Your Answer : (Not Answered)

Correct Answer : B

The Blue box has 45 balls.

Let the boxes hold \(R\), \(B\) and \(G\) balls. Red and Blue together are twice Green, and Green is twice Red:

\[ \begin{aligned} R + B &= 2G \\ R + B + G &= 90 \\ 3G &= 90,\ G = 30 \end{aligned} \]

\[ \begin{aligned} R &= G/2 = 15 \\ B &= 90 - 30 - 15 = 45 \end{aligned} \]

Check: Red and Blue together hold 60, twice Green's 30, and Green's 30 is twice Red's 15. The option 15 is the Red box and 30 the Green box, so they answer the wrong part of the question.

Your Answer : (Not Answered)

Correct Answer : C

Using the identity \(\sin^2 \theta + \cos^2 \theta = 1\):

\((\frac{a}{b})^2 + \cos^2 \theta = 1\)

\(\cos^2 \theta = 1 - \frac{a^2}{b^2} = \frac{b^2-a^2}{b^2}\)

\(\cos \theta = \sqrt{\frac{b^2-a^2}{b^2}} = \frac{\sqrt{b^2-a^2}}{b}\).

Your Answer : (Not Answered)

Correct Answer : A

The year 2004 is a leap year. So, it has 2 odd days.

But, Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only.

 The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.

Given that, 6th March, 2005 is Monday.

 6th March, 2004 is Sunday (1 day before to 6th March, 2005).

Your Answer : (Not Answered)

Correct Answer : D

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

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

\[ b + r = \frac{24}{4} = 6 \text{ km/hr}, \qquad b - r = \frac{24}{6} = 4 \text{ km/hr} \]

\[ b = \frac{6 + 4}{2} = 5 \text{ km/hr} \]

5 km/hr is not among the listed values, so the answer is none of these. The nearest option, 5.5, is the sort of near-miss these questions use to punish rounding.

Your Answer : (Not Answered)

Correct Answer : B

Let Cost price \(= Rs. 100.\) Then, Profit \(= Rs. 320\)

Selling price \(= Rs. 420.\)

New Cost price \(= 125\)% of \(Rs. 100 = Rs. 125\)

New Selling price \(= Rs. 420.\)

Profit \(= Rs. (420 - 125) = Rs. 295.\)

\(\therefore\) Required percentage \(= (\frac{295}{420} \times 100)\)% \(= \frac{1475}{21}\)% \(= 70\)%(approximately)

Your Answer : (Not Answered)

Correct Answer : D

Let the present ages of son and father be \(x\) and \((60-x)\) years respectively 

Then ,   \((60-x)-6=5(x-6)\)

\( \Rightarrow \)  \(54 - x=5x-30\)

\( \Rightarrow 6x=84\)

\( \Rightarrow x=14 \)

 \( \therefore \) Son's age after 6 years = \(( x+ 6)\)= 20 years

Your Answer : (Not Answered)

Correct Answer : E

Correct answer: All I, II and III are true

Translating this set’s code: \(\$\) is “neither greater nor smaller”, so \(=\); \(\delta\) is “neither greater than nor equal”, so \(<\); \(\%\) is “neither smaller than nor equal”, so \(>\); \(*\) is “not smaller than”, so \(\ge\); and \(\#\) is “not greater than”, so \(\le\). The statements become \( M \le Q \), \( Q = K \), \( A > K \) and \( V \ge A \). Since Q and K are equal they can be treated as one element, which lines the rest up as \[ V \ge A > K = Q \ge M. \]

That single descending chain settles all three conclusions.

I. \( K \ge M \): from \( M \le Q = K \). True.

II. \( A > Q \): from \( A > K = Q \). True.

III. \( A > M \): the run \( A > K = Q \ge M \) points one way and contains a strict link. True.

All three follow. Spotting the equality early is what makes this quick: an \(=\) link lets two letters be merged, and a chain with nothing but one reversal-free direction settles every comparison along it.

