GATE Questions

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Concave type of glasses are used in the headlights of the vehicles as the light from the bulb which is at focus will converges out and spreads and reflects back parallely.

Here to say which fraction is greater from the given options, the fraction with greater numerator with same denominator or smaller denominator with same numerator.

To find the greater fraction, among the given options, make the denominators same for the options by finding the LCM of all the denominators.

7/12, 9/16, 13/20, 32/80

Now, LCM of 12, 16, 20, 80 = 240.

Then,

140/240, 135/240, 156/240, 96/240

Here 

$$\begin{gathered} 156240 > 140240 > 135240 > 96240 \\ => 1320 > 712 > 916 > 3280 \end{gathered}$$

Hence, largest fraction = 13/20.

As parabola is a locus of a point, which moves so that its distance from focus and directrix is always equal.

The latus rectum of a conic section is the chord (line segment) that passes through the focus, is perpendicular to the major axis and has both endpoints on the curve. The length of the latus rectum is determined differently for each conic.

The length of a parabola's latus rectum is 4p, where p is the distance from the focus to the vertex.

During convection, cool and dense air falls through the warmer and less dense air. The warm air having less mass is being displaced by the cooler which is much heavy. Convection always involves the air rising through the atmosphere.

Price of 1kg fresh cashew = Rs.120
Therefore, price of 10kg = Rs.120 x 10 = Rs.1200

10% of 10kg which eaten by rodents = 10 x 10/100 = 1kg.

So, End of Year he had 10kg - 1kg = 9kg

So, he sells that 9kg with Rs.20 per kg profit = 9 x 140 = 1260.

He buy 10kg wooden box with cashew for Rs.1200 and sell that for Rs. 1260

So, profit = 1260 - 1200 = Rs.60 more money he get.

We know that, 

1 meter = 100 cms. 

=> 1 meter = 3.28084 feet.

15 girls are absent => b = 2(g-15)...... eqn...(1)

45 boys are absent => g - 15 = 5(b-45).....eqn...(2)

=> g = 5(b-45) + 15

=> b = 2((5(b-45)+15)-15)

=> b = 2(5b - 225 + 15 - 15)

=> b = 2(5b-225)

=> b = 10b - 450

=> 9b = 450

=> b = 50

so from equation(2)

g - 15 = 5(b - 45)

=> g - 15 = 5(50-45)

=> g - 15 = 5(5)

=> g = 25 + 15

=> g = 40

Therefore, the number of boys = 50 and girls = 40