Your Answer : (Not Answered)

Correct Answer : B

The difference between their present ages is 21 years.

Let the mother's present age be \(m\) and the daughter's \(d\).

\[ \begin{aligned} m - 15 &= 2(d - 15) \\ m &= 2d - 15 \end{aligned} \]

Three years from now their ages add up to 99:

\[ \begin{aligned} (m+3) + (d+3) &= 99 \\ m + d &= 93 \\ (2d - 15) + d &= 93 \\ d &= 36,\ m = 57 \end{aligned} \]

So the difference is \(57 - 36 = 21\) years. As a check, 15 years ago they were 42 and 21, and 42 is twice 21. The difference between two ages never changes, so the other options cannot be right once 42 and 21 check out.

Your Answer : (Not Answered)

Correct Answer : C

The sum is \(e - 1\).

The exponential series is

\[ \begin{aligned} e &= \frac{1}{0!} + \frac{1}{1!} \\ &+ \frac{1}{2!} + \frac{1}{3!} + \cdots \end{aligned} \]

The given series is the same except that it starts at \(\frac{1}{1!}\), so it leaves out the first term \(\frac{1}{0!} = 1\):

\[ \sum_{n=1}^{\infty} \frac{1}{n!} = e - 1 \approx 1.718 \]

\(e\) would include the missing 1, \(1 + e\) adds it instead of removing it, and \(\pi\) has nothing to do with this series.

Your Answer : (Not Answered)

Correct Answer : A

The ratio is 10:7.

The work equals 30 × 24 = 720 woman-days and also 24 × 21 = 504 man-days. So 720 woman-days equal 504 man-days, which means one man does as much as 720/504 = 10/7 women.

\[ \text{man : woman}=\frac{10}{7} \]

7:10 is the inverse and 3:5 and 5:3 do not match the numbers.

You can check the answer by computing the work of one man and one woman in a day. One woman does 1/720 of the work per day and one man does 1/504. The ratio man to woman is (1/504) : (1/720), which equals 720 : 504, and dividing by 72 gives 10 : 7.

Your Answer : (Not Answered)

Correct Answer : B

We use the complementary angle identity \(\sin(90° - \theta) = \cos \theta\).

\(\sin 65° = \sin(90° - 25°) = \cos 25°\).

The expression becomes \(\sin^2 25° + \cos^2 25°\).

Using the Pythagorean identity \(\sin^2 A + \cos^2 A = 1\), the value is 1.

Your Answer : (Not Answered)

Correct Answer : B

Correct answer: Rs. 20

The dividend is reckoned on the face value.

\[\text{Dividend per share} = \frac{8}{100} \times 25 = \text{Rs. } 2\]

For that Rs. 2 to represent a 10% return, the price paid must be

\[\frac{2}{10} \times 100 = \text{Rs. } 20\]

He must therefore buy below par, which is what raises his yield above the nominal 8%.

Your Answer : (Not Answered)

Correct Answer : D

Diameter of largest circle = 20 cm.
∴ Area of circle = 100π cm²
∴ Area of 6 circles = 6 × 100π = 600π cm² (∵ there are six faces in a cube)
Also, Area of cube = 6 × (20)² = 2400 cm²
Area of unpainted surface = 2400 - 600π
= 2400 - 600 × 22/7
= 514.28 cm².

Your Answer : (Not Answered)

Correct Answer : D

Correct answer: Either II or III and I are true

Combine the statements into what they jointly say. \( P = M \) ties two letters together, and \( P < R \le T < S \) runs from there up to S, while \( M \le V \) hangs V off the same point from below: \[ V \ge M = P < R \le T < S. \]

I. \( S > M \): reading right from M gives \( M = P < R \le T < S \), strict twice. True.

IV. \( T < P \): the same run shows \( T > P \), so this is definitely false.

II and III are the pair to think about. All we know of V is \( V \ge P \), from \( M \le V \) and \( P = M \). II claims \( V = P \) and III claims \( P < V \); neither is forced, because V could equal P or stand above it. But those two cases exhaust \( V \ge P \), so exactly one of them holds.

So I is definitely true, IV is definitely false, and either II or III is true - which is the keyed answer.

