Your Answer : (Not Answered)

Correct Answer : D

The correct relation is 3h = 2d.

Set the cylinder's volume equal to the sphere's, with the same radius \(r\):

\[ \begin{aligned} \pi r^{2} h &= \tfrac{4}{3}\pi r^{3} \\ h &= \tfrac{4}{3} r = \tfrac{2}{3} d \end{aligned} \]

since \(d = 2r\). Multiplying by 3 gives \(3h = 2d\). Option C reverses the ratio, and \(h = d\) or \(2h = d\) would make the cylinder too tall or too short to match the sphere's volume.

Your Answer : (Not Answered)

Correct Answer : A

First, express all bases as prime numbers.

\(4^{11} = (2^2)^{11} = 2^{22}\).

The expression is \(2^{22} \times 7^5 \times 11^2\).

The total number of prime factors is the sum of the exponents of the prime bases.

Total prime factors = 22 + 5 + 2 = 29.

Your Answer : (Not Answered)

Correct Answer : C

At 3 o'clock, the hands of the watch are 15 min. space apart.
To be in opposite directions, they must be 30 min. spaces apart. 
Minute hand must gain 45 min. space (15 + 30 min)
55 min spaces are gained in 60 min. 
45 min. spaces would be gained in (60/55 × 45) min.
Required time = 49 1/11 min. past 3.

Your Answer : (Not Answered)

Correct Answer : B

Find the radius from the area, then use it for the circumference.

\[ \pi r^{2} = 616 \quad\Longrightarrow\quad r^{2} = \frac{616 \times 7}{22} = 196 \]

\[ r = 14 \text{ cm} \]

\[ C = 2\pi r = 2 \times \frac{22}{7} \times 14 = 88 \text{ cm} \]

The two formulas share \( \pi \) but not the power of \( r \), so the radius must be extracted before the circumference can be found.

Your Answer : (Not Answered)

Correct Answer : C

Five consecutive numbers are symmetric about the middle one, so their total is five times that middle value. Writing the set as \( c-2,\, c-1,\, c,\, c+1,\, c+2 \):

\[ S = 5c \]

Removing one member cuts the total by 20 per cent, so the number removed is

\[ 0.20 \times 5c = c \]

which is the middle number, c.

The result holds whatever the five numbers are, since the arithmetic never uses their actual values - only that they are consecutive and so centred on \( c \).

Your Answer : (Not Answered)

Correct Answer : E

The statement mentions that after the amendment, no child below 14 years will be engaged in hazardous employment. This means that before the amendment, the practice of employing children below 14 years was in vogue. This in turn means that employers will have to abide by the amendment. So, both I and II follow.

Your Answer : (Not Answered)

Correct Answer : A

The region not in the Luni basin is Churu.

The Luni rises in the Aravalli hills near Ajmer and flows south-west past Jodhpur and Barmer to the Rann of Kutch. Its main tributaries come off the western slopes of the Aravallis, so its basin takes in Ajmer, Pali, Sirohi, Jalore, Jodhpur and Barmer.

Churu lies in the north of the Thar, in the region of inland drainage where rivers either do not exist or end in the sand without reaching the sea, so it belongs to no Luni catchment.

Your Answer : (Not Answered)

Correct Answer : D

Antaranga Sadhana includes Dharna (Dharana).

Patanjali's eight limbs of yoga are divided into two groups. The outer practices (Bahiranga) are Yama, Niyama, Asana, Pranayama and Pratyahara. The inner practices (Antaranga) are Dharana (concentration), Dhyana (meditation) and Samadhi.

Pratyahara, Niyama and Pranayama are among the outer limbs, so only Dharana fits.

The inner limbs are called 'inner' because they work on the mind directly, while the outer limbs prepare the body and the senses.

Your Answer : (Not Answered)

Correct Answer : B

The answer is Only B is correct.

Macronutrients are needed in large amounts: carbohydrates, proteins and fats (and water). Vitamins and minerals are needed in small amounts and are micronutrients, so Statement A is wrong.

