GATE Questions

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It is very hard to catch breathe when you run fast.

Given that three athletes can complete one round around a circular field in 16, 24 and 36 min respectively.

Now, required time after which they met for the first time = LCM of (16, 24 & 36) min

Now, LCM of 16, 24, 36 = 144 minutes = 2 hrs 24 min.

Siphon is a tube bent to form two legs of unequal length by which a liquid can be transferred from a reservoir and then down to a lower level of it.

Siphon will fail to work if, the level of the liquid in the two vessels are at the same height.

Required Number of ways = 4C2 × 3C2 × 2C1 = 36 = 36

No. of students will be 98 x 12 = 1176
let us consider n circles then 1 + 2 + 3 + ....+ n = 1176
n(n+1)/2 = 1176
n = 48 circles.

Cp1 = p2 - p1 ,
Cp2 = p3 - p2
..
..
..
Cp23 = p24 - p23
Sum of series = (p2-p1) + (p3-p2) + .....(p23-p22) + (p24-p23)
All terms get cancelled, except p1 = 2 and p24 = 89
So Sum = -p1 + p24
Sum of series = -2 + 89 = 87

The nearest stars to Earth are in the Alpha Centauri triple-star system, about 4.37 light-years away. One of these stars, Proxima Centauri, is slightly closer, at 4.26 light-years.

Of all the stars closer than 15 light-years, only two are spectral type G, similar to our sun: Alpha Centauri A and Tau Ceti. The majority are M-type red dwarf stars.

Only nine of the stars in this area is bright enough to be seen by the naked human eye from Earth. These brightest stars include Alpha Centauri A and B, Sirius A, Epsilon Eridani, Procyon, 61 Cygni A and B, Epsilon Indi A and Tau Ceti.

We know Compound Interest = C.I. = P1+r100t - 1

Here P = 2680, r = 8 and t = 2

C.I. = 26801 + 81002-1= 268027252-12= 26802725+12725-1= 2680 5225×225

= (2680 x 52 x 2)/625

= 445.95

Compound Interest = Rs. 445.95