Your Answer : (Not Answered)

Correct Answer : A

The z-score tells you how far a data point is from the Mean in terms of Standard deviations.

\(z = (x - \mu)/\sigma\). A z-score of 2 means the value is two standard deviations above the mean, and -1 one standard deviation below.

Percentages and likelihoods can be read from a z-table using the z-score, but the z-score itself is a distance in standard deviations, not a percentage or a probability, and not an average of deviations.

Your Answer : (Not Answered)

Correct Answer : B

The value of x is 3.

Simplify each root by taking out square factors:

\[ \begin{aligned} \sqrt{12} + \sqrt{147} &= 2\sqrt{3} + 7\sqrt{3} \\ &= 9\sqrt{3} \end{aligned} \]

So \(9\sqrt{x} = 9\sqrt{3}\) and \(x = 3\). Adding the numbers under the roots (12 + 147 = 159) is the common error and gives none of the options.

Your Answer : (Not Answered)

Correct Answer : C

Let D, R, and M be the sets of people who got medals in Dance, Dramatics, and Music respectively.

Given: n(D)=36, n(R)=12, n(M)=18, n(D ∪ R ∪ M)=45, n(D ∩ R ∩ M)=4.

We use the formula:

n(D∪R∪M) = n(D)+n(R)+n(M) - [n(D∩R) + n(R∩M) + n(M∩D)] + n(D∩R∩M)

45 = (36 + 12 + 18) - [Sum of intersections of pairs] + 4

45 = 66 - [Sum of pairs] + 4

45 = 70 - [Sum of pairs]

Sum of pairs = n(D∩R) + n(R∩M) + n(M∩D) = 25.

The number of people who received medals in exactly two categories is given by:

[n(D∩R) + n(R∩M) + n(M∩D)] - 3 × n(D∩R∩M)

= 25 - 3 × 4 = 25 - 12 = 13.

Your Answer : (Not Answered)

Correct Answer : B

The 4-digit numbers range from 1000 to 9999. The first 4-digit number divisible by 15 is 1005 (since \(1000 \div 15 = 66\) rem 10, so \(15-10=5\) needs to be added). The last 4-digit number divisible by 15 is 9990 (since \(9999 \div 15 = 666\) rem 9, so \(9999-9=9990\)). The numbers form an Arithmetic Progression. The number of terms is \(\frac{\text{Last Term} - \text{First Term}}{\text{Common Difference}} + 1 = \frac{9990 - 1005}{15} + 1 = \frac{8985}{15} + 1 = 599 + 1 = 600\).

Your Answer : (Not Answered)

Correct Answer : C

Each term is the previous one divided by 4.

\[ 40960 \to 10240 \to 2560 \to 640 \to 160 \to 40 \to 10 \]

The fifth term should be \( 640 \div 4 = 160 \), not 200.

So 200 is the wrong number - and \( 200 \div 4 = 50 \), which would not give the 40 that follows.

Your Answer : (Not Answered)

Correct Answer : B

The angle is measured from the observer's eye, 2 m above the ground, so the trigonometry gives only the part of the tower above eye level.

\[ \tan 30^{\circ} = \frac{x}{10\sqrt{3}} \]

\[ x = 10\sqrt{3} \times \frac{1}{\sqrt{3}} = 10 \text{ m} \]

Adding the observer's own height:

\[ \text{tower} = 10 + 2 = 12 \text{ m} \]

Forgetting to add the 2 m gives 10 m, which is offered as the first distractor. The \( 10\sqrt{3} \) is chosen so the radical cancels exactly.

Your Answer : (Not Answered)

Correct Answer : C

\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]

Quarterly compounding quarters the rate, and nine months is three quarters.

\[ \text{rate} = \frac{16}{4} = 4\% \text{ per quarter}, \qquad n = 3 \]

\[ A = 15625 \times (1.04)^{3} = 15625 \times 1.124864 = \text{Rs. } 17{,}576 \]

\[ \text{CI} = 17576 - 15625 = \text{Rs. } 1951 \]

The principal is \( 25^{3} \) and the amount \( 26^{3} \), since the factor is \( \left(\tfrac{26}{25}\right)^{3} \) - which is why both come out as whole numbers.

