Solution:

(sec8x - 1) / (sec4x - 1)

By taking LCM
= (1 - cos8x) cos4x / (1 - cos4x) cos8x

Now, (1-cos2x) = 2*(sinx)^2
Thus,
= 2*(sin4x)^2*cos4x / 2*(sin2x)^2*cos8x )]
=sin4x (2sin4xcos4x) / 2*(sin2x)^2*cos8x
= (2sin2xcos2x) sin8x / (2sin2xsin2x) cos8x
=cos2xsin8x / sin2xcos8x
=cot2xtan8x
=tan8x / tan2x

Solution:

If the number has to be divisible by 4, the last 2 digits of the number has to be 12, 24, 32, 44 or 52 i.e. there are 5 ways in which the last two digits can be arranged.

Now in that case, we find the number of possible ways in which the first 7 places can be filled
Which is 5^7 ways.

Thus the total number of ways = 5^7 * 5 = 5^8 ways

Solution:

Total age of x adults = 30x
Total age of twelve new adults = 32*12 = 384

Thus total age of x + 12 persons = (c + 12) * 31 = 30x + 384

Now as per the question
31x + 372 = 30x + 384
X = 12

Thus there are twelve students in the class.

Solution:

Suppose that the market price was Rs.100.

Now when the successive discounts were applied, the selling price will become 80 and 75 respectively with each discount.

Thus the selling price has become rs.75 but he managed a profit of 20%

Thus
Cost price = (75/120)*100 = 62.5

Percent Increase with respect to the market price = (37.5/62.5)*100
= 60%

Solution:

Let us assume that the xth term is zero

As per the question,
The 15th term must be (x + 12 d)
6th term be (x + 3d)
11th term be (x + 8d)
13th term be (x + 10d)

Now by the condition given,

2x + 12 d = 3x + 21d
X + 9d = 0

Now x + 9d will be the 12th term

Thus the 12th term in such an arithmetic progression will be 0.

Solution:

This problem might sound confusing but for the solution, all you have to do is take the LCM of 4, 8, 6 and 10 which is 120 min or 2 hours.

Thus the bells will toll again when the clock strikes 2 am + 2 = 4 am.

Solution:

This is a difficult one to crack as there are two series in the same series.

One is 2, 10 (2*5), 40 (2*5*4)
The other is 1, 4 (1*4), 16 (4*4), 64 (16*4)

Since we have to find just the next term, it will be linked with the 1, 4, 16, 64 series
And the next term will be (64*4) or 256.

Solution:

This is quite a tricky question. Do not go by the days mentioned in the question, they are put in there just to confuse you.

The answer is as simple as - Yesterday, Today and Tomorrow.

Solution:

Let us assume that the average age ten years ago was x
Now total age back then = 6x

The father died today so the number of members = 5

Thus total age after 10 years = 5(x + 10)

A baby was also born today but since he is 0 years old, the total age will be 5(x + 10) only

Now considering the question, the total age is same
i.e. 6x = 5(x + 10)
6x = 5x + 50
x = 50

Which means that the age 10 years back was 50 years.
Thus his father died at 50 + 10 = 60 years.

Solution:

QCEIL

If you look closely, it is quite an easy task.
The first letter is the previous with the corresponding letter.
The second is the next letter with the corresponding alphabet
The third letter is the next alphabet again.
The fourth letter is the previous with the corresponding letter.
The fifth and sixth letters are the next alphabets to the corresponding alphabets.
The seventh letter is the previous alphabet again.

So the patter is that one letter is the previous letter to the corresponding one and then the next two letters are the next letters of the corresponding alphabets and so on.

Thus RBDJK = QCEIL