GATE Questions

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The quadratic equation whose roots are reciprocal of 2x2+5x+3=0 can be obtained by replacing x by 1/x.

Hence, 2(1/x)(1/x)+ 5(1/x) + 3 = 0

=> 3x2+5x+2=0

Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 x 6 x 6 = 216. Of these attempts, one of them is a successful attempt.

Maximum number of unsuccessful attempts = 216 - 1 = 215.

Given M.P=45,S.P=42, Profit = 0.05

Let C.P=x , Then

Profit = (42-x)/x = 0.05
=> x = 40.

The given number series is 8, 11, 19, 23, 32, ?

It follows a pattern that

8 + 11 = 19

11 + 12 = 23

19 + 13 = 32

23 + 14 = 37

32 + 15 = 47

....

Hence, the next number in the given series = 37.

Let the present age of the man be 'P' and son be 'Q',
Given, P + Q = 64 or Q = (64 - P)
Now the man says "I am five times as old as you were, when I was as old as you are",
So, P = 5[B - (P - Q)]
We get 6P = 10Q,
Substitute value for Q,
6P = 10(64 - P),
Therefore P = 40, Q = 24.

The given number series 11, 12.2, 14.6, 18.2, ?

11

11 + 1.2 = 12.2

12.2 + 2.4 = 14.6

14.6 + 3.6 = 18.2

18.2 + 4.8 = 23

Hence, the next number in the given number series is 23.

The given number series is 1 8 36 ? 1100 7701

It follows a pattern that,

1

1 x 3 + 5 = 8

8 x 4 + 4 = 36

36 x 5 + 3 = 183

183 x 6 + 2 = 1100

1100 x 7 + 1 = 7701

Hence, the missing number in the given series is 183.

Ans. 
4.5 = 7 x 0.5 + 1
5.5 = 4.5 x 1 + 1
12 = 5.5 x 2 + 1
49 = 12 x 4 + 1
? = 49 x 8 + 1, i.e. ? = 393