Your Answer : (Not Answered)

Correct Answer : B

The value is 10.

Work from the innermost root outwards:

\[ \begin{aligned} \sqrt{121} &= 11 \\ \sqrt{70 + 11} &= \sqrt{81} = 9 \\ \sqrt{91 + 9} &= \sqrt{100} = 10 \end{aligned} \]

9 and 11 are the values of the inner roots, picked up by stopping too early, and 12 does not arise at any step.

Your Answer : (Not Answered)

Correct Answer : B

One value of \((a + b)\) is \(2\frac{4}{5}\).

Use the identity linking the sum and difference of two numbers with their product.

\[ \begin{aligned} (a + b)^{2} &= (a - b)^{2} + 4ab \\ &= \frac{121}{25} + 4 \times \frac{3}{4} \\ &= \frac{121}{25} + \frac{75}{25} = \frac{196}{25} \end{aligned} \]

So \(a + b = \pm \frac{14}{5}\), and one of the values is \(\frac{14}{5} = 2\frac{4}{5}\). The question says 'one of the values' because \(-\frac{14}{5}\) also works. Forgetting the factor 4 on \(ab\) gives \(\sqrt{121/25 + 3/4}\), which is none of the options.

Your Answer : (Not Answered)

Correct Answer : C

We rewrite the expression using identities:

\(\sec^2\theta + \csc^2\theta = (1+\tan^2\theta) + (1+\cot^2\theta) = 2 + \tan^2\theta + \cot^2\theta\).

Let \(y = \tan^2\theta\). The expression is \(2 + y + 1/y\). By AM-GM inequality, \(y+1/y \ge 2\sqrt{y \cdot 1/y} = 2\). The minimum value of \(y+1/y\) is 2.

Therefore, the minimum value of the entire expression is 2 + 2 = 4.

Your Answer : (Not Answered)

Correct Answer : B

Start from the curved surface area to find the radius, taking \( \pi = \tfrac{22}{7} \).

\[ \pi r l = 308 \quad\Longrightarrow\quad \frac{22}{7} \times r \times 14 = 308 \]

\[ 44r = 308 \quad\Longrightarrow\quad r = 7 \text{ cm} \]

Now the total surface area adds the base:

\[ \text{TSA} = \pi r(l + r) = \frac{22}{7} \times 7 \times (14 + 7) = 22 \times 21 = 462 \text{ cm}^{2} \]

So the true statement is that the total surface area is 462 cm².

Checking the others: the radius is 7 cm, not 14 - 14 cm is the slant height. The height is \( \sqrt{l^{2} - r^{2}} = \sqrt{196 - 49} = \sqrt{147} \approx 12.1 \) cm, which is the square root of 147, not its square.

Your Answer : (Not Answered)

Correct Answer : B

The 0.25 m border runs along all four sides, so each dimension loses twice that.

\[ \text{tiled area} = (4 - 0.5)(9 - 0.5) = 3.5 \times 8.5 = 29.75 \text{ m}^{2} \]

\[ \text{tile} = 0.25 \times 0.25 = 0.0625 \text{ m}^{2} \]

\[ n = \frac{29.75}{0.0625} = 476 \]

Subtracting only 0.25 m from each dimension instead of 0.5 is the usual slip - the space is left on both opposite sides.

Your Answer : (Not Answered)

Correct Answer : B

\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]

Simple interest of Rs. 40 over two years means Rs. 20 each year. Compound interest exceeds it by Re. 1, and that excess is one year's interest on the first year's Rs. 20:

\[ 20 \times \frac{R}{100} = 1 \quad\Longrightarrow\quad R = 5\% \]

Now use the simple interest to find the principal:

\[ \frac{P \times 5 \times 2}{100} = 40 \quad\Longrightarrow\quad P = \text{Rs. } 400 \]

Reading the two-year gap as a rate directly is the standard shortcut for these, and it works because over two years the excess is always \( \text{SI}_{1} \times R \).

Your Answer : (Not Answered)

Correct Answer : A

He is now facing South-east.

Follow the turns from north-west:

1. 90° clockwise from north-west: north-east.
2. 180° anticlockwise from north-east: south-west.
3. Another 90° anticlockwise (the same direction) from south-west: south-east.

Overall he turned 90° clockwise and 270° anticlockwise, a net 180°, so he faces the opposite of north-west, which is south-east. South-west is where he faces after the second turn only.

