MAH MBA CET Sample Paper 2025

Eight people are sitting in a straight line. Let us number the positions as 1 to 8 from left to right. A is second to the right of C and third to the left of H. Moreover, H is not sitting at an end position. So, the possibilities for C, A and H are 2, 4, 7 or 1, 3, 6. If they are sitting at 2, 4,7, then D and G must be sitting at 5 and 6. Now, F is not sitting at an end position, so the only possible place for him will be 3. In this case E will have to sit at 1. But contradicts the given information. Hence, this is not possible. Thus, C, A and H must be sitting at 1, 3 and 6 respectively. D and G can be 4/5 or 7/8. But in case of 7/8, there won’t be more people to the right of G then his left. Hence G must be fourth, D must be fifth. E must be 2. B should be at 8 and F should be at 7. Thus, we will have the following arrangement

Eight people are sitting in a straight line. Let us number the positions as 1 to 8 from left to right. A is second to the right of C and third to the left of H. Moreover, H is not sitting at an end position. So, the possibilities for C, A and H are 2, 4, 7 or 1, 3, 6. If they are sitting at 2, 4,7, then D and G must be sitting at 5 and 6. Now, F is not sitting at an end position, so the only possible place for him will be 3. In this case E will have to sit at 1. But contradicts the given information. Hence, this is not possible. Thus, C, A and H must be sitting at 1, 3 and 6 respectively. D and G can be 4/5 or 7/8. But in case of 7/8, there won’t be more people to the right of G then his left. Hence G must be fourth, D must be fifth. E must be 2. B should be at 8 and F should be at 7. Thus, we will have the following arrangement

Eight people are sitting in a straight line. Let us number the positions as 1 to 8 from left to right. A is second to the right of C and third to the left of H. Moreover, H is not sitting at an end position. So, the possibilities for C, A and H are 2, 4, 7 or 1, 3, 6. If they are sitting at 2, 4,7, then D and G must be sitting at 5 and 6. Now, F is not sitting at an end position, so the only possible place for him will be 3. In this case E will have to sit at 1. But contradicts the given information. Hence, this is not possible. Thus, C, A and H must be sitting at 1, 3 and 6 respectively. D and G can be 4/5 or 7/8. But in case of 7/8, there won’t be more people to the right of G then his left. Hence G must be fourth, D must be fifth. E must be 2. B should be at 8 and F should be at 7. Thus, we will have the following arrangement

Eight people are sitting in a straight line. Let us number the positions as 1 to 8 from left to right. A is second to the right of C and third to the left of H. Moreover, H is not sitting at an end position. So, the possibilities for C, A and H are 2, 4, 7 or 1, 3, 6. If they are sitting at 2, 4,7, then D and G must be sitting at 5 and 6. Now, F is not sitting at an end position, so the only possible place for him will be 3. In this case E will have to sit at 1. But contradicts the given information. Hence, this is not possible. Thus, C, A and H must be sitting at 1, 3 and 6 respectively. D and G can be 4/5 or 7/8. But in case of 7/8, there won’t be more people to the right of G then his left. Hence G must be fourth, D must be fifth. E must be 2. B should be at 8 and F should be at 7. Thus, we will have the following arrangement

B is sitting second to the left of both A and E. Therefore, one among A and E must be facing the centre and the other must be facing away from the centre. It has been given that A is facing the centre. Therefore, E must be facing away from the centre.

(In the diagram, the persons facing the centre are indicated by green colour and the persons facing away from the centre are indicated by the red colour).

H is sitting to the left of both A and B. Therefore, B must be facing away from the centre.

D is sitting third to the right of E. G and E are not sitting adjacent to each other. Therefore, G must be sitting near D. H,D and G face the same direction. We also know that 4 persons face towards the centre and 4 persons face away from the centre. B and E face away from the centre. Therefore, H, D and G must be facing the centre.

C is not sitting adjacent to G. Therefore, F must be sitting adjacent to D. The final arrangement is as follows:

B is sitting third to the left of F. Therefore, option B is the right answer.

B is sitting second to the left of both A and E. Therefore, one among A and E must be facing the centre and the other must be facing away from the centre. It has been given that A is facing the centre. Therefore, E must be facing away from the centre.

(In the diagram, the persons facing the centre are indicated by green colour and the persons facing away from the centre are indicated by the red colour).

H is sitting to the left of both A and B. Therefore, B must be facing away from the centre.

D is sitting third to the right of E. G and E are not sitting adjacent to each other. Therefore, G must be sitting near D. H,D and G face the same direction. We also know that 4 persons face towards the centre and 4 persons face away from the centre. B and E face away from the centre. Therefore, H, D and G must be facing the centre.

C is not sitting adjacent to G. Therefore, F must be sitting adjacent to D. The final arrangement is as follows:

C is sitting opposite to D. Therefore, option C is the right answer.

B is sitting second to the left of both A and E. Therefore, one among A and E must be facing the centre and the other must be facing away from the centre. It has been given that A is facing the centre. Therefore, E must be facing away from the centre.

(In the diagram, the persons facing the centre are indicated by green colour and the persons facing away from the centre are indicated by the red colour).

H is sitting to the left of both A and B. Therefore, B must be facing away from the centre.

D is sitting third to the right of E. G and E are not sitting adjacent to each other. Therefore, G must be sitting near D. H,D and G face the same direction. We also know that 4 persons face towards the centre and 4 persons face away from the centre. B and E face away from the centre. Therefore, H, D and G must be facing the centre.

C is not sitting adjacent to G. Therefore, F must be sitting adjacent to D. The final arrangement is as follows:

F is sitting second to the right of D. Therefore, option E is the right answer.

We know that Tushar is from Guwahati and Umesh is from Delhi.
Now Pawan visited Allahabad so, Pawan cannot be from Allahabad. Thus, one among, Rohit, Sanjay and Vivek has to be from Allahabad. However, from 3 we can rule out Rohit. Thus, either Sanjay or Vivek will be from Allahabad. However, from 2 and 5 we can infer that Sanjay is from Hyderabad and visited Lucknow. Thus, Vivek must be from Allahabad. One among Rohit and Pawan will be from Bhopal and the other one will be from Lucknow.
Now we know that Pawan visited Allahabad, Sanjay visited Lucknow, Rohit visited Guwahati and Vivek visited Delhi. Thus one among Tushar and Umesh will visit Hyderabad and the other one will visit Bhopal.
Thus we have the following table

We know that Tushar is from Guwahati and Umesh is from Delhi.
Now Pawan visited Allahabad so, Pawan cannot be from Allahabad. Thus, one among, Rohit, Sanjay and Vivek has to be from Allahabad. However, from 3 we can rule out Rohit. Thus, either Sanjay or Vivek will be from Allahabad. However, from 2 and 5 we can infer that Sanjay is from Hyderabad and visited Lucknow. Thus, Vivek must be from Allahabad. One among Rohit and Pawan will be from Bhopal and the other one will be from Lucknow.
Now we know that Pawan visited Allahabad, Sanjay visited Lucknow, Rohit visited Guwahati and Vivek visited Delhi. Thus one among Tushar and Umesh will visit Hyderabad and the other one will visit Bhopal.
Thus we have the following table

We know that Tushar is from Guwahati and Umesh is from Delhi.
Now Pawan visited Allahabad so, Pawan cannot be from Allahabad. Thus, one among, Rohit, Sanjay and Vivek has to be from Allahabad. However, from 3 we can rule out Rohit. Thus, either Sanjay or Vivek will be from Allahabad. However, from 2 and 5 we can infer that Sanjay is from Hyderabad and visited Lucknow. Thus, Vivek must be from Allahabad. One among Rohit and Pawan will be from Bhopal and the other one will be from Lucknow.
Now we know that Pawan visited Allahabad, Sanjay visited Lucknow, Rohit visited Guwahati and Vivek visited Delhi. Thus one among Tushar and Umesh will visit Hyderabad and the other one will visit Bhopal.
Thus we have the following table

All options represent the person and the city he visited. This is not followed in option A. Hence A is the odd one out.

