GATE Questions

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Given that x = 2+ 223 + 213

So x - 2 = 223 + 213

Now cubing on both sides, we get

=> x3-8-6x2+12x = 4 + 2 + 6(x-2)

Therefore, x3-6x2+6x = -6 + 8 = 2

Given Karthik’s age = 32 years

Karthik’s son age = 7 years

Difference between their ages = K - S = 32 - 7 = 25 years ….(1)

Now, required K = 2S ……(2)

Put (2) in (1)

2S - S = 25

=> S = 25 years

Hence, at the age of 25 years of Karthik’s son, Karthik will be twice as his son’s age.

25 - 7 = 18 years

Therefore, after 18 years the father be twice as old as the son.

The P wave in the ECG represents atrial depolarization, which results in atrial contraction, or atrial systole.

The P wave is a summation wave generated by the depolarization front as it transits the atria.

The four most common soil erosion prevention methods are vegetation, geotextiles, mulch, and retaining walls.

By planting grass in areas of concentrated water flow, farmers can prevent much of the soil erosion that results from runoff, as the grass stabilizes the soil while still providing an outlet for drainage.

Preventing soil erosion is critical in protecting your property and exposed soil, whether from wind, weather, running water, and even the after-effects of the forest fire.

3/8 as a Decimal :

In this we should convert the denominator into 10, 100, 1000, 10000, 100000,... to make it simple.

Now to make 8 into 1000, we multiply numerator and denominator with 125

=> 3 x 1258 x 125 = 3751000 = 0.375

1/10 as a Decimal :

1 divided into 10 parts of each 0.1.

Therefore, 3/8 = 0.375 and 1/10 = 0.1 in decimals.

A Mixture is a material made up of two or more different substances which are mixed.

Mixtures can be either homogeneous or heterogeneous.

* A homogeneous mixture is a type of mixture in which the composition is uniform and every part of the solution has the same properties.

* A heterogeneous mixture is a type of mixture in which the components can be seen, as there are two or more phases present.

Air is a homogeneous mixture of the gaseous substances nitrogen, oxygen, and smaller amounts of other substances.

Laconic means using only few words in his/her speech or while talking.

In the given options, talkative, wordy and long are all opposite to laconic and brief is the only word which is similar in meaning of laconic.