Your Answer : (Not Answered)

Correct Answer : A

The ratio a:c is 3:7.

Make the b terms equal. In the first ratio b is 9 and in the second 27, so multiply the first ratio by 3:

\[ \begin{aligned} a : b &= 5 : 9 = 15 : 27 \\ b : c &= 27 : 35 \\ a : c &= 15 : 35 = 3 : 7 \end{aligned} \]

7:3 inverts the ratio, and 4:7 and 7:4 do not follow from the given ratios.

Your Answer : (Not Answered)

Correct Answer : B

His monthly income is ₹ 1500.

If Ram spends 65% of his salary, he saves the remaining 35%, and that is ₹ 525:

\[ \begin{aligned} 0.35 \times S &= 525 \\ S &= \frac{525}{0.35} = 1500 \end{aligned} \]

Check: 65% of 1500 is 975 and 1500 - 975 = 525. The other options give savings of ₹ 420, ₹ 630 and ₹ 735, so none matches. A common slip is dividing 525 by 0.65 (giving about ₹ 808), which treats the savings as the spent share.

Your Answer : (Not Answered)

Correct Answer : C

The expression equals \(-4c\).

Use \(X^2 - Y^2 = (X + Y)(X - Y)\) with \(X = a - b + c\) and \(Y = a - b - c\):

\[ \begin{aligned} X + Y &= 2(a - b), \quad X - Y = 2c \\ X^2 - Y^2 &= 4c(a - b) \\ \frac{4c(a - b)}{b - a} &= -4c \end{aligned} \]

The sign comes from \(b - a = -(a - b)\); dropping it gives 4c, which is not offered, and 2c halves the result.

Your Answer : (Not Answered)

Correct Answer : A

An integral curve is a curve whose tangent at every point matches the direction the differential equation prescribes there - that is, a particular solution drawn in the plane.

The family of all such curves fills the direction field, and an initial condition picks out one of them.

Your Answer : (Not Answered)

Correct Answer : D

Each of the ten questions is answered independently as T or F.

\[ 2^{10} = 1024 \]

Since no two candidates matched, at most 1024 candidates could sit the paper. The 512 on offer is \( 2^{9} \), one question short.

Your Answer : (Not Answered)

Correct Answer : D

The gap closes at the difference of the two speeds.

\[ \text{relative speed} = 7 - 5 = 2 \text{ m/s} \]

\[ t = \frac{80}{2} = 40 \text{ s} \]

\[ \text{thief's distance} = 5 \times 40 = 200 \text{ m} \]

Ramesh covers 280 m in the same time - exactly 80 m more, which is the head start he had to make up. The question asks for the thief's distance, not Ramesh's.

Your Answer : (Not Answered)

Correct Answer : C

Correct answer: Fargo and Mercedes

Fiat stands at one end with Ambassador three places to its right; Fargo is four to Fiat’s right and Cadillac next beyond it. Maruti must lie between Ambassador and Bedford, which fills the two remaining places near the Fiat end, and Mercedes takes the last. From left to right the line reads Fiat, Bedford, Maruti, Ambassador, Fargo, Cadillac, Mercedes.

Cadillac stands sixth, with Fargo on one side and Mercedes on the other.

Your Answer : (Not Answered)

Correct Answer : C

Correct answer: A is true but R is false.

A leak can be smelt, so A is true. But LPG is odourless in itself: ethyl mercaptan is added in tiny quantities precisely so that leaks announce themselves. R is false as stated.

Your Answer : (Not Answered)

Correct Answer : D

Correct answer: Ornaments

The relation is metal : what it is used to make. Tungsten is drawn into the filament of a lamp, because it withstands white heat; bronze is cast into ornaments and statues. Copper and tin are what bronze is made of.

Your Answer : (Not Answered)

Correct Answer : D

The statement that follows is India will talk implies the terrorists are handed over.

‘P only if Q’ means that P cannot happen without Q, that is, if P then Q. Here P is 'India will talk' and Q is 'the terrorists are handed over', so talking implies the hand-over has happened.

• 'The terrorists are handed over, hence India will talk' reverses the condition (Q, so P), which 'only if' does not promise.
• 'India will not talk implies that the terrorists have not been handed over' (not P, so not Q) is equivalent to that same reversal.
• 'India will talk though the terrorists are not handed over' directly contradicts the statement.