We know that Tushar is from Guwahati and Umesh is from Delhi.
Now Pawan visited Allahabad so, Pawan cannot be from Allahabad. Thus, one among, Rohit, Sanjay and Vivek has to be from Allahabad. However, from 3 we can rule out Rohit. Thus, either Sanjay or Vivek will be from Allahabad. However, from 2 and 5 we can infer that Sanjay is from Hyderabad and visited Lucknow. Thus, Vivek must be from Allahabad. One among Rohit and Pawan will be from Bhopal and the other one will be from Lucknow.
Now we know that Pawan visited Allahabad, Sanjay visited Lucknow, Rohit visited Guwahati and Vivek visited Delhi. Thus one among Tushar and Umesh will visit Hyderabad and the other one will visit Bhopal.
Thus we have the following table

Let us try to tabulate the given information.
From the given hints we can form a partially filled table as shown below.

Now from statement 5 we know that the person from Maharashtra is pursuing Finance.
It is given that Bhavya is not pursuing Finance and Dani is not from Maharashtra.
From this we can infer that Farhan is from Maharashtra and is pursuing Finance.
Now we know that Eknath and Bhavya are not pursuing Marketing.
This means that Dani is pursuing Marketing.
Now we can conclude that Bhavya is from Telangana and is pursuing Strategy.
Now the completely filled table will be as shown below.

Let us try to tabulate the given information.
From the given hints we can form a partially filled table as shown below.

Now from statement 5 we know that the person from Maharashtra is pursuing Finance.
It is given that Bhavya is not pursuing Finance and Dani is not from Maharashtra.
From this we can infer that Farhan is from Maharashtra and is pursuing Finance.
Now we know that Eknath and Bhavya are not pursuing Marketing.
This means that Dani is pursuing Marketing.
Now we can conclude that Bhavya is from Telangana and is pursuing Strategy.
Now the completely filled table will be as shown below.

Let us try to tabulate the given information.
From the given hints we can form a partially filled table as shown below.

Now from statement 5 we know that the person from Maharashtra is pursuing Finance.
It is given that Bhavya is not pursuing Finance and Dani is not from Maharashtra.
From this we can infer that Farhan is from Maharashtra and is pursuing Finance.
Now we know that Eknath and Bhavya are not pursuing Marketing.
This means that Dani is pursuing Marketing.
Now we can conclude that Bhavya is from Telangana and is pursuing Strategy.
Now the completely filled table will be as shown below.

We know that all the cars sold by a particular company belong to one of these 4 types. Therefore, the total percentage must be 100.

Eg) 23% of cars sold by Koyota are hatchbacks.
12% of cars sold by Koyota are sedans.
15% of cars sold by Koyota are crossovers.
Therefore, the remaining 100 - (23+12+15) = 50% of the cars sold must be SUVs.

Similarly filling the other values we get the following table.

Let the total number of cars sold by Koyota be x.

We know that, the total number of cars sold by Gyundai is x.
Total number of cars sold by Donda = x.
Total number of cars sold by BM = 2*x = 2x
Total number of cars sold by Folksvagen = 2*2x = 4x.

Total number of hatchbacks sold = 925
0.23x + 0.26x + 0.17*4x + 0.18*2x + 0.32x = 925
0.23x + 0.26x + 0.68x + 0.36x + 0.32x = 925
1.85x = 925
x = 500.

Now, we can find the number of cars of each type sold by a particular company.
Eg) 23% of cars sold by Koyota are hatchbacks.
Koyota sold 500 cars in total.
Therefore, Number of hatchbacks sold by Koyota = 0.23*500 = 115.
Similarly, we can fill the entire table. The final table is as shown below:

As we can see, the total number of cars sold by the 5 companies put together is 4500. Therefore, option B is the right answer.

We know that all the cars sold by a particular company belong to one of these 4 types. Therefore, the total percentage must be 100.

Eg) 23% of cars sold by Koyota are hatchbacks.
12% of cars sold by Koyota are sedans.
15% of cars sold by Koyota are crossovers.
Therefore, the remaining 100 - (23+12+15) = 50% of the cars sold must be SUVs.

Similarly filling the other values we get the following table.

Let the total number of cars sold by Koyota be x.

We know that, the total number of cars sold by Gyundai is x.
Total number of cars sold by Donda = x.
Total number of cars sold by BM = 2*x = 2x
Total number of cars sold by Folksvagen = 2*2x = 4x.

Total number of hatchbacks sold = 925
0.23x + 0.26x + 0.17*4x + 0.18*2x + 0.32x = 925
0.23x + 0.26x + 0.68x + 0.36x + 0.32x = 925
1.85x = 925
x = 500.

Now, we can find the number of cars of each type sold by a particular company.
Eg) 23% of cars sold by Koyota are hatchbacks.
Koyota sold 500 cars in total.
Therefore, Number of hatchbacks sold by Koyota = 0.23*500 = 115.
Similarly, we can fill the entire table. The final table is as shown below:

As we can see, the total number of sedans sold by the 5 companies put together is 1435. Therefore, option B is the right answer.

We know that all the cars sold by a particular company belong to one of these 4 types. Therefore, the total percentage must be 100.

Eg) 23% of cars sold by Koyota are hatchbacks.
12% of cars sold by Koyota are sedans.
15% of cars sold by Koyota are crossovers.
Therefore, the remaining 100 - (23+12+15) = 50% of the cars sold must be SUVs.

Similarly filling the other values we get the following table.

Let the total number of cars sold by Koyota be x.

We know that, the total number of cars sold by Gyundai is x.
Total number of cars sold by Donda = x.
Total number of cars sold by BM = 2*x = 2x
Total number of cars sold by Folksvagen = 2*2x = 4x.

Total number of hatchbacks sold = 925
0.23x + 0.26x + 0.17*4x + 0.18*2x + 0.32x = 925
0.23x + 0.26x + 0.68x + 0.36x + 0.32x = 925
1.85x = 925
x = 500.

Now, we can find the number of cars of each type sold by a particular company.
Eg) 23% of cars sold by Koyota are hatchbacks.
Koyota sold 500 cars in total.
Therefore, Number of hatchbacks sold by Koyota = 0.23*500 = 115.
Similarly, we can fill the entire table. The final table is as shown below:

The number of SUVs sold by Folksvagen is 380. Therefore, option A is the right answer.

