GATE Questions

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Let the two no's be a and b;
Given product of the no's is p = ab;
If the each nos is increased by 2 then the new product will be
(a+2)(b+2) = ab + 2a + 2b + 4
= ab + 2(a+b) + 4
= p + 2(a+b) + 4
Hence the new product is (p+4) times greater than twice the sum of the two original numbers.

False. The ankle is not the third-class lever in the body.

Levers are typically labeled as first class, second class, or third class. All three types are found in the body, but most levers in the human body are third class.

First-class levers in the human body are rare and have the axis (fulcrum) located between the weight (resistance) and the force. One example is the joint between the head and the first vertebra.

In a second-class lever, the weight (resistance) is located between the axis (fulcrum) and the force. An example of a second-class lever in the human body is found in the lower leg when someone stands on tiptoes

In a third-class lever, the most common in the human body, force is applied between the resistance (weight) and the axis (fulcrum). There are numerous third-class levers in the human body; one example can be illustrated in the elbow joint.

Given speed of the first train = 60 km/hr = 60 x 5/18 = 50/3 m/s

Let the speed of the second train = x m/s

Then, the difference in the speed is given by

503 - x = 12018

=> x = 10 m/s

=> 10 x 18/5 = 36 km/hr

ALPHABET is the only has the most letters in it.

Alphabet has all the 26 letters from A - Z. 

Hence, ALPHABET is one word that has the most letters in it.

The Lami's theorem states that " If three forces coplanar and concurrent forces acting on a particle keep it in equilibrium, then each force is proportional to the sine of the angle between the other two and the constant of proportionality is the same." This theorem is derived from the Sine rule of triangles.

Given numbers are 1, 2 and 3

Factors of 1 = 1

Factors of 2 = 1, 2

Factors of 3 = 1, 2 and 3

Common factors = 1

Hence, the HCF of 1, 2 and 3 = 1.

The term biodiversity refers to the variety of life on Earth at all its levels, from genes to ecosystems, and the ecological and evolutionary processes that sustain it.

Let the total length of the pencil = x cms

From the given data,

'x/8' is black

Remaining part = x - x/8 = 7x/8

1/2 of 7x/8 is white

=> 7x/16 is white (Remaining part is 7x/16)

And given that the remaining part is blue and is 3 1/2 cm = 7/2 = 3.5 cm

That remaining part = 7x/16

Therefore,

7x/16 = 7/2

x = 16/2 = 8

Hence, the total length of the pencil = x = 8 cm.