Your Answer : (Not Answered)

Correct Answer : B

Step V: growth 02 next 14 problem 41 57 82 trend purchase
Step VI: growth 02 next 14 problem 41 purchase 57 82 trend
Step VII: growth 02 next 14 problem 41 purchase 57 trend 82

Your Answer : (Not Answered)

Correct Answer : A

Correct answer: 102

The steps run 4, 4, 20, 4, which grow and then fall back, so a single operation cannot account for them. Two operations are applied in turn, and continuing the alternation from 34 gives 102. As a check, the step from 34 to the answer is 68, which breaks the run of preceding gaps exactly as an alternating rule demands. Reading the steps in pairs rather than singly is what makes an alternating rule visible.

Your Answer : (Not Answered)

Correct Answer : A

Neurospora is favoured as genetic material because its life cycle is only about ten days.

It is also haploid, so every mutation shows at once, and the products of a single meiosis are held in order in the ascus, which lets crossing over be read directly. Beadle and Tatum used it for the one gene–one enzyme hypothesis.

Your Answer : (Not Answered)

Correct Answer : A

A computer that requests files from another is a client.

The machine that supplies them is the server. The distinction is one of role, not of hardware: the same computer can be a client of one service and a server of another.

Your Answer : (Not Answered)

Correct Answer : B

The transformer that generates the high voltage in a television is the flyback.

It works from the rapid collapse of current at the end of each horizontal scan line - the flyback - and steps that pulse up to about 25,000 volts for the picture tube.

Your Answer : (Not Answered)

Correct Answer : B

Google is a search engine.

It crawls the web, indexes what it finds and ranks results, originally by the PageRank algorithm which treats a link as a vote. FTP is a file transfer protocol, Archie an early FTP index and ARPANET the internet's predecessor.

Your Answer : (Not Answered)

Correct Answer : B

Ammonium sulphate, (NH₄)₂SO₄, contains about 21 per cent nitrogen by mass:

\[ \frac{2 \times 14}{132} \times 100 = 21.2\% \]

It is a straight nitrogenous fertiliser, valued for also supplying sulphur, though urea at 46 per cent nitrogen is far more concentrated.

Your Answer : (Not Answered)

Correct Answer : C

The World Day of Remembrance for Road Traffic Victims falls on the third Sunday of November.

The UN adopted it in 2005. About 1.19 million people die in road crashes each year, and it is the leading cause of death for those aged 5 to 29.

Your Answer : (Not Answered)

Correct Answer : B

Kalpana Chawla was an astronaut.

Born at Karnal in Haryana, she flew on the Space Shuttle Columbia in 1997 and again in 2003, becoming the first woman of Indian origin in space. She died with the rest of the crew when Columbia broke up on re-entry on 1 February 2003.

Your Answer : (Not Answered)

Correct Answer : C

For transforming the barren village of Ralegan Siddhi.

Anna Hazare organised watershed development, tree planting and a ban on liquor in the drought-prone Maharashtra village from 1975, turning it into a model of rural self-reliance. He received the Padma Bhushan in 1992.

Your Answer : (Not Answered)

Correct Answer : A

Bamiyan is famous for them.

Two standing Buddhas, 55 m and 38 m high, were carved into the cliff in Afghanistan in the sixth century, the largest such statues in the world. The Taliban destroyed them with explosives in March 2001.

Your Answer : (Not Answered)

Correct Answer : D

The cumulonimbus is the thundercloud.

It grows vertically from near the ground to the tropopause, sometimes 12 km or more, spreading into an anvil at the top where it meets the stable stratosphere. Its violent updraughts separate charge, producing lightning, hail and heavy rain.

Your Answer : (Not Answered)

Correct Answer : A

The Shanti Swarup Bhatnagar Prize for Science and Technology of 2021, given by the Council of Scientific and Industrial Research, went to Dr Binoy Kumar Saikia of the CSIR North East Institute of Science and Technology at Jorhat in the field of Earth, Atmosphere, Ocean and Planetary Sciences, according to the CSIR list of the 2021 winners. The other names in the options are scientists who are not the winners of this category in that year, so they are not correct. The answer is Dr Binoy Kumar Saikia, option A.