Answer : A

Five tosses give \( 2^{5} = 32 \) outcomes. Only one of them - all heads - has no tail, so use the complement.

\[ P(\text{no tail}) = \frac{1}{32} \]

\[ P(\text{at least one tail}) = 1 - \frac{1}{32} = \frac{31}{32} \]

"At least one" is almost always easier through the complement than by counting one, two, three, four and five tails separately.

Your Answer : (Not Answered)

Correct Answer : A

Only the \( a \) terms are alike.

\[ 6a - 11a = -5a \]

\[ \therefore\ -5a + 8b \]

Since \( 11 > 6 \), the result is negative; the \( 8b \) is unlike and stays put.

Your Answer : (Not Answered)

Correct Answer : A

Correct answer: Maruti is next left of Ambassador.

Fiat stands at one end with Ambassador three places to its right; Fargo is four to Fiat’s right and Cadillac next beyond it. Maruti must lie between Ambassador and Bedford, which fills the two remaining places near the Fiat end, and Mercedes takes the last. From left to right the line reads Fiat, Bedford, Maruti, Ambassador, Fargo, Cadillac, Mercedes.

Maruti stands third and Ambassador fourth, so Maruti is immediately to Ambassador’s left. Of the others: Bedford is not next to Fiat on that side, Bedford is not at an end, and Fiat lies two places to Maruti’s left.

Your Answer : (Not Answered)

Correct Answer : D

Correct answer: 1,3,5,2,4

The words run in order of the steps from schooling to a livelihood: Study → Examination → Apply → Job → Earn.

Your Answer : (Not Answered)

Correct Answer : C

Correct answer: None of these

Translating the code: \(@\) is “greater than”, \(\#\) is “greater than or equal to”, \(\%\) is “less than or equal to”, \(*\) is “equal to” and \(\$\) is “less than”. The statements read \( R < S \), \( S > T \) and \( T \ge U \). Chaining the last two gives \( S > T \ge U \), so \( S > U \). Conclusion III is \( S @ U \), that is \( S > U \) - true. But conclusion I is \( U \% S \), that is \( U \le S \), and \( S > U \) certainly makes \( U \le S \) hold - so I is true as well. Conclusion II is \( T < R \); here \( R < S \) and \( T < S \) both point at S from below, which fixes no order between R and T, so II does not follow. Conclusions I and III are true and II is not, and no option offers that combination - hence “None of these”. The trap is reading \(\le\) as requiring equality to be possible; a strict inequality satisfies it.

Your Answer : (Not Answered)

Correct Answer : B

The alphabets are coded as shown :

So, in SEARCH,

S ia coded as 2,
E as 1,
A as 4,
R as 6,
C as 7,
H as 3.
Thus, the code for SEARCH is 214673

Your Answer : (Not Answered)

Correct Answer : D

AOL stands for America Online.

It was the dominant consumer internet service of the 1990s in the United States, its CDs mailed to millions of households. Its merger with Time Warner in 2000 is often cited as the worst in corporate history.

Your Answer : (Not Answered)

Correct Answer : B

Bromine is the non-metal that is liquid at room temperature - a dense, dark red-brown liquid giving off a choking red vapour.

It is the only liquid non-metal; mercury is the only liquid metal. Chlorine is a gas, phosphorus a solid, and helium a gas.

Your Answer : (Not Answered)

Correct Answer : C

Quit India Day is celebrated on 9 August.

Gandhi launched the movement with his 'Do or Die' speech at Gowalia Tank in Bombay on 8 August 1942, and the entire Congress leadership was arrested at dawn on 9 August.

Your Answer : (Not Answered)

Correct Answer : D

The theme of World Environment Day 2012 was ‘Green Economy: Does it include you?’

Brazil hosted it, in the year of the Rio+20 conference. A green economy is one that improves human well-being while reducing environmental risk and ecological scarcity.

Your Answer : (Not Answered)

Correct Answer : B

It was Victor Hugo.

Les Miserables, published in 1862, follows Jean Valjean, imprisoned nineteen years for stealing bread, through the Paris of the 1832 uprising. One sentence in it runs to over 800 words.

Your Answer : (Not Answered)

Correct Answer : A

The Sea of Japan is noted for its fishing. The cold Oyashio and the warm Tsushima currents meet in it, and the mixing brings up nutrients that make plankton and therefore fish abundant.

Sardine, squid, salmon and crab support major Japanese, Korean and Russian fisheries there.

Your Answer : (Not Answered)

Correct Answer : C

The Equator is the largest circle of latitude, about 40,075 km round.

It is the only parallel that is a great circle - its plane passes through the centre of the Earth. Every other parallel is a smaller circle, shrinking to a point at each pole.