Your Answer : (Not Answered)

Correct Answer : A

Correct answer: Four

Number the letters of HORIZON and their alphabet positions: H(8) O(15) R(18) I(9) Z(26) O(15) N(14). A pair qualifies when the count of letters between them in the word equals the count between them in the alphabet, and four pairs do. H and N have five letters between them in the word (O, R, I, Z, O) and five in the alphabet (I to M). R and the second O have two in the word (I, Z) and two in the alphabet (P, Q). R and N have three in the word (I, Z, O) and three in the alphabet (O, P, Q). And the second O and N are adjacent in both, with none between. Note that only H–N runs in the same direction in the word as in the alphabet, so a solver taught to count forward pairs alone would answer one.

Your Answer : (Not Answered)

Correct Answer : B

The longest river flowing entirely within Rajasthan is the Banas.

The Banas rises in the Khamnor hills of the Aravallis near Kumbhalgarh in Rajsamand district and flows north-east through Bhilwara, Tonk and Sawai Madhopur before joining the Chambal, all within the state, a course of about 512 km.

The Chambal is longer but rises in Madhya Pradesh, and the Luni ends in the Rann of Kutch in Gujarat. The Banganga flows on into Uttar Pradesh, and is in any case much shorter.

Your Answer : (Not Answered)

Correct Answer : D

Statement D is not correct. Under Article 4, a law made under Article 2 or 3 to form new states or alter boundaries or names is not treated as an amendment of the Constitution for the purpose of Article 368, so it does not fall under the amendment procedure. The other three statements describe Article 3: Parliament may form a new state by law, the Bill needs the President's recommendation, and the President refers it to the state legislature for its views.

Your Answer : (Not Answered)

Correct Answer : C

Karnam Malleswari played weight lifting.

She won a bronze medal in weightlifting at the Sydney Olympics in 2000, becoming the first Indian woman to win an Olympic medal. She was also a world champion in her category in the 1990s.

She was not a wrestler, cricketer or chess player; those options name other sports in which Indian women have done well.

Your Answer : (Not Answered)

Correct Answer : B

P.M. Sayeed had the longest tenure from one constituency among those listed, representing Lakshadweep for ten consecutive terms from 1967 to 2004.

He served as Union Power Minister and as Deputy Speaker of the Lok Sabha.

Your Answer : (Not Answered)

Correct Answer : D

The wavelength is the distance between crest and crest, or trough and trough.

It is the length of one complete cycle, so any two corresponding points in phase are a wavelength apart. Crest to the adjacent trough is only half a wavelength.

Your Answer : (Not Answered)

Correct Answer : D

VVS Laxman was out for 0 on his one-day international debut, against Zimbabwe at Bulawayo in April 1998.

He never settled into the one-day side, playing only 86 ODIs, but in Tests he made 8,781 runs, including the 281 at Kolkata in 2001 that turned a match India were following on in.

Your Answer : (Not Answered)

Correct Answer : B

A spider is a program that catalogues websites.

Also called a crawler or bot, it follows links from page to page, fetching each and passing it to the indexer. It is how a search engine discovers what exists on the web.

Your Answer : (Not Answered)

Correct Answer : A

World COPD Day was observed on 18 November in 2015.

It falls on the third Wednesday of November, so the date moves. Chronic obstructive pulmonary disease is the third leading cause of death worldwide, caused chiefly by smoking and by indoor air pollution from cooking fires.

Your Answer : (Not Answered)

Correct Answer : D

The correct answer is None of these.

No book of this title belongs to any of the authors listed: V.S. Naipaul wrote A House for Mr Biswas and A Bend in the River, Chetan Bhagat Five Point Someone, and Vikram Seth A Suitable Boy. Check each name against its known works before choosing.

Your Answer : (Not Answered)

Correct Answer : D

The Kalam Effect: My Years with the President was written by P.M. Nair.

He was secretary to President Abdul Kalam, and the book records the working of Rashtrapati Bhavan during those five years.

Your Answer : (Not Answered)

Correct Answer : A

Groundwater whose flow is not bounded above by an impermeable layer is unconfined. Its upper surface is the water table, free to rise and fall, unlike a confined aquifer held under pressure.

Your Answer : (Not Answered)

Correct Answer : D

The Ministry of Finance formulates fiscal policy.

It decides taxation, expenditure and borrowing, and gives them effect through the annual budget. Monetary policy is the Reserve Bank's, and the Finance Commission recommends how resources are shared between the Centre and the states.