Your Answer : (Not Answered)

Correct Answer : C

The cost price is Rs. 74,000.

Let the cost price be \(C\). The loss at Rs. 70,000 is \(C - 70000\), and the gain at Rs. 82,000 is twice that loss:

\[ \begin{aligned} 82000 - C &= 2(C - 70000) \\ 82000 + 140000 &= 3C \\ C &= 74000 \end{aligned} \]

Check: the loss is Rs. 4,000 and the gain Rs. 8,000, double the loss. 73,000 would make the gain 9,000 against a loss of 3,000, three times rather than twice.

Your Answer : (Not Answered)

Correct Answer : C

The correct order is \(\frac{11}{13} \lt \frac{15}{17} \lt \frac{13}{14}\).

Each fraction is 1 minus a small part, so compare the parts left over: the fraction with the smaller gap from 1 is the larger.

\[ \begin{aligned} 1 - \tfrac{11}{13} &= \tfrac{2}{13} \approx 0.154 \\ 1 - \tfrac{15}{17} &= \tfrac{2}{17} \approx 0.118 \\ 1 - \tfrac{13}{14} &= \tfrac{1}{14} \approx 0.071 \end{aligned} \]

So \(\frac{11}{13}\) is the smallest and \(\frac{13}{14}\) the largest. In decimals they are about 0.846, 0.882 and 0.929.

The option \(\frac{11}{13} \lt \frac{13}{14} \lt \frac{15}{17}\) assumes that a fraction with bigger numbers is bigger, which is not true; the other two put \(\frac{11}{13}\) or \(\frac{13}{14}\) in the wrong place.

Your Answer : (Not Answered)

Correct Answer : C

The change is 33.33% (a decrease).

Since x = k y / z², raising y and z by 50% multiplies y by 1.5 and z² by 2.25.

\[ \frac{1.5}{2.25}=\frac{2}{3} \]

So x becomes two-thirds of its old value, a fall of 33.33%. 15%, 30% and 35% do not match this factor.

When one quantity is directly proportional to y and inversely proportional to the square of z, the new value is found by multiplying the old value by the changes. A rise of 50% is a factor 1.5. Dividing by 1.5 squared, 2.25, and multiplying by 1.5 gives the factor 2/3.

Your Answer : (Not Answered)

Correct Answer : B

In stock problems, a "\( r\% \) stock at \( m \)" means Rs. 100 of face value costs Rs. \( m \) and pays Rs. \( r \) a year, so the yield on money invested is \( \tfrac{r}{m} \).

\[ \text{yield} = \frac{10}{96} \]

\[ \text{investment} = 650 \times \frac{96}{10} = \text{Rs. } 6240 \]

Each Rs. 96 invested returns Rs. 10, so the investment is the income scaled by \( \tfrac{96}{10} \).

Your Answer : (Not Answered)

Correct Answer : A

With \( b \) the still-water speed and \( r \) the stream's,

\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]

\[ \frac{30}{15 - r} + \frac{30}{15 + r} = 4.5 \]

Over the common denominator \( 225 - r^{2} \):

\[ \frac{30(15 + r) + 30(15 - r)}{225 - r^{2}} = \frac{900}{225 - r^{2}} = 4.5 \]

\[ 225 - r^{2} = 200 \quad\Longrightarrow\quad r^{2} = 25 \quad\Longrightarrow\quad r = 5 \text{ km/hr} \]

The \( r \) terms cancel in the numerator, leaving a simple equation. Checking: 30 km at 10 km/hr takes 3 hours and at 20 km/hr takes 1½.

Your Answer : (Not Answered)

Correct Answer : B

The authenticity of the given statement cannot be deduced. So, I does not follow. Since, the advertisement talks of quick returns, it implies that people want their money to grow, as an advertisement always imbibes comments and features that attract the attention of the people immediately. So, II follows.

Your Answer : (Not Answered)

Correct Answer : A

It is Aquila chrysaetos.

The golden eagle is one of the most widely distributed birds of prey in the northern hemisphere. Chrysaetos means golden eagle in Greek, from the colour of its nape feathers.

Your Answer : (Not Answered)

Correct Answer : B

The potato is a modified stem - a tuber, the swollen tip of an underground branch.

Its buds are the eyes, and the scale leaves beside them confirm it as a stem rather than a root. Sweet potato, by contrast, is a modified root.

Your Answer : (Not Answered)

Correct Answer : A

True. This is Archimedes' principle.

The apparent loss in weight equals the weight of the fluid displaced: \[F_B = \rho_{fluid}V_{displaced}\,g\] It follows from the pressure being greater at the bottom of the immersed body than at the top.

