Your Answer : (Not Answered)

Correct Answer : A

Expand the square of the sum.

\[ (a+b)^{2} = a^{2} + b^{2} + 2ab \]

\[ 22^{2} = 404 + 2ab \quad\Longrightarrow\quad 484 - 404 = 2ab \]

\[ ab = 40 \]

The two numbers turn out to be 2 and 20.

Your Answer : (Not Answered)

Correct Answer : A

We solve this continued fraction from the bottom up.

Step 1: \(1+\frac{1}{2} = \frac{3}{2}\).

Step 2: The expression becomes \(1 + \frac{1}{1+\frac{1}{3/2}} = 1 + \frac{1}{1+\frac{2}{3}}\).

Step 3: \(1+\frac{2}{3} = \frac{5}{3}\).

Step 4: The expression becomes \(1 + \frac{1}{5/3} = 1 + \frac{3}{5}\).

Step 5: \(1 + \frac{3}{5} = \frac{5+3}{5} = \frac{8}{5}\).

Your Answer : (Not Answered)

Correct Answer : B

For a frustum the slant height spans the difference of the radii horizontally and the height vertically.

\[ l = \sqrt{h^{2} + (R - r)^{2}} \]

\[ l = \sqrt{4^{2} + (5-2)^{2}} = \sqrt{16 + 9} = \sqrt{25} = 5 \text{ cm} \]

It is the difference of the radii, not their sum, that forms the horizontal leg - using \( 5+2 \) would give \( \sqrt{65} \), the third option.

Your Answer : (Not Answered)

Correct Answer : B

B works in factory Y.

Factory X must hold W and D (they are not in Y) and M (who cannot be in T's factory Y). That fills X, so the other three, T, B and H, are in Y.

No one works in both factories, and the data are sufficient.

The key step is that M must be in factory X: T is in Y and M cannot share T's factory, so X is completed by W, D and M, and B has to be in Y with T and H.

Your Answer : (Not Answered)

Correct Answer : E

Clearly, I directly follows from the statement. So, I is implicit. Also, according to the statement, this particular book gives 'most comprehensive' information on the issue. So, it can be assumed that other books are also available on this topic. Thus, II is also implicit.

Your Answer : (Not Answered)

Correct Answer : C

The missing number is 20.

Each term is the product of two consecutive numbers:

\[ \begin{aligned} &1 \times 2,\ 2 \times 3,\ 3 \times 4, \\ &4 \times 5,\ 5 \times 6 \end{aligned} \]

which gives 2, 6, 12, 20, 30. Equivalently, the differences grow by 2 each time: 4, 6, 8, 10, so the gap after 12 must be 8 and the gap before 30 must be 10. Each wrong option breaks this: 15 would leave gaps of 3 and 15, 18 gaps of 6 and 12, and 25 gaps of 13 and 5.

Your Answer : (Not Answered)

Correct Answer : A

Correct answer: True

This is a straightforward chain: the Taj is inside Agra, and Agra is inside India, so the Taj must be inside India. Containment carries through, and the conclusion is true.

Your Answer : (Not Answered)

Correct Answer : D

The key's answer is M. V. Kamath.

Madhav Vittal Kamath was a veteran journalist, a former editor of The Illustrated Weekly of India and later chairman of Prasar Bharati, and wrote many books on Indian public life. The paper credits India of our dreams to him.

Do not confuse the title with India of My Dreams, a compilation of Mahatma Gandhi's writings. Dr. Rajendra Prasad is known for India Divided and Dr. S. Radhakrishnan for The Hindu View of Life, so neither is the author here.

Your Answer : (Not Answered)

Correct Answer : C

The water level remains the same.

A floating ice cube displaces its own weight of water. When it melts it becomes exactly that weight of water, which occupies exactly the volume it was displacing, so the level does not change. This is why melting sea ice does not by itself raise sea level, whereas melting land ice does.

Your Answer : (Not Answered)

Correct Answer : C

Rangana Herath of Sri Lanka was the first left-arm spinner to take 400 Test wickets, reaching the mark in 2017.

