Your Answer : (Not Answered)

Correct Answer : C

\(r_{2} = 7 - 4\sqrt{2}\) cm.

Each circle is tangent to the two sides at its corner, so its centre lies on the diagonal WY, at a distance \(r\sqrt{2}\) from the corner. The diagonal is \(4\sqrt{2}\), and along it lie the corner distance of \(C_{1}\), both radii, and the corner distance of \(C_{2}\):

\[ \begin{aligned} r_{1}\sqrt{2} + r_{1} + r_{2} + r_{2}\sqrt{2} &= 4\sqrt{2} \\ (r_{1} + r_{2})(\sqrt{2} + 1) &= 4\sqrt{2} \\ r_{1} + r_{2} &= 4\sqrt{2}(\sqrt{2} - 1) = 8 - 4\sqrt{2} \\ r_{2} &= 7 - 4\sqrt{2} \approx 1.34 \end{aligned} \]

\(4 - 3\sqrt{2}\) is negative and \(1 + 2\sqrt{2} \approx 3.83\) and \(5 + 3\sqrt{2}\) are too big to fit in a 4 cm square beside a 1 cm circle.

Your Answer : (Not Answered)

Correct Answer : B

The largest revenue share comes from Executive.

Add the four quarters for each razor and multiply by its price:

\[ \begin{aligned} \text{Elegance} &= 102510 \times 48 = 4920480 \\ \text{Smooth} &= 80059 \times 63 = 5043717 \\ \text{Soft} &= 72186 \times 78 = 5630508 \\ \text{Executive} &= 39284 \times 173 = 6796132 \end{aligned} \]

Executive sells the fewest pieces but its price is more than twice that of any other razor, so it earns the most. Elegance sells the most pieces, which is the trap, but at the lowest price it earns the least.

Your Answer : (Not Answered)

Correct Answer : B

Correct answer: 2

Divide 1,056 by 23: \( 23 \times 45 = 1035 \), leaving a remainder of \( 1056 - 1035 = 21 \). To reach the next multiple of 23, add the difference between the divisor and the remainder: \[ 23 - 21 = 2. \] Checking, \( 1056 + 2 = 1058 = 23 \times 46 \). The distractor 21 is the remainder itself, and it is the answer to the opposite question - the least number to be subtracted to make the figure divisible. Reading which is asked is where marks are usually lost. The two rules are worth stating together. To make a number divisible by \( d \), subtract the remainder \( r \), or add \( d - r \). If the remainder is zero the number is already divisible and nothing need be added. The same reasoning extends to finding the nearest multiple in either direction.

Your Answer : (Not Answered)

Correct Answer : A

When the hands coincide they point in exactly the same direction, so the angle between them is 0°.

They are 180° apart when opposite and 90° apart at a right angle - the other two configurations these questions ask about.

Your Answer : (Not Answered)

Correct Answer : A

The corresponding A.P. has a 3rd term of 7 and a 5th term of 11. So, \(a+2d=7\) and \(a+4d=11\). Subtracting the equations gives \(2d=4\), so \(d=2\). Substituting back, \(a+2(2)=7 \Rightarrow a+4=7 \Rightarrow a=3\). The first term of the A.P. is 3. The first term of the H.P. is the reciprocal, 1/3.

Your Answer : (Not Answered)

Correct Answer : D

Asteroids, stars and planets are natural bodies found in space.

A rocket is man-made - a vehicle built to travel through space, not an object that occurs there.

So Rocket does not belong.

Your Answer : (Not Answered)

Correct Answer : A

Correct answer: C

Facing the centre, each person’s left is the next seat clockwise and their right the next seat anticlockwise. Fix B; A sits three to B’s right, F four beyond A, K four to B’s left and D three to K’s left. Of the four seats left, C three to H’s right fits in only one way, and E two to G’s left then fills the last two. Clockwise the circle reads B → G → F → E → K → C → A → D → H.

Counting four seats to G’s left - clockwise - gives F, E, K and then C. The arrangement is fully determined, so the data are not inadequate.