Your Answer : (Not Answered)

Correct Answer : D

It has been found at Dholavira.

The excavators identified a structure at Dholavira, in the Rann of Kutch, as an observatory, its alignments answering to the solstices and equinoxes. The site is also known for its water reservoirs and its large signboard of Indus characters.

Your Answer : (Not Answered)

Correct Answer : C

It is Samoan.

Samoan and English are both official. Samoan is a Polynesian language, closely related to Tongan and Maori, and is spoken by nearly all Samoans.

Your Answer : (Not Answered)

Correct Answer : B

Myopia, or short-sightedness, is a defect of the eye.

The eyeball is too long or the lens too strong, so light focuses in front of the retina and distant objects blur. It is corrected with a concave (diverging) lens.

Your Answer : (Not Answered)

Correct Answer : C

The popping crease is a cricket marking - the line four feet in front of the stumps behind which the batsman must ground his bat to be safe, and behind which the bowler's front foot must land.

It runs the full width of the pitch, and it is what a stumping or run-out decision is measured against.

Your Answer : (Not Answered)

Correct Answer : B

X-rays have wavelengths of the order of 1 angstrom, that is 10⁻¹⁰ m.

This happens to be about the spacing of atoms in a crystal, which is why crystals diffract X-rays - the basis of X-ray crystallography and of the discovery of the structure of DNA.

Your Answer : (Not Answered)

Correct Answer : D

Bulo C. Rani was associated with motion pictures.

He was a music director in Hindi cinema from the 1940s, best remembered for the score of Jogan (1950), whose songs Geeta Dutt sang.

Your Answer : (Not Answered)

Correct Answer : C

The Sun's diameter is about 1,392,000 km, that is roughly 14 lakh kilometres - some 109 times the Earth's diameter of 12,756 km.

Put another way, about 1.3 million Earths would fit inside it, and it holds 99.8 per cent of all the mass in the solar system.

Your Answer : (Not Answered)

Correct Answer : B

There are seven continents: Asia, Africa, North America, South America, Antarctica, Europe and Australia. Some traditions merge Europe and Asia into Eurasia, or the two Americas into one, which is where the counts of six and five come from.

Your Answer : (Not Answered)

Correct Answer : B

The co-operative credit societies have a three-tier structure.

Primary agricultural credit societies at village level, central co-operative banks at district level, and a state co-operative bank at the apex. Long-term credit runs through a parallel two-tier structure of land development banks.

Your Answer : (Not Answered)

Correct Answer : C

Greenhouse gases trap thermal radiation.

Short-wave sunlight passes through the atmosphere almost unhindered and warms the ground. The ground re-radiates that energy as long-wave infrared, and carbon dioxide, methane and water vapour absorb it and re-emit it in all directions, including downward. The gases are transparent to the incoming radiation and opaque to the outgoing.

Your Answer : (Not Answered)

Correct Answer : A

The Supreme Court at Calcutta was set up by the Regulating Act of 1773.

It had a chief justice and three other judges appointed by the Crown, with jurisdiction over British subjects in Bengal, Bihar and Orissa. It was the first court in India established by Parliament rather than by the Company.

Your Answer : (Not Answered)

Correct Answer : C

Correct answer: The number of stations that recorded the event

How many instruments happened to be operating is a property of the network, not of the motion, and it tells you nothing about what the ground did at a site. The other three are all genuine parameters: bracketed duration measures how long, Arias intensity how much energy, and peak ground velocity how large the intermediate-frequency motion was.

Your Answer : (Not Answered)

Correct Answer : C

The ratio is \(\frac{1}{6}\).

With \(u/U_{\infty} = \eta = y/\delta\), the momentum thickness is

\[ \begin{aligned} \theta &= \delta\int_{0}^{1} \eta(1 - \eta)\,d\eta \\ &= \delta\left(\frac{1}{2} - \frac{1}{3}\right) = \frac{\delta}{6} \end{aligned} \]

\(1/2\) is the displacement thickness ratio for the same profile, \(\int_{0}^{1}(1 - \eta)\,d\eta\), and \(1/3\) and \(1/4\) do not come from either integral.