GATE Questions

---

We know that zero can't be in hundreds place. But let's assume that our number could start with zero.

The formula to find sum of all numbers in a permutation is

111 x no of ways numbers can be formed for a number at given position x sum of all given digits

No of 1 s depends on number of digits

So,the answer us

111 x 20 x (0+1+2+3+4+5) = 33300

We got 20 as follows. If we have 0 in units place we can form a number in 4*5 ways. This is for all numbers. So we have substituted 20 in formula.

Now, this is not the final answer because we have included 0 in hundreds place. so we have to remove the sum of all numbers that starts with 0.

This is nothing but the sum of all 2 digits numbers formed by 1 2 3 4 5. Because 0 at first place makes it a 2 digit number.

So the sum for this is 11 x 4 x (1+2+3+4+5).
=660

Hope u understood why we use 4. Each number can be formed in 4x1 ways

So, the final answer is 33300-660 = 32640

Let the slower pipe alone fill the tank in x min.

Then, faster pipe will fill it in x/3 min.

1/x + 3/x = 1/36 

Principle amount = Rs. 29000

Interest = Rs. 10440

Let rate of interest = r%

=> So, time = r years

According to the question,

10440 = 29000 x r x r/100

290 x r x r = 10440

r x r = 1044/29 = 36

r = 6

Hence, the rate of interest = 6% and time = 6 yrs.

True, the given statement that Carbon in the ocean originates from the atmosphere is absolutely correct. Carbondi oxide in the atmosphere is absobed by the ocean surface and is dissolved as inorganic carbon in the oceans.

The endomembrane system is composed of the different membranes that are suspended in the cytoplasm within a eukaryotic cell. These membranes divide the cell into functional and structural compartments or organelles. In eukaryotes, the organelles of the endomembrane system include the nuclear membrane, the endoplasmic reticulum, the Golgi apparatus, lysosomes, vesicles, endosomes and the cell membrane, among others.

3/4 divided by 2

= 3/4/2

= 3/4x2

= 3/8.

Hence, 3/4 divided by 2 is equal to 3/8.