CAT Questions

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Number of positive integral solutions =  n-1Cr-1 = C220 = 190

As given in the question, Marked price is 25% more than the Cost price.

=> C.P of the article = 34 x 400 = 300

Now, 

Let the original S.P of the article be Rs. P

Now the new S.P = P + 16.666 +13.333300 x P

=> S.P = 7P6

According to the question,

7P6 - 300 = 2P - 300

=> 5P = 1800

=> P = Rs. 360

Hence, the increased S.P = 360 x 7/6 = Rs. 420. 

Probability between z = 0 and z = 3.01 is given by

P(0<z<3.01) = P(z<3.01) - P(z<0)

Reading from the z-table, we have

P(z<0) = 0.5

P(z<3.01) = 0.9987

Hence, P(0<z<3.01) = 0.9987 - 0.5 = 0.4987.

Ratio of investments for 1 year

=> (P : Q : R) = (2x2 + 2.4x10) : (3x2 + 3.3x10) : (5x12)

=> (P : Q : R) = 28 : 39 : 60

Now R share = 190500 x 60/127 = Rs. 90000.

A standing wave also known as a stationary wave, is a wave in which its peaks or any other point on the wave do not move spatially.

This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions. The most common cause of standing waves is the phenomenon of resonance, in which standing waves occur inside a resonator due to interference between waves reflected back and forth at the resonator's resonant frequency.

Hence, standing wave occurs when a wave reflects upon itself.

Distance = 70 x 1 ½ = 105 km

Relative Speed = 85 – 70 = 15

Time = 105/15 = 7 hrs

4:30 + 7 hrs = 11.30 p.m.

4 x 27 x 3125 = 22 × 33 × 55 ;

8 x 9 x 25 x 7 = 23 × 32 × 52 × 7

16 x 81 x 5 x 11 x 49 = 24 × 34 × 5 × 11 × 72

H.C.F = 22 × 32 × 5 = 180.

We know that the day repeats every 7 days, 14 days, 21 days,...

So if today is Monday, after 7 days it is again Monday, after 14 days again it is Monday.

Hence, after 2 weeks i.e, 14 days the day repeats and is the same day.