Your Answer : (Not Answered)

Correct Answer : D

Count the factors of 3 first, then pair them up. Legendre's rule gives the exponent of a prime in a factorial:

\[ \left\lfloor\frac{99}{3}\right\rfloor + \left\lfloor\frac{99}{9}\right\rfloor + \left\lfloor\frac{99}{27}\right\rfloor + \left\lfloor\frac{99}{81}\right\rfloor = 33 + 11 + 3 + 1 = 48 \]

So \( 3^{48} \) divides 99! and no higher power does. Because \( 9 = 3^{2} \), each factor of 9 consumes two of those threes:

\[ \text{highest power of } 9 = \left\lfloor\frac{48}{2}\right\rfloor = 24 \]

Answer 48 is the trap for stopping at the power of 3 without halving it.

Your Answer : (Not Answered)

Correct Answer : A

Correct answer: Both A and R are true and R is the correct explanation of A.

Bats emit ultrasonic pulses and listen for the echoes, building a picture of obstacles and prey from the time each echo takes to return. That echolocation is exactly what lets them fly and hunt in complete darkness. Both are true and R explains A.

Your Answer : (Not Answered)

Correct Answer : B

Correct answer: Circumlocutory

The relation is word : its opposite. Dilatory - slow and delaying - is the opposite of expeditious; direct is the opposite of circumlocutory, going round about instead of straight to the point. Tortuous describes a winding path rather than winding speech.

Your Answer : (Not Answered)

Correct Answer : B

The translator was C. Achutha Menon.

C. Achutha Menon, Chief Minister of Kerala from 1969 to 1977, was also a writer, and among his works is a Malayalam translation of H.G. Wells' A Short History of the World.

E.M.S. Namboodiripad wrote widely on Kerala's history and Marxism, E.K. Nayanar wrote memoirs and political essays, and P.K. Vasudevan Nair was a journalist, but the Wells translation is Achutha Menon's.

Your Answer : (Not Answered)

Correct Answer : B

CNG is mainly methane.

Compressed Natural Gas is natural gas compressed to about 200 to 250 times atmospheric pressure for use as a vehicle fuel. Natural gas is mostly methane (CH₄), typically 80 to 90 per cent or more, with small amounts of ethane, propane and other gases. Because methane burns more cleanly than petrol or diesel, CNG produces less particulate pollution.

Butane and propane are the main components of LPG (liquefied petroleum gas), the cooking gas, and ethane is only a minor component of natural gas.

Your Answer : (Not Answered)

Correct Answer : D

A child's protoplasm is identical only to that of an identical twin.

Identical twins arise from a single fertilised egg that splits, so they carry exactly the same genes. A child receives half its genes from each parent and so is identical to neither.

Your Answer : (Not Answered)

Correct Answer : D

FTP stands for File Transfer Protocol.

It is one of the oldest internet protocols, defined in 1971, and uses two connections - one for commands and one for the data itself. It sends credentials in plain text, so SFTP and FTPS have largely replaced it.

Your Answer : (Not Answered)

Correct Answer : A

Johannes Gutenberg invented it.

At Mainz in the 1440s he combined movable metal type cast in a hand mould, an oil-based ink and a screw press adapted from wine-making. His Bible of about 1455 was the first substantial book printed in Europe with movable type.

Your Answer : (Not Answered)

Correct Answer : A

The International Day of Non-Violence falls on 2 October, Gandhi's birthday.

The UN General Assembly adopted it in 2007. In India the same day is Gandhi Jayanti and is one of three national holidays, with Independence Day and Republic Day.

Your Answer : (Not Answered)

Correct Answer : D

A Passage to India was written by E.M. Forster, published in 1924.

It turns on what did or did not happen in the Marabar Caves, and on whether an Englishman and an Indian can be friends under empire. Forster wrote no further novel in the remaining 46 years of his life.

Your Answer : (Not Answered)

Correct Answer : A

The book caused a furore because it allegedly asked Hindus to leave Pakistan.

Books published abroad that touch on communal questions have repeatedly provoked protest and demands for banning in India, and the Customs Act allows the import of a publication to be prohibited.

Your Answer : (Not Answered)

Correct Answer : B

Yisrael Kristal was certified as the world's oldest man.

Born in Poland in 1903, he survived Auschwitz and settled in Haifa. Guinness recognised him in 2016, and he died in August 2017, a month short of his 114th birthday.

Your Answer : (Not Answered)

Correct Answer : D

Jude Felix is a famous Indian hockey player.

He captained the national team in the 1990s, played at the 1992 and 1996 Olympics, and received the Arjuna Award in 1994. He later coached the junior national side.