General Aptitude

The first triple names one idea in rising strength: sick (unwell), infirm (weak from age or long illness) and moribund (close to death). The second triple must do the same for foolishness, ending at daft (senseless, crazy).

Of the options, only vain is an adjective that can describe a lack of sense: besides “conceited”, it means empty, idle or foolish, as in “vain talk”. The others do not fit: frown is a facial expression, fawn is a young deer or a verb meaning to flatter, and vein, which only sounds like vain, is a blood vessel.

Answer: D

The three sectors of the circle all touch one another, so they need three different colours: say 1 (upper left), 2 (bottom) and 3 (upper right).

In the band around the circle, the left part touches sectors 1 and 2, so it must be 3, and the right part touches sectors 2 and 3, so it must be 1. The part below the circle touches sector 2, the left part (3) and the right part (1), so it needs a fourth colour. Three colours are not enough.

Four are: colour the top band part 2 and the bottom band part 4, the outer top and bottom parts 1, the outer left and right parts 2, and all four outer corner parts 3.

Answer: A

A number is divisible by 3 exactly when its digit sum is. The five digits add up to \(1 + 3 + 4 + 6 + 7 = 21\), and a 4-digit number with distinct digits from this set leaves out exactly one digit, so its digit sum is 21 minus the digit left out.

That is a multiple of 3 only when the digit left out is a multiple of 3, i.e. 3 or 6. Each choice leaves four distinct non-zero digits, which can be arranged in \(4! = 24\) ways.

Total \(= 2 \times 24 = 48\).

Answer: B

After the leading 2, the terms are two geometric series interleaved: the powers of \(\tfrac{1}{2}\) (\(\tfrac{1}{2}, \tfrac{1}{4}, \tfrac{1}{8}, \tfrac{1}{16}, \ldots\)) and the powers of \(\tfrac{1}{3}\) (\(\tfrac{1}{3}, \tfrac{1}{9}, \tfrac{1}{27}, \ldots\)). All terms are positive, so they may be regrouped. With \(\frac{a}{1 - r}\) for each series:

\[\frac{1/2}{1 - 1/2} = 1, \qquad \frac{1/3}{1 - 1/3} = \frac{1}{2}.\]

Sum \(= 2 + 1 + \tfrac{1}{2} = \tfrac{7}{2}\).

Answer: B

The chart shows shares of the valid votes, so remove the invalid ones first: 1,15,000 − 5,000 = 1,10,000 valid votes.

B and C together hold 25% + 20% = 45% of these: 0.45 × 1,10,000 = 49,500.

Option (C), 51,750, is the trap of taking 45% of all 1,15,000 votes cast, including the invalid ones.

Answer: B

The passage says that mutations in one gene gave the early dairy farmers the ability to digest dairy milk. So, in human beings, the ability to digest dairy milk came from a mutated gene, which is option (D).

(A) fails because the passage speaks only of some people. (B) contradicts the passage, since these people did gain the ability. (C) goes beyond the passage, which never says that digesting milk is essential for humans.

Answer: D

Each of the three children is independently a boy or a girl with probability \(\tfrac{1}{2}\), so all \(2^{3} = 8\) ordered outcomes are equally likely.

Two girls and one boy happens as GGB, GBG or BGG: \(\binom{3}{1} = 3\) outcomes, one for each choice of which child is the boy. The probability is \(\tfrac{3}{8}\).

The tempting \(\tfrac{1}{8}\) counts only one particular birth order.

Answer: A

Let the annual return of fund A be \(r\). Each person invests ₹50,000 in total, so it is enough to compare the returns.

• Person 1: \(10{,}000r + 0.15 \times 40{,}000 = 10{,}000r + 6{,}000\)
• Person 2: \(20{,}000r + 0.15 \times 30{,}000 = 20{,}000r + 4{,}500\)

Person 1 gets ₹500 more, so \((10{,}000r + 6{,}000) - (20{,}000r + 4{,}500) = 500\), which gives \(1{,}500 - 10{,}000r = 500\) and \(r = 0.10\), i.e. 10%.

Answer: B

Face 5 touches 4 and 1 (view 1) and 6 and 2 (view 3), so 3 is opposite 5. Face 4 touches 5 and 1 (view 1) and 6 and 3 (view 2), so 2 is opposite 4. That leaves 1 opposite 6.

In each net, the four squares of the vertical strip fold into a ring, so its 1st and 3rd squares are opposite, as are its 2nd and 4th; the two side squares are opposite too.

• (A): 1–6, 4–2 and 5–3, all as required.
• (B) and (C): 1 opposite 2, wrong.
• (D): 4 opposite 3 and 5 opposite 2, wrong.

Folding (A) also shows each view’s three faces in the same clockwise order, so it makes this dice.

Answer: A

Joined base to base, the two cones share one axis, which passes through both vertices and the centre of the common base. A plane through both vertices therefore contains this axis and cuts each cone in an isosceles triangle: its base is a diameter of the circle and its equal sides are slant heights.

The two triangles sit on opposite sides of the same diameter, so the outer boundary is a quadrilateral whose four sides are all equal slant heights: a rhombus. It cannot be an ellipse, because a plane through the axis meets a cone’s curved surface in straight lines.

Answer: A