We know that all the cars sold by a particular company belong to one of these 4 types. Therefore, the total percentage must be 100.

Eg) 23% of cars sold by Koyota are hatchbacks.
12% of cars sold by Koyota are sedans.
15% of cars sold by Koyota are crossovers.
Therefore, the remaining 100 - (23+12+15) = 50% of the cars sold must be SUVs.

Similarly filling the other values we get the following table.

Let the total number of cars sold by Koyota be x.

We know that, the total number of cars sold by Gyundai is x.
Total number of cars sold by Donda = x.
Total number of cars sold by BM = 2*x = 2x
Total number of cars sold by Folksvagen = 2*2x = 4x.

Total number of hatchbacks sold = 925
0.23x + 0.26x + 0.17*4x + 0.18*2x + 0.32x = 925
0.23x + 0.26x + 0.68x + 0.36x + 0.32x = 925
1.85x = 925
x = 500.

Now, we can find the number of cars of each type sold by a particular company.
Eg) 23% of cars sold by Koyota are hatchbacks.
Koyota sold 500 cars in total.
Therefore, Number of hatchbacks sold by Koyota = 0.23*500 = 115.
Similarly, we can fill the entire table. The final table is as shown below:

The number of cross overs sold by BM is 310. Therefore, option D is the right answer.

From statement 1, 2, and 7 we can gather the following information:

Now, as per statement 2 Tanya will be interviewed either on Tuesday or Thursday and Sachin will be interviewed on either Saturday or Sunday.

If Tanya is interviewed on Thursday and Sachin is interviewed on Saturday then Gayatri must be interviewed on Sunday since statement 5 says at least a one day gap is required between Mahima and Gayatri's interview. So, Abhinav will have to be interviewed on Tuesday. [Case 1]

Similarly, If Tanya is interviewed on Thursday and Sachin is interviewed on Sunday then Gayatri must be interviewed on Saturday since statement 5 says at least a one day gap is required between Mahima and Gayatri's interview. However, Gayatri is asked questions on Indian Bankruptcy Code (IBC) (from statement 6) while the person interviewed on Saturday is asked admin law (statement 1) so this case is not possible.

If Tanya is interviewed on Tuesday and Sachin on Sunday then Gayatri will have to be interviewed on Thursday since she is asked about IBC and not admin law.

From statement 4 we know that the ones wearing blazers must be on consecutive days apart from the weekend. Also, Digivijay does not wear a blazer (statement 1) so the ones wearing a blazer can either be on Monday and Tuesday or Thursday and Friday. From statement 3 we know that the ones carrying files are interviewed before Thursday, so on any two of the days among Monday, Tuesday and Wednesday. 

Even if one of the days is Wednesday, at least one person must carry a file on Monday and Tuesday. So, the ones wearing a blazer must be on Thursday and Friday.

In Case 1, upon placing the information we get the following:

However, as per statement 8, this is not possible. So, this case can be eliminated.

Similarly we can eliminate other cases. The only possible way, all the conditions are followed is:

So Option C is correct.

From statement 1, 2, and 7 we can gather the following information:

Now, as per statement 2 Tanya will be interviewed either on Tuesday or Thursday and Sachin will be interviewed on either Saturday or Sunday.

If Tanya is interviewed on Thursday and Sachin is interviewed on Saturday then Gayatri must be interviewed on Sunday since statement 5 says at least a one day gap is required between Mahima and Gayatri's interview. So, Abhinav will have to be interviewed on Tuesday. [Case 1]

Similarly, If Tanya is interviewed on Thursday and Sachin is interviewed on Sunday then Gayatri must be interviewed on Saturday since statement 5 says at least a one day gap is required between Mahima and Gayatri's interview. However, Gayatri is asked questions on Indian Bankruptcy Code (IBC) (from statement 6) while the person interviewed on Saturday is asked admin law (statement 1) so this case is not possible.

If Tanya is interviewed on Tuesday and Sachin on Sunday then Gayatri will have to be interviewed on Thursday since she is asked about IBC and not admin law.

From statement 4 we know that the ones wearing blazers must be on consecutive days apart from the weekend. Also, Digivijay does not wear a blazer (statement 1) so the ones wearing a blazer can either be on Monday and Tuesday or Thursday and Friday. From statement 3 we know that the ones carrying files are interviewed before Thursday, so on any two of the days among Monday, Tuesday and Wednesday. 

Even if one of the days is Wednesday, at least one person must carry a file on Monday and Tuesday. So, the ones wearing a blazer must be on Thursday and Friday.

In Case 1, upon placing the information we get the following:

However, as per statement 8, this is not possible. So, this case can be eliminated.

Similarly we can eliminate other cases. The only possible way, all the conditions are followed is:

So Option A is correct.

From statement 1, 2, and 7 we can gather the following information:

Now, as per statement 2 Tanya will be interviewed either on Tuesday or Thursday and Sachin will be interviewed on either Saturday or Sunday.

If Tanya is interviewed on Thursday and Sachin is interviewed on Saturday then Gayatri must be interviewed on Sunday since statement 5 says at least a one day gap is required between Mahima and Gayatri's interview. So, Abhinav will have to be interviewed on Tuesday. [Case 1]

Similarly, If Tanya is interviewed on Thursday and Sachin is interviewed on Sunday then Gayatri must be interviewed on Saturday since statement 5 says at least a one day gap is required between Mahima and Gayatri's interview. However, Gayatri is asked questions on Indian Bankruptcy Code (IBC) (from statement 6) while the person interviewed on Saturday is asked admin law (statement 1) so this case is not possible.

If Tanya is interviewed on Tuesday and Sachin on Sunday then Gayatri will have to be interviewed on Thursday since she is asked about IBC and not admin law.

From statement 4 we know that the ones wearing blazers must be on consecutive days apart from the weekend. Also, Digivijay does not wear a blazer (statement 1) so the ones wearing a blazer can either be on Monday and Tuesday or Thursday and Friday. From statement 3 we know that the ones carrying files are interviewed before Thursday, so on any two of the days among Monday, Tuesday and Wednesday. 

Even if one of the days is Wednesday, at least one person must carry a file on Monday and Tuesday. So, the ones wearing a blazer must be on Thursday and Friday.

In Case 1, upon placing the information we get the following:

However, as per statement 8, this is not possible. So, this case can be eliminated.

Similarly we can eliminate other cases. The only possible way, all the conditions are followed is:

From statement 1, 2, and 7 we can gather the following information:

Now, as per statement 2 Tanya will be interviewed either on Tuesday or Thursday and Sachin will be interviewed on either Saturday or Sunday.

If Tanya is interviewed on Thursday and Sachin is interviewed on Saturday then Gayatri must be interviewed on Sunday since statement 5 says at least a one day gap is required between Mahima and Gayatri's interview. So, Abhinav will have to be interviewed on Tuesday. [Case 1]

Similarly, If Tanya is interviewed on Thursday and Sachin is interviewed on Sunday then Gayatri must be interviewed on Saturday since statement 5 says at least a one day gap is required between Mahima and Gayatri's interview. However, Gayatri is asked questions on Indian Bankruptcy Code (IBC) (from statement 6) while the person interviewed on Saturday is asked admin law (statement 1) so this case is not possible.