Your Answer : (Not Answered)

Correct Answer : A

Correct answer: T

Facing the centre, each person’s left is the next seat clockwise and their right the next seat anticlockwise. Fix P; V sits two to P’s left and W two beyond V. Of the two ways to place Q with T three seats to Q’s right, only one keeps T off V’s shoulder, and R and S then fit in one way only. Clockwise the circle reads P → Q → V → S → W → T → R.

Counting three seats to V’s left - clockwise - gives S, W and then T.

Your Answer : (Not Answered)

Correct Answer : A

The statement mentions that adventure stories are liked by everybody. This does not mean that there is no other reading material or nobody loves reading any other material. So, neither I nor II is implicit. Besides, 'everybody' in the statement stands for 'all literate people' and not for 'all people'. So, III is also not implicit.

Your Answer : (Not Answered)

Correct Answer : A

END only forms a meaningful word.

Adding B in front gives BEND, BMAT, BJAR and BBED. Only BEND is an English word. The others are not words.

So MAT only, both END and MAT, and both JAR and BED are all wrong.

Test each word one at a time: BEND is a common English word meaning to curve, BMAT, BJAR and BBED are not words at all. Since just one of the four forms a word, the answer is END only, and any option naming MAT, JAR or BED fails.

Your Answer : (Not Answered)

Correct Answer : D

Correct answer: I said, “How many discoveries go unheeded?”

Working backwards: I wondered how many discoveries went unheeded is a reported question whose past tense comes from the backshift, so the original was the present go unheeded. The option keeping went shifts the tense twice.

Your Answer : (Not Answered)

Correct Answer : D

Correct answer: mercy is the noblest form of revenge.

The passage sets forgiveness against vengeance throughout: yielding to resentment is easy, restraining it takes a strong character, and the man who forgives proves himself the superior of the wrongdoer and puts him to shame.

That last clause is decisive. Forgiveness here is not merely kind - it defeats the offender more completely than retaliation would, which is exactly what calling mercy a form of revenge means.

Your Answer : (Not Answered)

Correct Answer : C

It is seize.

To seize is to take by force or legal authority. Seas are bodies of water and sees is the verb to see; all three are pronounced identically.

Your Answer : (Not Answered)

Correct Answer : C

Correct answer: Multiprocessing

Multiprocessing means two or more processors executing programs at the same instant, which is what the question describes. Multiprogramming and time sharing keep several programs in memory but interleave them on a single processor, so only one instruction is executing at any moment.

Your Answer : (Not Answered)

Correct Answer : B

The Indian Nursing Council Act was enacted in 1947.

It constituted the Indian Nursing Council to prescribe uniform standards of nursing education and to maintain the register of qualified nurses, midwives and health visitors.

Your Answer : (Not Answered)

Correct Answer : C

The Revenue Recovery Act was enacted in 1890.

It enables arrears of land revenue due in one state to be recovered in another, by transmitting a certificate to the collector of the district where the defaulter or the property is.

Your Answer : (Not Answered)

Correct Answer : C

It is attributed to Voltaire.

The sentence was not written by Voltaire but by his biographer Evelyn Beatrice Hall in 1906, as a summary of his attitude to Helvetius. It has been quoted as his ever since.

Your Answer : (Not Answered)

Correct Answer : D

It was Bharatendu Harishchandra.

His play Bharat Durdasha of 1880 is an allegory on India's condition under colonial rule. He is regarded as the father of modern Hindi literature and of Hindi theatre.

Your Answer : (Not Answered)

Correct Answer : A

Shirin Ebadi is from Iran.

The lawyer and human rights activist received the Nobel Peace Prize in 2003 for her work on democracy and the rights of women and children - the first Muslim woman and the first Iranian to receive it.

Your Answer : (Not Answered)

Correct Answer : B

This is called transhumance.

Herders move flocks to high pasture in summer and back to the valleys in winter, following the grass. In India the Gujjars, Bakarwals and Gaddis of the western Himalayas practise it, as do the Bhotias of Uttarakhand.