Your Answer : (Not Answered)

Correct Answer : D

Manju joined after 6 months.

Profits are shared in the ratio of capital multiplied by time. Equal shares mean equal products. Bharati invested for 12 months; let Manju invest for \(m\) months:

\[ \begin{aligned} 18000 \times 12 &= 36000 \times m \\ m &= 6 \end{aligned} \]

Manju's money was at work for 6 months, so she joined 12 - 6 = 6 months after the start. Joining after 10, 5 or 8 months would leave her capital working for 2, 7 or 4 months, giving products of 72,000, 252,000 or 144,000 against Bharati's 216,000.

Your Answer : (Not Answered)

Correct Answer : B

Correct answer: 100 sq. cm

For a square of side \(a\), the diagonal is \(a\sqrt{2}\).

\[a\sqrt{2} = 10\sqrt{2} \quad\Longrightarrow\quad a = 10 \text{ cm}\]

\[\text{Area} = a^2 = 100 \text{ sq. cm}\]

Equivalently, the area of a square is half the square of its diagonal: \(\tfrac{1}{2}(10\sqrt{2})^2 = 100\).

Your Answer : (Not Answered)

Correct Answer : A

A cone's lateral surface is what the cardboard has to supply, so find the radius first.

\[ r = \sqrt{l^{2} - h^{2}} = \sqrt{25^{2} - 24^{2}} = \sqrt{625 - 576} = \sqrt{49} = 7 \text{ cm} \]

\[ \text{CSA} = \pi r l = \frac{22}{7} \times 7 \times 25 = 550 \text{ cm}^{2} \]

\[ \text{sheet area} = 8 \times 550 = 4400 \text{ cm}^{2} \]

A cone rolled from a sheet has no base, so only the curved surface counts - adding \( \pi r^{2} \) would overstate each cone by 154 cm².

Your Answer : (Not Answered)

Correct Answer : B

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

The rates differ by year, so multiply the two growth factors rather than raising one to a power. The second year's rate is \( 10 + 2 = 12\% \).

\[ A = 77500 \times 1.10 \times 1.12 \]

\[ = 77500 \times 1.232 = 95{,}480 \]

\[ \text{CI} = 95480 - 77500 = \text{Rs. } 17{,}980 \]

Averaging the rates to 11% and squaring would give Rs. 17,975.98 - close, but not the same, because compounding is not linear in the rate.

Your Answer : (Not Answered)

Correct Answer : A

With \( b \) the still-water speed and \( r \) the stream's,

\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]

\[ \frac{35}{b + 1} + \frac{35}{b - 1} = 12 \]

\[ \frac{35(b - 1) + 35(b + 1)}{b^{2} - 1} = \frac{70b}{b^{2} - 1} = 12 \]

\[ 70b = 12b^{2} - 12 \quad\Longrightarrow\quad 6b^{2} - 35b - 6 = 0 \]

\[ b = \frac{35 + \sqrt{1225 + 144}}{12} = \frac{35 + 37}{12} = 6 \text{ kmph} \]

Checking: 35 km at 7 kmph takes 5 hours and at 5 kmph takes 7 - twelve hours in total.

Your Answer : (Not Answered)

Correct Answer : B

Correct answer: Pilot

Everyone faces the centre, so each person’s left is the next seat clockwise and their right the next seat anticlockwise.

Put G in place. The politician sits three to G’s right, and C beside G; of C’s two possible seats, only one leaves room for an architect two seats to C’s right without clashing with the politician. B three to H’s right, with H barred from both the politician’s and the architect’s seat, then leaves one workable placing, and A and F must be neighbours with neither of them the politician - which forces E into the politician’s seat and settles A and F. The banker two to A’s left and the doctor two to A’s right complete the picture.

Clockwise the table reads G (pilot) → C (engineer) → H (doctor) → F (teacher) → A (businessman) → E (politician) → D (banker) → B (architect). The teacher is two seats from C as required, the engineer three from D, and the pilot G is clear of the politician.

Once the other seven professions are placed, only the pilot is left for G - and the seat suits it, since the pilot may not sit beside the politician and G’s neighbours are B and C.

Your Answer : (Not Answered)

Correct Answer : D

Correct answer: Both I and II follow

Conclusion I follows directly: only good dancers are invited, and good dancers have charming personalities, so every invitee has one. Conclusion II is the contrapositive of that same chain - anyone without a charming personality is not a good dancer, and so is not invited. A statement and its contrapositive are logically equivalent, so if the first follows the second must.

Your Answer : (Not Answered)

Correct Answer : D

Correct answer: 35

Each term is one less than a square: \( 2^2-1=3 \), \( 3^2-1=8 \), \( 4^2-1=15 \), \( 5^2-1=24 \), so the next is \( 6^2-1 = \mathbf{35} \), followed by \( 7^2-1 = 48 \).

Your Answer : (Not Answered)

Correct Answer : B

The Union Budget is generally presented in February.