If Tanya is interviewed on Tuesday and Sachin on Sunday then Gayatri will have to be interviewed on Thursday since she is asked about IBC and not admin law.

From statement 4 we know that the ones wearing blazers must be on consecutive days apart from the weekend. Also, Digivijay does not wear a blazer (statement 1) so the ones wearing a blazer can either be on Monday and Tuesday or Thursday and Friday. From statement 3 we know that the ones carrying files are interviewed before Thursday, so on any two of the days among Monday, Tuesday and Wednesday. 

Even if one of the days is Wednesday, at least one person must carry a file on Monday and Tuesday. So, the ones wearing a blazer must be on Thursday and Friday.

In Case 1, upon placing the information we get the following:

However, as per statement 8, this is not possible. So, this case can be eliminated.

Similarly we can eliminate other cases. The only possible way, all the conditions are followed is:

Option D is correct.

In the North Direction Rahul has travelled (12 + 10 - 1)m = 21m.
In the East Direction Rahul has travelled (15+6-1) m = 20m.
By Pythagoras Theorem, total distance travelled => d
=> d = $$\sqrt{20^2+21^2}$$ = 29 m

If Rahul stops at E, he travels (12+10-1) = 21m in the North Direction
and he has travelled (15 + 6) = 21m in the East Direction.
Therefore, Rahul is currently in the North-East direction with respect to the initial position.
So, he should look in opposite , i.e. , South-West direction to see his initial position.

From B to E, we can see that Ram would be travelling in a straight line parallel to the line CD and the distance would be same as the length of CD. Therefore, the shortest distance between B and E would be 3 km. Hence, option C is correct

From Home to E, Ram has traveled 5 km in south direction
and Ram has traveled ( 3 + 3 ) km = 6 km in West direction.
The shortest distance would be => $$ \sqrt{ 6^2 + 5^2 } $$ km = $$ \sqrt{61} $$ km
Hence, option D is correct

The given situation can be represented through the following figure. Let S, C be the starting and current points of Neeraj.

Hence the distance from S to C can be obtained by using Pythagoras theorem.
SC = $$\sqrt{8^{2} + 1^{2}} = \sqrt{65}$$

An assumption that individual rights is disadvantageous does not lead to favouring community right does any without assessing whether community right does any good to them or not. Hence, a is not implicit. Choice b could be the worry of the forest department but not an assumption of the tribals based on which they turned down the offer. Choice c could be an assumption of the forest department but not of the tribals. Hence, c is not implicit. Choice d is not in the scope of the statement. It is given that the tribals have asked for community rights while individual rights are offered to them, which they have turned down. This indicates that the tribals are under the assumption that community right is more beneficial to them as compared to the individual rights. Hence, e is implicit. Choice e

A => Government has ordered for the relief fund for the people affected from the flood.

B => Since, cyclone hit the area and many people became homeless

C => Cyclone has been the possible cause of the disruption of telephone lines

D => Because of the cyclone, government orders to keep offices and schools closed

Hence, all of the options are correct. Therefore, option E should be selected.

It can be seen from the paragraph that only conclusion II follows. It is not clear how the population of developing countries will not increase in the future.

Gender of all the members of the family can be found out. We can make the following diagram to show relations:

We can see that P is the brother of N. L is the mother of P. So N is a daughter of L. Hence, L is the mother of N.
Hence option B is the correct option.

Arun is the son-in-law of Ramesh. Suresh is the son of Ramesh. Radha is the daughter of Suresh. Suresh is also the father of Priya. So, Priya is the granddaughter of Ramesh.

Thomas is the maternal uncle of Rishabh’s son. So, Rishabh’s wife is Thomas’s sister. This means that Rishabh is the brother-in-law of Thomas.

All mangoes are guavas and all guavas are grapes. Hence, all mangoes are also grapes. Thus, conclusion I logically follows from the given statement. Conclusion II does not follow from the given statements as all apples may not be sour. Thus, only conclusion I follows. Hence, option A is the correct answer.

Since dogs is a subset of tigers and no tiger is a lion, it follows that no dog is a lion. So, conclusion 1 is true. Also, since cats is a subset of tigers and no tiger is a lion, so it follows that no cat is a lion. So, conclusion 2 need not be true.

Therefore,

The coded word is formed by replacing each letter in the original word by a letter that is two places away from the original letter. So, A is replaced by C, B by D and so on. So, to get back the original word from the coded word, we have to replace each letter in the coded word by a letter that is 2 letters before it in the original alphabet. So, T is replaced by R, G is replaced by E and so on.
The answer is option c) REGITRATION

The code is formed by rearranging the letters of the original word in alphabetical order. So, the code for ‘SAURAV’ is ‘AARSUV’. Option c) is the correct answer.

C is replaced by B (the letter preceding it)
A is replaced by B (the letter succeeding it)
D is replaced by C (the letter preceding it)
A is replaced by B (the letter succeeding it)
V is replaced by U (the letter preceding it)
E is replaced by F (the letter succeeding it)
R is replaced by Q (the letter preceding it)

As we can see, vowels are replaced by the letter succeeding them and consonants are replaced by the letter preceding them in the alphabetical series.

To retrace a letter from a code, every letter in the code must not follow a vowel in the alphabetical series.

GYPSY will be coded as FXORX.
RHYTHM will be coded as QGXSGL.
CRYPT will be coded as BQXPS.
HYMN will be coded as GXLM.

Both RHYTHM and HYMN satisfy this condition. Therefore, option E is the right answer.

The logic based on which the code was written is as shown below.

Similarly the code for the word "VIDEO" would be “XGFCQ”

If A is reprensented as 1, B is represented as 2 and so on till Z is represented as 26, then the code is the number corresponding to each letter.
In BLUE, B represents 2, L represents 12, U represents 21 and E represents 5.

$$121 = 5^3 - 4$$
$$211 = 6^3 - 5$$
$$337 = 7^3 - 6$$
Therefore, $$505 = 8^3-7$$
Hence, the Option B is the answer

7*10 = 64 => 7 X 10 - 2(10-7) = 64
3*8 = 24 => 3 X 8 - 2(8-3) = 14
=> 11*12 = 11 X 12 - 2(12-11) = 132 - 2 = 130

All the letters are replaced by the letter that is 4 places ahead and then, the positions are reversed.
F + 4 = J, G + 4 = K, H + 4 = L, S + 4 = W.
Now, the order of the letters is reversed. Hence, the code for FGHS will be WLKJ.
For ASTV the code will be,
A + 4 = E, S + 4 = W, T + 4 = X, V + 4 = Z. Now, the order is reversed. The final code will be ZXWE.
Hence, option D is the correct answer.

Expression = GMW : EIOKUY : : FPT : ?

The pattern followed is that the preceding and next alphabets of each letter is written on the right side.

Eg : G-2=E; G+2 = I

M+2=O; M-2=K

W-2=U; W+2 = Y

Thus, GMW : EIOKUY

Similarly, 

=> FPT : DHRNRV

The triangle is rotating anti-clockwise and the arrow is attached to the top vertex pointing towards the base.
Hence, option D is the correct answer.

