Your Answer : (Not Answered)

Correct Answer : B

The edge of the new cube is 9 cm.

No metal is lost, so the new volume is the sum of the three volumes:

\[ \begin{aligned} V &= 8^{3} + 6^{3} + 1^{3} \\ &= 512 + 216 + 1 = 729 \\ a &= \sqrt[3]{729} = 9\ \text{cm} \end{aligned} \]

Adding the edges (15 cm) is the trap; volumes add, edges do not. 8 cm is the largest original cube and must be exceeded, while 10 cm and 7 cm give volumes of 1000 and 343, not 729.

Your Answer : (Not Answered)

Correct Answer : B

The values are x = 30° and y = 40°.

RP passes through the centre, so it is a diameter, and an angle in a semicircle is a right angle. So angle RSP = 90° and angle RQP = 90°.

\[ \begin{aligned} \text{In } \triangle RSP: y &= 180^\circ - 90^\circ - 50^\circ = 40^\circ \\ \text{In } \triangle RQP: x &= 180^\circ - 90^\circ - 60^\circ = 30^\circ \end{aligned} \]

The first option gives the same two numbers in the wrong order (x = 40°, y = 30°), the commonest mistake here. 50° and 40° reuse the given angle instead of working out x.

Your Answer : (Not Answered)

Correct Answer : A

Correct answer: \(\sqrt{80}\)

The radius is the distance from the centre to any point on the circle, so apply the distance formula to (3, 2) and (-5, 6).

\[r = \sqrt{(-5-3)^2 + (6-2)^2} = \sqrt{(-8)^2 + 4^2} = \sqrt{64+16} = \sqrt{80}\]

This simplifies to \(4\sqrt{5} \approx 8.94\), which is why neither 8 nor 10 is correct - the radius falls between them.

Your Answer : (Not Answered)

Correct Answer : A

We use Euler's Totient Theorem. First, find \(\phi(15) = \phi(3 \times 5) = \phi(3)\phi(5) = (3-1)(5-1) = 2 \times 4 = 8\). According to the theorem, \(2^8 \equiv 1 \pmod{15}\). We need to find the remainder of the power \(2024\) when divided by 8. The rule for divisibility by 8 is to check the last three digits. \(024\) is divisible by 8. So, \(2024\) is a multiple of 8. We can write \(2024 = 8k\). The expression becomes \((2^8)^k \equiv 1^k \equiv 1 \pmod{15}\). The remainder is 1.

Your Answer : (Not Answered)

Correct Answer : C

Multiply as whole numbers, then place the decimal point using the total number of decimal places in the factors.

(i) \( 261 \times 13 = 3393 \); two places plus one is three, so

\[ 2.61 \times 1.3 = 3.393 \]

(ii) \( 21693 \times 14 = 303702 \); four places plus one is five, so

\[ 2.1693 \times 1.4 = 3.03702 \]

(iii) \( 4 \times 4 \times 4 \times 40 = 2560 \); one, two and three places with none from the 40 gives six, so

\[ 0.4 \times 0.04 \times 0.004 \times 40 = 0.002560 \]

Your Answer : (Not Answered)

Correct Answer : B

Ten's digit = 7 ⇒ units digit =8 ⇒ Hundred's digit =1,2,3,4,5,6.
⇒ Number of ways =1×6

Ten's digit = 6 ⇒ units digit =7,8 ⇒ Hundred's digit =1,2,3,4,5.
⇒ Number of ways =2×5

Ten's digit = 5 ⇒ units digit =6,7,8 ⇒ Hundred's digit =1,2,3,4
⇒ Number of ways =3×4

Ten's digit = 4 ⇒ units digit =5,6,7,8 ⇒ Hundred's digit =1,2,3.
⇒ Number of ways =4×3

Ten's digit = 3 ⇒ units digit =4,5,6,78 ⇒ Hundred's digit =1,2
⇒ Number of ways =5×2

Ten's digit = 2 ⇒ units digit =3,4,5,6,7,8 ⇒ Hundred's digit =1
⇒ Number of ways =6×1

Total number of ways =6+10+12+12+10+6= 56.

Your Answer : (Not Answered)

Correct Answer : D

Correct answer: Both A and R are false.

Both statements are the wrong way round. Bangladesh is one of the world’s great producers of raw jute and exports it; and it is India that holds most of the jute mills, concentrated along the Hooghly. Both A and R are false.

Your Answer : (Not Answered)

Correct Answer : C

You should reach the auditorium and sit wherever seats are available.

The seating is first come, first served, so arriving late means accepting the seats that remain. That respects the rule and the people who came on time.