Your Answer : (Not Answered)

Correct Answer : C

The mirror image is option (c).

APPROPRIATE has eleven letters. Reflected in a mirror at the side, the order of the letters is reversed, giving E, T, A, I, R, P, O, R, P, P, A, and each letter is flipped left to right, so the R and P are turned the other way.

Option (c) has the right order of letters. Option (a) puts the O before the R after the I, option (b) puts the O just after the R and before the P, and option (d) puts P before R in the middle, so each has two letters in the wrong order.

Your Answer : (Not Answered)

Correct Answer : D

Correct answer: 75

The gaps are 9, 15, 21, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is three times the square of its position: position 1 gives 3 and position 4 gives 48. The next position is 5, which gives 75. As a check, the same rule applied to the earlier positions reproduces 3, 12, 27, 48 exactly, so it accounts for every term shown and not merely the last. The presence of a very large final term often signals a multiplicative rule rather than an additive one.

Your Answer : (Not Answered)

Correct Answer : D

Pithora painting belongs to the Bhil tribe.

Pithora paintings are ritual wall paintings made by Bhil and Bhilala communities, including the Rathwa, in western Madhya Pradesh and eastern Gujarat, especially in the Jhabua and Alirajpur region. Brightly coloured horses, riders and scenes of daily life are painted on the house wall to honour the deity Pithora, often to fulfil a vow.

The Gond are known for their own dot-and-line painting style; the Kol and Sahariya are not associated with Pithora.

Your Answer : (Not Answered)

Correct Answer : B

Fission is caused by the impact of a neutron.

Being uncharged, the neutron feels no electrostatic repulsion from the nucleus and can approach and be absorbed even at low energy. A proton or alpha particle would be repelled by the positive nuclear charge; an electron is far too light to disturb the nucleus.

Your Answer : (Not Answered)

Correct Answer : A

Accessories is a program group.

A program group is a folder in the Start menu holding related shortcuts - Accessories contains Notepad, Paint, Calculator and WordPad. Excel, Word and Paint are individual programs within such groups.

Your Answer : (Not Answered)

Correct Answer : A

World Environment Day is not in October - it falls on 5 June.

The others all are: the International Day of Non-Violence on 2 October, Indian Air Force Day on 8 October and United Nations Day on 24 October.

Your Answer : (Not Answered)

Correct Answer : A

Correct answer: By the President, after an address by both Houses passed by a special majority

A judge of the Supreme Court or a High Court can be removed only by an order of the President, made after an address by both Houses of Parliament in the same session, each supported by a majority of the total membership of that House and by two thirds of those present and voting, on the ground of proved misbehaviour or incapacity. The procedure is set out in the Judges (Inquiry) Act of 1968: the motion is admitted by the presiding officer, a three-member committee investigates the charges, and only if it finds the judge guilty does the motion proceed. The word impeachment is commonly used but is not the constitutional term, which is removal by address. No judge has ever been removed. Justice V. Ramaswami survived a motion in 1993 when the Congress abstained and the address failed for want of a majority; Justice Soumitra Sen resigned in 2011 after the Rajya Sabha passed the motion but before the Lok Sabha took it up.

Your Answer : (Not Answered)

Correct Answer : A

Telangana's population at the 2011 census was about 35 million - 35.19 million, or roughly 2.9 per cent of India's.

The figure was derived after the bifurcation of Andhra Pradesh in 2014, since the census had been taken while the state was undivided.

Your Answer : (Not Answered)

Correct Answer : D

Correct answer: Certain enteroviruses

When the older classification into polioviruses, coxsackieviruses and echoviruses proved unable to accommodate newly isolated agents, later ones were simply numbered in a single series, beginning at enterovirus 68. Enterovirus 71 is the best known of them, a cause of hand-foot-and-mouth disease that can also produce severe neurological illness.

Your Answer : (Not Answered)

Correct Answer : A

A plaque forms where an infection has spread through neighbouring cells and killed them, leaving a clear patch in an otherwise intact monolayer. Viruses form no colonies, because they do not grow on media, only in cells.