The pattern followed is as follows:
a + 1 = b
b+ 2 = d
d+ 3 = g
g + 4 = k
For the second letter,
F + 2 = h
h+ 2 = j
j + 2 = l
l + 2 = n

G is preceded by F in the alphabetical series. D is 2 places before F in the alphabetical series.
J is 3 places after G in the alphabetical series.

J is preceded by I in the alphabetical series. G is 2 places before I in the alphabetical series.
M is 3 places after J in the alphabetical series.

M is preceded by L in the alphabetical series. J is 2 places before L in the alphabetical series.

P is 3 places after M in the alphabetical series. Therefore, the following term must start with P.
P is preceded by O in the alphabetical series. M is 2 places before P in the alphabetical series. Therefore, the next term must be POM. Hence, option E is the right answer.

Each letter in the series is just the fifth letter to the right of the original letter in the alphabetic series.

NDIUDKAXIUZIUSDIUWPTEDSXJIDSPNXRDYM
Three D’s are neither immediately preceded by a consonant nor immediately followed by a vowel.
Hence, option c is the correct answer.

The course of action suggested in I might not be relevant since the issue is specific to certain parts of the city, and publishing such information widely without any addendums, such as a safety advisory or a travel restriction notice, would do little to help with our cause. III resolves this issue - we offer specific advice to people, asking them to stay indoors during the period, which should help avoid any casualties due to the expected waterlogging. Similarly, II directly address the issue of waterlogging. Therefore, both II and III are relevant courses of action. 

Let's analyze each of the statements in relation to the argument that we must follow the policy of peace and non-violence because Gandhiji used to practice it:

Statement I reinforces the argument by suggesting that the principle of non-violence is deeply rooted in our culture and religious beliefs, providing additional support for following this policy.

Statement II weakens the argument because it suggests that just because Gandhiji practised non-violence doesn't automatically make it the best course of action for everyone - it introduces the idea that political leaders' actions may not always be the best guidance for individual behaviour.

Statement III strengthens the argument by indicating that non-violence is not just a personal choice but a legal obligation as well; it implies that adhering to non-violence is not only a moral or cultural imperative but also a legal one.

Thus, Statements I and III strengthen the argument, while Statement II weakens it. Only Option A presents a correct representation.

Difficulty cannot be the reason for abandoning search for survivors because one’s life is invaluable. Had the houses been evacuated search operation would not have been initiated. Hence, b is not a possible reason. Since those who are trapped under mud cannot survive for more than two days there will not be any chance of finding survivors. Hence, c is a possible reason. Non recurrence of landslides cannot be the reason for stopping the present search operation. Hence, d is not a possible reason. When people cannot survive land slide the search operation would not have been initiated. Hence, e is not a possible reason. Thus c is a possible reason for abandoning the search operation. Choice c

Because using a single brand of soap for a long time leaves a residue on the skin, the advertisers are hoping that customers will not stick to a single brand for a long time and periodically use their brand. Option d) is the correct answer.

2016 is a leap year. So, an extra day should be added. So, the number of days to be added to Saturday is 5 + 1 = 6.
So, Jan 15th 2020 is a Friday. So, Jan 29th 2020 is a Friday and Jan 30th 2020 is a Saturday.

In a 12-hour period, the hour and minute hands will overlap 11 times. This is because, every time the minute hand catches up to the hour hand, it happens a bit later than the previous overlap. The first overlap occurs at exactly 12:00, and the subsequent overlaps occur roughly every 1 hour and 5 minutes, but not exactly at the hour mark each time. After 12 hours, the hands overlap 11 times.

Since the pattern repeats every 12 hours, the hands will overlap 11 more times in the second 12-hour period.

Thus, in a 24-hour period, the hour and minute hands overlap 22 times (11 times in the first 12 hours, and 11 more times in the second 12 hours).

Number of days between the birthdays of the two people = 2 + 31 + 30 +13 = 76. 76 days has 10 complete weeks and 6 odd days. Hence, Sumit’s birthday will lie on Friday + 6 = Thursday.

Let's check option A first to understand the series.
N is the 14th letter, Z is the 26th letter, A is the 1st letter and M is the 13th letter in the aphabetical series.
So, the position of the first letter 'N' from the beginning of the alphabetical series is equal to the position of the last letter 'M' from the end of the alphabetical series. Both are 14.
Similarly, the position of the second letter 'Z' from the first in the alphabetical series is equal to the position of the second last letter from the end of the alphabetical series. Both are 1.
Let's check if this holds true for the second option.
The position of the letter F is 6 and I is 9. The position of the letters R and U from the end of the alphabetical series is 9 and 6 respectively.
Hence, this logic holds true. The option that doesn't follow this logic is wrong.
In option D, E is 5th letter and V is 22nd letter. C and X are 24th and 3rd letters respectively from the end of the alphabetical series. Hence it is wrong.

In each of the options the third letter is the letter is n places away from the first letter where ‘n’ is the number which is given between the two letters. For example, G is third letter after D, T is seventh letter after M and so on. This rule is not followed in option D. As per the rule, it should be N5S. Thus, option D is the odd one out.

All the numbers except 225 are squares of prime numbers. Hence 225 is the odd one out. Thus option D is the correct answer.

The series is third_letter --> fourth_letter --> second_letter --> first_letter.
The third letter, fourth letter and the second letter are in a series while there is a gap of one letter between the first letter and the second letter.
This logic is not followed by option C as there is no gap of 1 letter between O and P.
Hence, C is the answer.

As we know that for making mirror image, We have to rotate entire figure from left to right. After rotation, We got the figure which is given in the option(b).
Hence, option b is the correct answer.

Let H and T be the sets of Hindu and Times of India readers. $$n(H \cup T)=100-6=94=n(H)+n(T)-n(H \cap T)=80+64-x$$. Hence $$x=50$$. $$n(H)=n(H \cap T')+ n(H \cap T)=y+50=64$$. Hence $$y=14.$$

Only Trump is 11
Only Abe is 8
and only Modi is 7
atleast two are invloved in the manufacture of 22 bombs.

So, the total bombs being manufactured = 11 + 8 + 7 + 22 = 48

So, the number of bombs being manufactured by all three together = 48/16 = 3

The number of bombs that Modi and Trump are manufacturing together without Abe is 6.
So, number of bombs that Modi and Abe are preparing without Trump = 20 - 7 - 3 -6 = 4

So, the number of bombs that Abe and Trump are manufacturing together without Modi = 48 - 11 - 8 - 7 - 4 - 6- 3 = 9

Let the number of people who read both the newspapers be x. So, the number of people who read the Hindu but not the Times of India is 28 - x and the number of people who read the Times of India but not the Hindu is 32 - x.
So, total number of people who read at least one newspaper = 28-x + x + 32-x = 60-x.
But, there is no information about the number of people in the locality. So, we cannot determine the value of x.
So, with the information that is available to us, we cannot determine the number of people who read the Time of India but not the Hindu.