Folic acid (vitamin B9) is a micronutrient needed for making DNA and red blood cells and for preventing neural tube defects in the developing foetus, so Statement B is correct.

Your Answer : (Not Answered)

Correct Answer : C

The Oaths Act was enacted in 1969.

It prescribes the oaths and affirmations to be made by witnesses, interpreters and jurors, and provides that a witness may affirm rather than swear.

Your Answer : (Not Answered)

Correct Answer : D

Bacterial replication begins with DNA replication.

The circular chromosome is copied from a single origin; the two copies then attach to the plasma membrane and are drawn apart as the cell grows, and only then does the membrane pinch inward and the daughter cells separate.

Your Answer : (Not Answered)

Correct Answer : A

Nitrogen makes air a moderate supporter of combustion.

Being chemically inert under ordinary conditions, it dilutes the oxygen. In pure oxygen things burn fiercely and fires would be uncontrollable; with 78 per cent nitrogen present, combustion proceeds at a manageable rate.

Your Answer : (Not Answered)

Correct Answer : A

X-rays are produced in a Coolidge tube.

A heated tungsten filament emits electrons, which are accelerated through tens of kilovolts onto a tungsten target. Their sudden deceleration gives bremsstrahlung, and knocked-out inner-shell electrons give the characteristic lines. The hot cathode lets the tube's current and voltage be controlled independently, which the older gas tubes could not do.

Your Answer : (Not Answered)

Correct Answer : A

Sound travels fastest in steel.

Its speed is \(v = \sqrt{E/\rho}\), and a solid's elastic modulus is enormously larger than a liquid's or a gas's. Sound moves at about \(5,960\ \mathrm{m\,s^{-1}}\) in steel, \(1,500\) in water and \(343\) in air. In vacuum it cannot travel at all.

Your Answer : (Not Answered)

Correct Answer : C

They were made for Louis XIV.

The king, who was short, had heels made for himself and decreed that only nobles might wear red ones. Heels had earlier been worn by Persian cavalry to hold the foot in the stirrup.

Your Answer : (Not Answered)

Correct Answer : B

Bhanu Athaiya was the first Indian to share an Oscar.

She won for costume design in Richard Attenborough's Gandhi in 1983, sharing the award with John Mollo. Satyajit Ray received an honorary Oscar for lifetime achievement in 1992.

Your Answer : (Not Answered)

Correct Answer : A

Correct answer: New York

The United Nations has its headquarters in New York City, on a site beside the East River that is international territory rather than United States soil. The General Assembly and the Security Council both sit there. The organisation is deliberately dispersed, however, and several of the options name genuine UN centres. Geneva hosts the second largest office, along with the Human Rights Council, the WHO, the ILO and the WTO. Vienna hosts the International Atomic Energy Agency and the office on drugs and crime. Nairobi hosts the UN Environment Programme. Paris is the seat of UNESCO, but not of the UN itself. One principal organ sits elsewhere entirely: the International Court of Justice is at The Hague in the Netherlands. The UN was founded in 1945 with 51 members and now has 193; India was a founding member.

Your Answer : (Not Answered)

Correct Answer : A

Mauritius is the most densely populated country in Africa, with roughly 640 people per km². Its small island area of about 2,040 km² carries a population of some 1.3 million.

Rwanda, the densest mainland country, has about 500 people per km², and Burundi about 450.

Your Answer : (Not Answered)

Correct Answer : C

The Singareni coalfields lie in the Godavari valley.

They stretch along the Pranhita-Godavari basin in Telangana and are the only significant coal deposit in peninsular India south of the Damodar valley. Singareni Collieries is one of India's oldest coal companies, dating from 1889.

Your Answer : (Not Answered)

Correct Answer : A

Curvature \( \kappa \) measures how fast the tangent direction turns per unit arc length, and the radius of curvature is \( \rho = 1/\kappa \). It is the radius of the circle that matches the curve in position, tangent and second derivative at the point, so a straight line has zero curvature and infinite radius