Asking a friend to reserve seats for latecomers defeats the first-come rule. Fighting with the authorities is aggressive and unjustified, and jumping traffic signals is illegal and dangerous.

Your Answer : (Not Answered)

Correct Answer : C

Correct answer: X

Reversing the second half leaves the series A B C D E F G H I J K L M Z Y X W V U T S R Q P O N. Counting from the right, the seventeenth letter is J, which stands tenth from the left. Counting seven places to the right from J - taking J itself as the first - gives J, K, L, M, Z, Y, X, so the letter arrived at is X. The stem’s phrase “in the middle of 7th and 7th letter” is garbled in this record; the arithmetic that yields the keyed letter is the one shown.

Your Answer : (Not Answered)

Correct Answer : D

The Jallianwala Bagh tragedy took place in 1919.

On 13 April 1919, Baisakhi day, troops under General Dyer opened fire on an unarmed crowd in the Jallianwala Bagh at Amritsar, gathered to protest against the Rowlatt Act and the arrest of local leaders. Hundreds were killed.

1914 is the start of the First World War, 1921 the time of the Non-Cooperation Movement, and 1930 the Salt Satyagraha.

Your Answer : (Not Answered)

Correct Answer : C

The Code of Criminal Procedure came into effect on 1st April, 1974.

The Code of Criminal Procedure, 1973 replaced the Code of 1898. Although it bears the year 1973, it was enacted as Act 2 of 1974 and came into force on 1 April 1974. It sets out the procedure for investigation, arrest, bail, trial and appeal in criminal cases, and was itself replaced by the Bharatiya Nagarik Suraksha Sanhita from 1 July 2024.

The dates in 1973 are the trap, taken from the Code's title. 15 August 1974 is not connected with it.

Your Answer : (Not Answered)

Correct Answer : C

The name that is not a painter is Nana Saheb Panse.

Nana Saheb Panse is remembered as a master of the mridang or pakhawaj, titled Mridangsamrat, and a court musician at Indore. The Panse school of pakhawaj playing is named after him, and a memorial music festival at Bakayan in Damoh district bears his name. He is a musician, not a painter.

The other three names are given in the question as painters of the state. I did not check each of them separately; the answer follows from Panse being a musician.

Your Answer : (Not Answered)

Correct Answer : A

It is Malay.

Malaysian Malay, or Bahasa Malaysia, is the national and official language. It is essentially the same language as Indonesian, differing in spelling conventions and in loanwords - English in Malaysia, Dutch in Indonesia.

Your Answer : (Not Answered)

Correct Answer : B

A particle with 13 protons and 10 electrons is the \(\mathrm{Al^{3+}}\) ion.

Thirteen protons identifies aluminium. Having three fewer electrons than protons gives a charge of \(+3\), and the remaining ten electrons are the neon configuration.

Your Answer : (Not Answered)

Correct Answer : B

Kapil Dev was named India's Cricketer of the Century by Wisden in 2002.

He was the all-rounder who led India to its first World Cup in 1983, took 434 Test wickets and scored 5,248 Test runs.

Your Answer : (Not Answered)

Correct Answer : A

1994–2004 was the International Decade of the World's Indigenous People - the first of two.

The second ran from 2005 to 2014. Together they produced the Permanent Forum on Indigenous Issues and the 2007 Declaration on the Rights of Indigenous Peoples.

Your Answer : (Not Answered)

Correct Answer : B

Mokshagundam Visvesvaraya.

The engineer who built the Krishnaraja Sagar dam and designed the flood protection system for Hyderabad served as Diwan of Mysore from 1912 to 1918, and received the Bharat Ratna in 1955. His birthday, 15 September, is Engineer's Day.

Your Answer : (Not Answered)

Correct Answer : C

Burkina Faso was called Upper Volta until 1984, when Thomas Sankara renamed it - the new name means "land of upright people". The old name came from the three Volta rivers that rise there.

Your Answer : (Not Answered)

Correct Answer : B

Both are true, but (R) is not the correct explanation of (A).

India is a developing economy, and disguised unemployment - more people working on a farm than the work requires, so that the marginal product of some is near zero - is certainly present. But it is a symptom of underdevelopment rather than the reason for the classification, which rests on per capita income and structure.

Your Answer : (Not Answered)

Correct Answer : B

The interaction is Commensalism.

In commensalism one species benefits and the other is neither harmed nor helped, as with an orchid growing on a mango branch, or barnacles on a whale.

In mutualism (often loosely called symbiosis) both partners benefit; in parasitism one benefits at the other's expense; exploitation also harms one partner.

A classic animal example is the cattle egret, which feeds on insects disturbed by grazing cattle without affecting them.