We know that
n( A U B ) = n(A) + n( B ) - n (A ∩ B)
=> Here we know that 60 percent students have failed in English and 30 % failed in Hindi. Thus, for passed students we have
n( A U B ) = 60 + 30 - 20
=> n( A U B ) = 70
Hence, 70 % people failed in at least one subject.
Thus, 30 % must have passed in both the subjects.

Following is the correct order of words as found in dictionary-
mild, milieu, militant, military, mindless
Hence, option C is the right answer.

Enthuse

Enthusiastic

Enthusiasm

Enthrall

Enthralled

We need to look after the bold part as the bold part is common to all the words. 

use, usiastic, usiasm, rall, ralled

So, the arrangement would be rall, ralled, use, usiasm, usiastic

Hence, the arrangement would be 4, 5, 3, 2, 1

It is given that C and F are sitting opposite each other. So let’s first place C and F in opposite positions.
Now from statement 2 we know that E is to the immediate left of C.
From statement 1 we know that D and E are neighbours. This means that D must be sitting in between E and F.

Now we know that D is sitting to the immediate right of F.
Hence Option C.

I: The arrangement is either ECA or ACE. Thus, the question can’t be answered from this.
II: Either A is on right end or left end. Again the answer cannot be answered from this alone.
From I and II: Two arrangements are possible.
(i) ACE_ _
(ii) _ _ ECA
We can see that nothing can be said conclusively using even both the information together.

From statement 1, we only come to know about the maximum limit of the building
From statement 2, we can infer that the families might live on 1,3,5 or 2,4,6. The number of floors can be 5 or 6.
Hence the correct answer is option e.

The logic followed in the question is that in first step the smallest number is brought to the start and in next step the highest word is sent to the left end. This process is repeated in the same way.
So if
Input: 65 monkey zoo 23 lion 61

Step 1 : 23 65 monkey zoo lion 61
Step 2 : 23 65 monkey lion 61 zoo
Step 3 : 23 61 65 monkey lion zoo
Step 4 : 23 61 65 lion monkey zoo

Hence option B is the correct choice.

Input: visitor 39 75 bravery 24 boldly cleverly 14
Step 1 : 14 visitor 39 75 bravery 24 boldly cleverly
Step 2 : 14 39 75 bravery 24 boldly cleverly visitor
Step 3 : 14 24 39 75 bravery boldly cleverly visitor
Hence option D is the correct option.

Assertion A: Electric vehicles (EVs) are indeed being promoted globally as a more sustainable alternative to traditional gasoline-powered vehicles. This is in line with growing environmental concerns.

Reason R: The widespread adoption of EVs reduces greenhouse gas emissions since they produce zero tailpipe emissions, and it decreases the reliance on fossil fuels, which are a major source of pollution.

Hence, both Assertion A and Reason R are true, and Reason R correctly explains Assertion A.

Answer: (A)

Assertion (A) is true: A balanced diet is no doubt necessary for maintaining overall health, as it makes sure the body gets all the nutrients required for proper functioning.

Reason (R) is true: A balanced diet does provide important nutrients like carbohydrates, proteins, fats, vitamins, and minerals to the body.

R correct explains that a balanced diet has all the nutrients which are necessary for the body to stay healthy. 

The arrows in the figure rotate anti clock wise by 90 from quadrant 1 to 4.
So, (?) must have the arrow facing South-East Direction.
Thus, only option A and C are possible.
Now, the first quadrant has 1 dark bar, second has 2, and third has 3. Thus, fourth must have 4 bars.
Among A and C, only C has 4 dark bars. Thus, C is the correct answer.

The alphabets are rotating one step in the clockwise direction in every step. Hence the correct answer is (a) or (b).

In every two steps, the alphabets also move in the anticlockwise direction. So, (b) is the correct answer as the alphabets move in the anticlockwise direction after 2 steps.

The square moves one and a half side of the box (in the counterclockwise direction) from the first diagram to second. Then it moves one side from second to third diagram. Then it moves one and a half side again and so on. The letter T turns in the clockwise direction by 135 degrees from first diagram to second. Then it turns 90 degrees from second diagram to third. Then it turns 135 degrees again and so on.

In figures 1-2, the element at the center and at the bottom right interchange their position and the elements in the first column interchange their positions.
In figures 2-3, the elements in the top row interchange their positions. Same happens with the elements of the bottom row.
This process is continued throughout.

Two patterns are alternatively followed by the given figures,

Pattern 1:The elements in the upper triangle (P,Q,R in figure 1) or the ones in lower triangle(P,N,3 in figure 3) are shifted diagonally. The elements in the diagonal are shifted by 1 position with the elements moving in the North-West direction.

Pattern 2: The middle element is replaced by a new element.

For the formation of figure 6, pattern 1 is to be applied on figure 5. The figure thus formed is option B.

Taking the mirror image of the given image place the mirror below the image. 

The pair of images given in option E satisfies the condition of mirror image and hence option E is the answer.

Rotating the figure by $$90^{\circ\ }$$ in clockwise direction. Option D follows the same analogy.

The star is in the right most position so in the mirror image the star will be in the left most position. So, option A and D can be eliminated. 

Out of the remaining two the correct mirror image of the given picture must be -

Hence, option C is the right choice.

Correct answer is Option D

Here, first we have the following triangles:

So, 12 triangles.

So, 6 triangles:

2 triangles:

Hence, the figure has 12 + 6 + 2 = 20 triangles

Last symbol is shifted to first position not changing the positions of remaining symbols. Following the same sequence, we will get option C.

We can see that the square frame, along with the four figures in the corners is getting rotated by 90 degrees in the clockwise direction in each subsequent step. Therefore, only options A and C are logical continuations.
In the first figure, triangle ( 3 sided figure) is included in the centre.
In the second figure, square (4 sided figure) is included in the centre.
Therefore, in the answer, a hexagon (6 sided figure) must be included in the centre. Therefore, option C is the right answer.

We can see that in each upcoming diagram we are erasing one square without changing position of the remaining squares. Hence in next figure only 1 square will be left either in north or south part of the rectangle. Hence Option E is the right choice.

When the given box would be folded, Opposite face sets would be (1) Star and Arrow ,(2) Dot and Square ,(3) Triangle and Circle

(B) Dot and Star would be on adjacent faces

(C) Circle and Arrow would be on adjacent faces

(D) Triangle and Dot would be on adjacent face

Hence, Option A is the Correct answer

For the images represented in options A, B, D, E the second figure inside the square is generated when the first figure is rotated by 90 degrees in the clockwise direction. The same is not true for option C.

All other options other than option D have their digits adding up to 15. 

In D, we have the question figure which is shown in red colour in the figure below -  

Hence, option D is the right choice.

We have,
7 % 6 h $ & 2 d s ) ! 8 # 5 p a 3 * c ? 1 b \ e
% 6 and h are three consecutive characters with the last character ‘h’ in between the other 2.
Next character ‘&’ is two places to the right of ‘h’. Further same logic continues.
)8! Are consecutive character and ‘5’ comes two places to the right of ‘8’. Thus, ‘5’ must be next in the given sequence.
Hence, option A is the correct choice.

In the word " SEMBLANCE " the pairs having as many letters between the words as they have in the English alphabet series are :

AE - 3 letters.

LN - 1 letter.