Under Article 112 the government lays the Annual Financial Statement before Parliament every year. By long practice it was presented on the last working day of February, and since 2017 it has been presented on 1 February, so that it can be passed before the financial year starts on 1 April.

A full budget has been presented in July only in election years, after a new government takes office (an interim budget in February is followed by the full one later, as in 2014 and 2019). January and December are never the regular months.

Your Answer : (Not Answered)

Correct Answer : A

The famous Kushan ruler was Kanishka.

Kanishka, who ruled in the late first or early second century CE from Purushapura (Peshawar), was the greatest of the Kushan kings. He was a patron of Mahayana Buddhism, and the Fourth Buddhist Council is said to have been held in Kashmir under his rule.

The other names belong to different dynasties. Pulakeshin (printed Pulukesin) was a Chalukya king of Badami, Pushyamitra (printed Pushyamita) founded the Shunga dynasty after the Mauryas, and Bimbisara was a Haryanka king of Magadha in the Buddha's time.

Your Answer : (Not Answered)

Correct Answer : D

All three statements are true, so the answer is A, B and C.

The nuclear fuel cycle is the series of industrial processes involved in producing electricity from uranium in nuclear power reactors (A). It begins with mining uranium ore and ends with the disposal of nuclear waste (B), so it covers both the front end, before the reactor, and the back end, after it.

To prepare uranium for a reactor it is mined, milled into uranium oxide concentrate (yellowcake), converted into uranium hexafluoride gas, enriched to raise the share of uranium-235, and fabricated into fuel pellets and assemblies (C). These three statements follow the standard description, so no option leaving one out is correct.

Your Answer : (Not Answered)

Correct Answer : A

It was 1951.

Experimental Breeder Reactor I in Idaho lit four light bulbs on 20 December 1951 - the first electricity generated from nuclear energy. The first station to supply a grid was Obninsk in the Soviet Union in 1954.

Your Answer : (Not Answered)

Correct Answer : D

Correct answer: Egypt

Egypt’s official language is Arabic. Iran’s is Persian and Turkey’s is Turkish, neither of which is an Arabic language, and Israel’s official language is Hebrew.

Your Answer : (Not Answered)

Correct Answer : D

Stellar distances are measured in light years.

A light year is the distance light travels in one year, about \(9.46\times10^{15}\) m. Proxima Centauri, the nearest star, is 4.24 light years away, so we see it as it was more than four years ago.

Your Answer : (Not Answered)

Correct Answer : D

The Argumentative Indian was written by Amartya Sen, published in 2005.

It argues that India has a long tradition of public debate and heterodoxy, and that this, rather than any imported idea, is the ground of its democracy. Sen won the Nobel Prize in Economics in 1998.

Your Answer : (Not Answered)

Correct Answer : C

It is at Tarapur.

The Tarapur Atomic Power Station in Maharashtra was commissioned in 1969 with two American-built boiling water reactors, under a 1963 agreement with General Electric - India's first nuclear power station.

Your Answer : (Not Answered)

Correct Answer : C

Rome is called the Eternal City, a name going back to the Roman poets Tibullus and Ovid, who held that the city would endure whatever became of its empire.

It is the capital of Italy and encloses Vatican City, the world's smallest sovereign state.

Your Answer : (Not Answered)

Correct Answer : C

Correct answer: Lake Baikal

Lake Baikal in southern Siberia reaches about 1,642 metres, making it the deepest lake in the world and the largest by volume - it holds roughly a fifth of all the unfrozen fresh water on the surface of the planet, more than all five North American Great Lakes together. Its depth comes from its origin: it lies in a continental rift, where the crust is pulling apart, so the basin is still deepening. It is also the oldest lake known, at about 25 million years, and that long isolation has produced a remarkable endemic fauna, including the world’s only exclusively freshwater seal. Lake Superior is the largest freshwater lake by surface area, and Lake Victoria the largest in Africa and the second largest by area, but both are comparatively shallow. The Caspian is the largest enclosed body of water on Earth, but it is saline and generally classed as a sea.

Your Answer : (Not Answered)

Correct Answer : A

Take the cost price as 2 and the marked price as 3, and let the discount be \( d \% \). The profit percentage is then \( 1.5d \), since profit and discount are in the ratio 3 : 2.

The selling price can be written two ways:

\[ 3\left(1 - \frac{d}{100}\right) = 2\left(1 + \frac{1.5d}{100}\right) \]

\[ 3 - 0.03d = 2 + 0.03d \quad\Rightarrow\quad 0.06d = 1 \quad\Rightarrow\quad d = 16.67 \]

So the discount is 16.66%, or one-sixth.

Your Answer : (Not Answered)

Correct Answer : C

He readjusted to life on earth at Houston.

Group Captain Shubhanshu Shukla (printed 'Shubhansu') flew to the International Space Station on the Axiom-4 mission in June 2025, the first Indian to visit the station. After splashdown off California on 15 July 2025, he went through about a week of supervised rehabilitation in Houston, Texas, to readapt to Earth's gravity.

Hamilton and Washington had no role in the recovery, and Lucknow is his home town, where he was welcomed later.