GATE Questions

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Let the two digits be x & y

From given data in the question, we get

x + y = 3(x - y)

x + y = 3x - 3y

=> 2x = 4y

x/y = 2/1

For having the 2:1, numbers satisfying are

12, 21, 24, 42, 36, 63, 48, 84

From this 36 is eleminated because it is a perfect square and no others are prime or perfect squares.

Hence, there exists 7 such 2-digit numbers => 12, 21, 24, 42, 63, 48, 84.

Ans. 
Let B’s investment = x rs.
∴ A’s investment =( x + 1200) rs.
Ratio of the profits of A and B = (x+1200)*(15+4):x*15 = {19(x+1200)}:15x
Now,let the total profit of A =y
∴ total profit of B = (y-280)
But total profit = 1240
⇒y+(y-280)=1240
⇒2y=1520
⇒y= 760
∴profit of A = 760rs.
Profit of B = 760-280=480 rs.
Ratio of profits= 760:480 = 19:12
According to the question,

19(x+1200)/15x = 19/12

12x+14400 = 15x

⇒3x = 14400
⇒x = 4800 rs.
⇒investment of A = 4800+1200
                          = 6000 rs.

Galileo Galilei (1564-1642) was an Italian Astronomer who

1) Discovered 4 satellites of Jupiter

2) Developed Telescope

3) Discovered that the movement of pendulum produces a regular time measurement

He is Physicist, Mathematician, inventor, and philosopher Too.

Carbon dioxide is present under pressure in soft drinks.

Number = 271 x 96 + 0 = 26016

=> 95) 26016 (273
           25935
           --------
              81

Required number = 81.

These two events cannot be disjoint because P(K) + P(L) > 1.

P(AꓴB) = P(A) + P(B) - P(AꓵB).

An event is disjoint if P(A ꓵ B) = 0. If K and L are disjoint P(K ꓴ L) = 0.8 + 0.6 = 1.4

And Since probability cannot be greater than 1, these two mentioned events cannot be disjoint.

Let the monthly salary of Shankar be = Rs.x
Amount invested on expenditure = 25% = x/4;
Remaning amount = 3x/4;
Amount invested on children education = 20% i.e = 3x/20;
Remaining amount = 3x/4 - 3x/20 = 3x/5;
Remaining amount invested in three different schemes i.e is 1/3(3x/5)
=> x/5 = 5600
Therefore x = 28000
Hence, Monthly salary of Shankar is Rs. 28,000.