AC - 1 letter.

A total of 3 possible pairs.

The letters that can be used are: " P, E, N, T, O ".

The possible words that can be formed include:  " PEN ", " PET ", " NET ", " PENT ", " TEN ", " OPEN ", " PEON ",  " POET ", " NOTE ",....

When the alphabets of the word RECOGNITION are arranged from left to right in an orderly fashion :

The order is given by :  CEGIINNOORT.

The alphabet with index value 4 = O.

The alphabet with index value 7 = I.

The number of alphabets in between is: 5

Hence option E is the answer.

In the word MODULAR the possible pairs of letters that satisfy the condition that each of which has as many letters between them in the word as they have in between English alphabetical series :

The possible pairs of letters are :

" O - L ".

" A - D ".

" R - U ". 

The possible words which can be generated using the words :

"B", "U", "R", "T", "E".

BUT,  TUBE, BRUTE, RUT,  TRUE, TUB, BET, RUB .....................

Hence the answer is greater than six.

Tank filled in an hour when all of them are working simultaneously = 1/3 + 1/6 - 1/9 = 7/18
Hence time taken to fill up the tank = 18/7 h

Let the volume of the tank = V
Let the efficiency of the tap A = V/A = V/6
And efficiency of the tap B = V/B = V/8
Efficiency of tap C to empty the tank = V/C = V/12
Let T be the total time taken by the system to fill the tank.
T*(V/6 + V/8 - V/ 12) = V
==> T = 24/5 = 4.8 hours.
So the correct option to choose is B - 4.8 hours.

Let the total work be 200 units.
A’s rate of work = 200 units/10 days = 20 units per day
B’s rate of work = 200 units/20 days = 10 units per day
So, work done by A and B together in 4 days = (20+10)*4 = 120 units
Work left = 200 - 120 = 80 units
Time taken by B to complete the remaining work = 80 units/10 units per day = 8 days

Let the distance between A and B be D.

Time taken = D/58 + D/52 = 110*D/(58*52)

So, average speed for the whole journey = 2D/Time = 58*52*2D/110D = 54.8363636 kmph = 55kmph approximately

Average speed = (Total Distance travelled)/(Total time taken)
= (100+200)/(100/25 + 200/40) = 300/(4+5) = 100/3 = 33.33km/hr

Relative speed of train A with respect to B = 5 km/h
Distance to be covered = 200 km
Time taken = $$\frac{200}{5}$$ = 40 h

Let the speed of the first train be v m/s
Then
400/10 = v
=> v = 40 m/s
Now the speed of the second train = 72 km/hr = 20 m/s
Since both the trains are running in the same direction, the relative speed between the two trains is 40 - 20 = 20 m/s
Distance to be covered = 400 + 300 = 700m
Hence the required time = 700/20 = 35 seconds.

The average = 24. So, the numbers are 24 - 3, 24 - 1, 24 + 1 and 24 + 3.
ie. 21, 23, 25, 27
So, the sum of squares = $$21^2 + 27^2 = 441+729 = 1170$$
Hence, the average is $$1170/2 = 585$$

Let the number of students in the two sections be 3k and 4k.
Total weight of the class = 3k * 40 + 4k * 42 = 120k + 168k = 288k
So, average weight of the class = 288k/(3k + 4k) = 288/7 = 41.14 kg

Average monthly investment made by Ram = $$\dfrac{60000*6 + 20000*6}{12}$$ = Rs. 40000
Average monthly investment made by Shyam = Rs. 40000
Hence Ram’s share = $$\dfrac{40000}{40000+40000}\times 6000$$ = Rs. 3000
Therefore, we can say that option E is the correct answer.

Let 9 litres of the first solution be mixed with 18 litres of the second solution.
Therefore, total volume of the solution = (9 + 18) litres = 27 litres
Quantity of alcohol in the first solution = $$\dfrac{7}{9} * 9$$ litres = 7 litres
Quantity of alcohol in the second solution = $$\dfrac{5}{6} * 18$$ litres = 15 litres
Total quantity of alcohol = (7 + 15) litres = 22 litres
% of milk = $$\dfrac{22}{27} * 100\% = 81.48\%$$
Hence, option E is the correct answer.

Let the initial volume of the solution be 5V out of which milk is 4V and water is V.
After adding 40 ml water the ratio becomes 2:1. So we get,
$$\frac{4V}{V+40}=\frac{2}{1}$$
$$=>V=40$$ ml
So the volume of the solution now = 5V+40 = 5*40+40 = 240 ml
Hence Option C.

The Marked Price of apples per kg = 72/.8 = Rs 90
The Cost price of apples per kg = 90/1.5 = Rs 60

SP of 20 apples - CP of 20 apples = CP of 4 apples
SP of 20 apples = CP of 24 apples
SP of 1 apple/CP of 1 apple = 24/20 = 1.2
Profit % = (1.2-1)*100 = 20%

The discount is calculated on the the marked price always. So, the selling price is 145 - 145 * 25% = Rs. 108.75

As we know that selling price of the product is Rs. 1200
Let’s say cost price of the product is x
Now after making a profit of 30%, selling price will be = $$x \times 1.3$$ = 1.3x
So 1.3x = 1200
x= $$\frac{1200}{1.3}$$ = 923

Let the cost price be c.
The marked price of the article will be 1.3c
If a discount of 10% is offered the selling price will be 1.3c * (0.8) = 1.04c

Profit = 0.04c = 60
C = 1500
Hence, the cost price is Rs. 1500

Let the rate of interest = r
==> 36(1+2r/100) = 48.24
==> r = 17%
63 rupees after three years = 63(1+3r/100) = 95.13 rupees.
So, the correct option to choose is B.

Interest at simple interest = P X r X t/100 = (50000 X 20 X 3)/100 = Rs 30000
Interest at compound interest = $$P[(1+\frac{r}{100})^n - 1] = 50000[(1.2)^3 - 1] = 36400$$
So, the difference is Rs 6400.

We should try it by putting up the values given in the option.
As putting up duration = 2 years, Simple Interest = 5000*10*2/100 = 1000
And compound interest will be = 5000(110/100)(110/100) = 1050
Hence answer will be b

Let the amount borrowed by Arjun be x.
SI = $$\frac{PRT}{100}$$
Given,
$$\frac{9*x*3}{100} + \frac{6*x*2}{100}+\frac{14*x*4}{100} = 2180$$
$$\frac{95*x}{100} = 2280$$
x = 2400
Option C

By applying the formula of alligation we get,
20 50
\ /
40
/ \
10 20

Thus the solutions A and B must be mixed in the ratio 10:20 = 1:2.

Number of chocolates each boy gets = 0.2*25 = 5
==> Total number of chocolates distributed among boys = 5*15 = 75
Number of chocolates each girl gets = 0.15*(15+25) = 6
==> total number of chocolates distributed among girls = 6*25 = 150
==> Total number of chocolates distributed in the class = 150+75 = 225

Let the maximum marks be x.
32% of x = 360-88
8/25 of x = 272
x = 850

Let x be the positive number
Given, x - 13 = 48$$\times\frac{1}{x}$$
$$x^2 -13x -48 = 0$$
Thus, (x - 16)(x + 3) = 0
=> x = 16 and x = -3
Since, x is positive , x = 16

$$x^{2} - 15x +26 = 0$$
$$(x-2)(x-13)=0$$
X = 2 or 13

$$y^{2} + 9y - 22= 0$$
$$(y+11)(y-2) = 0$$
Y= 2 or -11

Therefore, x is greater than or equal to y. option A.