He finished with 433 in 93 Tests, most of them taken after he turned 30 - a career shaped by the years he spent behind Muttiah Muralitharan.

Your Answer : (Not Answered)

Correct Answer : D

Glenn McGrath was nicknamed Pigeon, a reference to his very thin legs when he first arrived in state cricket.

He took 563 Test wickets, more than any other fast bowler at the time of his retirement in 2007.

Your Answer : (Not Answered)

Correct Answer : A

Collagen is the major ingredient of leather - the fibrous protein of animal skin.

Tanning cross-links its fibres so they no longer rot or dry hard. Collagen is also the commonest protein in the body, forming the framework of skin, tendon, bone and cartilage.

Your Answer : (Not Answered)

Correct Answer : A

It was built at Thumba.

The Thumba Equatorial Rocket Launching Station near Thiruvananthapuram was set up in 1962 and made its first launch in November 1963, chosen because the earth's magnetic equator passes over it. The first rocket parts were carried to the pad on a bicycle.

Your Answer : (Not Answered)

Correct Answer : D

All four processes operate at the macro scale. Laterisation works in the hot wet tropics, podsolisation in cool humid forests, calcification in semi-arid grasslands, salinisation in arid basins, and gleisation in waterlogged ground.

Each is a broad, climate-controlled soil-forming regime, so the option covering them all is correct.

Your Answer : (Not Answered)

Correct Answer : B

Correct answer: Eleven

There are eleven Fundamental Duties in Article 51-A. Ten were inserted by the 42nd Amendment in 1976, and the eleventh - requiring a parent or guardian to provide educational opportunity to a child between six and fourteen - was added by the 86th Amendment in 2002. That last amendment is worth noting for doing two things at once: it created the right to education as Article 21-A and added the corresponding duty. The ten original duties include abiding by the Constitution and respecting the national flag and anthem, cherishing the ideals of the freedom struggle, upholding the sovereignty and integrity of India, defending the country, promoting harmony and renouncing practices derogatory to the dignity of women, valuing the composite culture, protecting the natural environment, developing the scientific temper, safeguarding public property and abjuring violence, and striving towards excellence. They were recommended by the Swaran Singh Committee, are borrowed in conception from the constitution of the former USSR, apply to citizens only, and are not enforceable by any court.

Your Answer : (Not Answered)

Correct Answer : D

Self bias makes the gate negative of the source, but an enhancement device needs the gate positive of the source to form a channel at all, so the arrangement cannot start. Gate current is zero either way, and the remaining objections do not arise. That two members of one family need opposite gate polarities is the first thing to establish before choosing a bias circuit for either.

Your Answer : (Not Answered)

Correct Answer : D

Inverting the relation:

\[ \alpha = \frac{\beta}{1+\beta} = \frac{99}{100} = 0.99 \]

giving 0.99. The value 1.01 is impossible, since alpha must be less than one for a device that cannot deliver more collector current than emitter current. Checking that a computed alpha lies below unity is a quick sanity test, and it catches the commonest algebraic slip in this pair of formulae.

Your Answer : (Not Answered)

Correct Answer : D

Each diode conducts for half the cycle, working with its diagonal partner, which is why the average current per diode is half the load current. With a capacitor filter the conduction narrows to a burst near each peak, so the last option describes a real effect but not the resistive-load case the question asks about. Establishing the resistive-load behaviour first and then adding the filter's effect is the reliable way through these circuits. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Your Answer : (Not Answered)

Correct Answer : C

An exponent of four means the power falls as the fourth power of range, which in decibels is forty per decade, against twenty for free space. Per doubling it is twelve decibels rather than four times the loss in decibels, which is the trap in the third option. Expressing a power law as decibels per decade is the most useful form for coverage work, because measured data are plotted that way and the exponent can be read straight off the slope.

Your Answer : (Not Answered)

Correct Answer : B

All three hold. The presence of arbitrary functions is the essential difference from the ordinary case, and it is why one boundary curve rather than a few numbers is needed to pin a solution down. The discriminant test mirrors the classification of conics, and for the same algebraic reason