Your Answer : (Not Answered)

Correct Answer : B

The West Indies won the 2016 ICC World Twenty20, beating England by four wickets in the final at Kolkata.

Carlos Brathwaite hit Ben Stokes for four sixes in the last over, with 19 needed off six balls. The West Indies women won their final on the same day.

Your Answer : (Not Answered)

Correct Answer : D

The most ancient geological formations are dated by the uranium–lead method, which reaches back about 4,500 million years.

Uranium-238 decays to lead-206 with a half-life of 4,470 million years, so the ratio of the two dates the rock. Carbon-14, with a half-life of 5,730 years, is useless beyond about 50,000 years and works only on once-living material.

Your Answer : (Not Answered)

Correct Answer : C

Hindi Diwas is celebrated on 14 September.

The Constituent Assembly adopted Hindi in Devanagari as an official language of the Union on that date in 1949, and the day has been observed since 1953. World Hindi Day, a separate observance, falls on 10 January.

Your Answer : (Not Answered)

Correct Answer : A

National Road Safety Week is observed in January.

It is organised by the Ministry of Road Transport and Highways. About 150,000 people die on Indian roads each year, the highest number of any country.

Your Answer : (Not Answered)

Correct Answer : C

The Golden Temple is at Amritsar.

Harmandir Sahib stands in the middle of the Amrit Sarovar, the pool from which the city takes its name. Its four doors on four sides signify that it is open to people of every caste and creed.

Your Answer : (Not Answered)

Correct Answer : C

States earn most from commercial taxes.

Sales tax, now the state GST, is by far the largest source of a state's own revenue, followed by state excise on liquor and stamp duty. Land revenue, once the mainstay of the exchequer, has become negligible.

Your Answer : (Not Answered)

Correct Answer : A

Correct answer: Karakoram Pass

The Karakoram Pass, at about 5,540 metres, lies on the watershed between the Indus and Tarim basins and carried the old caravan route from Ladakh to Yarkand in Central Asia. The distractors are all real passes but in different places, and the set is worth knowing. Nathu La is in Sikkim and connects India with Tibet; it was reopened for border trade in 2006. The Palghat Gap is not a mountain pass at all but a 30 km break in the Western Ghats, the principal route between Kerala and Tamil Nadu. Bhor Ghat is a pass in the Western Ghats on the road and rail route between Mumbai and Pune. Other Himalayan passes commonly examined are Zoji La, linking Srinagar with Leh; Rohtang and Baralacha La in Himachal Pradesh; Shipki La and Lipulekh in the central Himalaya; and Bomdi La in Arunachal Pradesh.

Your Answer : (Not Answered)

Correct Answer : C

It will be 0630 hours GMT.

Indian Standard Time is set by the 82°30′E meridian, which passes near Allahabad, and is 5 hours 30 minutes ahead of Greenwich: \[12{:}00 - 5{:}30 = 06{:}30\] The offset is that odd half hour because the country spans nearly 30 degrees of longitude and a single central meridian was chosen.

Your Answer : (Not Answered)

Correct Answer : B

The Reliance refinery is at Jamnagar in Gujarat.

Commissioned in 1999, the complex is now the largest refinery in the world by capacity at a single site, processing over a million barrels a day.

Your Answer : (Not Answered)

Correct Answer : D

The work done is −15.

The resultant force and the displacement from A to B are

\[ \begin{aligned} \mathbf{F} &= (2 - 1)\mathbf{i} + (-5 + 2)\mathbf{j} + (6 - 1)\mathbf{k} \\ &= \mathbf{i} - 3\mathbf{j} + 5\mathbf{k} \\ \overrightarrow{AB} &= 2\mathbf{i} + 4\mathbf{j} - \mathbf{k} \end{aligned} \]

Work is their dot product:

\[ W = (1)(2) + (-3)(4) + (5)(-1) = 2 - 12 - 5 = -15 \]

The negative sign means the force opposes the displacement on balance. 2 and −5 are single terms of the sum, and 12 drops the signs.

Your Answer : (Not Answered)

Correct Answer : C

A diagonal matrix is a special case of a triangular one, so its characteristic determinant factorises directly:

\[ \det(A-\lambda I) = (2-\lambda)(3-\lambda)(7-\lambda) = 0 \quad\Rightarrow\quad \lambda = 2,\;3,\;7 \]

Their sum \( 2+3+7=12 \) is the trace and their product \( 2\times3\times7=42 \) the determinant, as the general relations require.