Let the breadth of the rectangle be ‘x’. So its length would be 2x.
Thus the area of the rectangle would be $$2x^{2}$$
Now the new length would be 2.4x and new breadth would be .6x
Hence the new area would be $$2.4x*.6x = 1.44x^{2}$$.
Hence we can see that the area has got reduced.
Percentage reduction = $$\frac{56}{200}*100 = 28\%$$
Hence the correct answer is option D.

Let the base and height be b and h respectively. Hence, the original area is = 1/2*b*h. After changing the base and height, area= 1/2 * (0.9b) * (1.1h) = 0.99 (1/2*b*h) = 198 sq-cm
Hence, (1/2*b*h) = 198/0.99 = 200 sq-cm

Given, the diagonal is 13x and the side is 5x.

Let the other side be b.

$$(13x)^2 = (5x)^2 + b^2$$
b = 12x

68 = 2 (12x + 5x)
x = 2m

Hence, the sides are 10m and 24m

Area = 240 sq. m

Volume of the initial sphere = $$\frac{4}{3}*\pi *r^3$$ = $$\frac{4}{3}*\pi *6^3$$
Volume of each of the smaller spheres = $$\frac{4}{3}*\pi *r^3$$
==> 3*$$\frac{4}{3}*\pi *r^3$$ = $$\frac{4}{3}*\pi *6^3$$ ==> $$r^3 = 6^3/3$$ ==> $$r^3 = 72$$ ==> $$r = 2*\sqrt[3]{9}$$
So the correct option to choose is E.

The area of square = 10*10 = 100$$cm^2$$
Now the side of the square is equal to the diameter of the square.
Hence the diameter of the circle is 10cm
So the radius of the circle will be 5 cm.
Hence the area of the circle = $$\pi*r^2$$ = $$\pi*5^2$$ = 78.5$$cm^2$$
Thus, the remaining area = 100 - 78.5 = 21.5 $$cm^2$$

1321 = 29 x 45 + 16
Since 16 is the remainder when 29 divides 1321, 29-16 = 13 should be added to 1321 to make it divisible by 29.

$$10800 = 2^4 * 5^2 * 3^3$$

Number of divisors = (4+1) (2+1) (3 + 1) = 60

Quotient when 800 is divided by 24 is 33.
There are 33 numbers up to 800 divisible by 24

Unit digit in 476 x 198 x 359 x 242

= unit digit in 6 x 8 x 9 x 2 = 4

LCM of the fractions = (LCM of the numerator/ HCF of the denominator)
LCM of 3, 4 and 2 = 3*4 = 12
HCF of 7, 3, 9 = 1
Therefore, LCM of the given fractions = 12/1 = 12.

Let the required number be x.
When numbers 595, 853 and 486 is divided by x remainders are 3, 2 and 5 respectively.
So 595 - 3 = 592, 853 - 2 = 851 and 486 - 5 = 481 must be divisible by x
Greatest value of ‘x’ = HCF(592, 851, 481) = 37
Hence, option D is the right answer.

P will be in the form of LCM of n(4,5,6,8)+3
LCM of 4,5,6 and 8 is 120
Therefore required number is 120+3=123
When 123 is divided by 9 remainder is 6

Let the first term be "a" and the common difference of the AP be "d".

So, 14th terms of AP will be a+13d.

a+13d = 202 ----equation (1)

19th term of AP will be a+18d.

a+18d = 277    --------equation (2)

solving both equations, we get a = 7 and d = 15

Therefore, first term = 7

8th term = a+7d = 7+7*15 = 112

So, ratio = 7:112 = 1:16

Given that the first term of GP is 16 and sum till infinity is 24

So, $$S_∞=\dfrac{a}{1-r}$$, where $$a$$ is the first term and $$r$$ is the common ratio.

$$S_∞=\dfrac{16}{1-r}=48$$

$$1-r=\dfrac{16}{48}=\dfrac{1}{3}$$

or, $$r=\dfrac{2}{3}$$

Now, we have to find sum till infinity of another GP whose first term is 76 and common ratio is $$r_1=\left(r-\dfrac{1}{6}\right)=\dfrac{2}{3}-\dfrac{1}{6}=\dfrac{1}{2}$$

$$S_∞=\dfrac{76}{1-\dfrac{1}{2}}$$

$$S_∞=152$$

Hence, the answer is 152

The probability that the first ball is not yellow is $$\frac{7}{12}$$
The probability that the second ball is not yellow is $$\frac{6}{11}$$
Hence, the total probability is $$\frac{7}{12}*\frac{6}{11}=\frac{7}{22}$$

Number of favourable cases = 6
Total number of cases = 6*6 = 36
So, probability = 1/6

Total number of letters = 6 of which 3 are the same.

Therefore, number of ways of arranging = $$\frac{6!}{3!}$$ = $$\frac{720}{6}$$ = 120

MIRACLE contains I,A,E as vowels apart from M, R, C, L as consonants. Group I, A, E as one unit.
Total number of ways = 5!
Now I, A, E can be arranged in 3! ways.
Total number of ways = 5!*3! = 120*6 = 720 ways

If it is known that x, y and z are distinct natural numbers then what is the value of 16x+4y+8z? 
Statement I: 3x+y+2z = 22
Statement II: 14x+3y+6z = 96

In statement I, it is given that 3x+y+2z = 22. There are multiple triplets of x, y and z for which this statement is true. Hence, we can uniquely determine the value of 16x+4y+8z.
In statement I, it is given that 14x+3y+6z = 92. There are multiple triplets of x, y and z for which this statement is true. Hence, we can uniquely determine the value of 16x+4y+8z.
By using statement (1)  and (2) : 

3x+y+2z = 22 ... (1)
14x+3y+6z = 92 ... (2)

By substituting (2) - 3*(1), we get

14x+3y+6z - 3*(3x+y+2z) = 96 - 3*22
5x = 30 => x = 6. Also, y + 2z = 4.
We are given that both y and z are distinct natural number. Hence, we can say that y = 2 and z = 1. Now that we have unique value of x, y and z, we can find out the value of 16x+4y+8z. Hence, we can say that this question can be answered using both the statements together. Therfore, option C is the correct answer. 

Using statement 1,
x is divisible by 13 but we cannot say whether it is divisible by 13*7 or not.
Using statement 2,
We can say that x is divisible by 7.
Using both the statements, we can say that x is divisible by 13*7 = 91.
Hence the answer is d.

The total number of people with protein deficiency = 40 + 30 + 80 + 55 + 70 = 275
So, the average = 275 / 5 = 55

Patients with vitamin deficieny fell only in 2001 and 2002. % fall from 2001 to 2002 = 100* (50 - 60)/60 = 16.67% fall
%fall from 2002 to 2003 = 100 * (15 - 50)/50 = 70% fall