CAT Questions

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K = 100 L = 130
130------ 30
100------- ? => 23 1/13 %

Let S be the sample space. Then,
n(s) = number of ways of drawing 4 pearls out of 14

= C414 ways = 14×13×12×114×3×2×1= 1001

Let E be the event of drawing 4 pearls of the same colour.
Then, E = event of drawing (4 pearls out of 5) or (4 pearls out of 4) or (4 pearls out of 5)

  ⇒C15+ C44+ C15 = 5+1+5 =11

 P(E) = n(E)n(S)=111001=191  

 Required probability = 1-191=9091

The Indian Space Research Organisation (ISRO) has successfully launched its 3136 kg GSAT-19 communication satellite with its brand new and heaviest – Geosynchronous Satellite Launch Vehicle Mark-III D-1 (GSLV-Mk III D-1) satellite into Geosynchronous Transfer Orbit (GTO) from the Satish Dhawan Space Centre (SDSC) in Sriharikota, Andhra Pradesh on June 5, 2017. The satellite GSAT-19 has an intended life span of 10 years and is developed to improve telecommunication and broadcasting areas. The GSLV-Mk III is popularly known as “fat boy” and is developed for 15 years at a cost of around Rs 300 crore. The rocket is capable of carrying payloads of up to 4,000 kg into the GTO and 10,000 kg into the Low Earth Orbit (LEO). The GSLV-Mk III is a three stage rocket. Its first stage is made of two strap on motors filled with solid fuel. The second stage uses the liquid fuel and the third is the cryogenic upper stage “C25”, which is powered by the highly complex indigenous cryogenic engine “CE20”. The number 20 denotes the 20-ton thrust it generates for the rocket to reach the intended height with the heavy mass on board.

$$\begin{gathered} 78 x 448 + 67 x 3374 \\ => 392 + 2892 \\ => 3284 \end{gathered}$$

Remaining % of amount with Rohan

= 100 - (24 + 34 + 17 + 19)

= 100 - 94

= 6%

=> 6% = 540

=> 100% = ?

540 x 100/6 = Rs. 9000

Now, Money spent on insurance and food is

= 34 + 24 = 58% of 9000

= 58 x 9000/100

= 58 x 90

= Rs. 5220

Total distance = 150 + 210 = 360 mts

Time taken to cross each other when moving in opposite direction = 10.8 sec

Relative speed of trains = (350/10.8) x 18/5 = 3600/30 = 120 kmph

Speed of shorter train = (150/12) x 18/5 = 45 kmph

Hence, speed of longer train = 120 - 45 = 75 kmph.