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If the letters of the word `MATHS` are rearranged to form 5 letter words such that none of the words repeat and the results are arranged in ascending order as in a dictionary, then what is the rank of the word `MATHS'?

In each question below, a sentence with four underlined words is given. These are numbered as (1), (2), (3) and (4). One of these four words may be either wrongly spelt or inappropriate in the context of the sentence. Find out the word which is wrongly spelt or inappropriate, if any.

We must feal (1) / love for all, no matter (2) / whether (3) / they are of our own family or strangers or whether they are rich or poor. (4) / All correct (5)

The remainder obtained when $(1^1+2^2+3^3+4^4+5^5+\dots {10}^{10})$ is divided by 4 is

In a simultaneous toss of n coins, find the probability that no head occurs.

S consists of a set of numbers from -50 to 50 (zero inclusive), we have to pick a set K such that K consists of {A, B, C} such that the sum of numbers in set K is equal to zero. How many such sets are possible?

The shares sold by company D in Chennai is what percent less than the shares sold by company C in the same city? Round off your answer to two digits after the decimal.

The ring $M_1$ and block $M_2$ are held in the position shown in figure. Now the system is released. If $M_1$ $>$ $M_2$ find when the ring $M_1$ has descended along the smooth fixed vertical rod by the distance $y$.

In groups of five, discuss what you enjoy doing alone and what you like doing in a group.

Now prepare a list as shown below.

Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs.1000 as remuneration. If this amount is shared by them in proportion to their work, then Kamal's share, in rupees, is

Question 85(i)

If principal = Rs. 100000, rate if interest = 10 $\%$ compounded half - yearly.

Find Interest for 6 months.

Let ABCD be a square of a side length l, Let P, Q, R, S be points in the interiors of the sides AD, BC, AB, CD, respectively, such that PQ and RS intersect at right angles. If PQ = $\frac{3\sqrt{3}}{4}$, then RS equals

$\text{If a = 1.8, b = 1.9 and c = - 3.7,}\text{then the value of}{a}^3+b^3+c^3=$

The given shape ABCD shown below has to be dilated about Vertex A by a shape factor of $\frac{3}{2}$, so the correct obtained image will be?

In ABC, produce a line from B to AC, meeting at D, and from C to AB, meeting at E. Let BD and CE meet at X.Let $\Delta$ BXE have area a, $\Delta$ BXC have area b, and $\Delta$ CXD have area c. Find the area of quadrilateral AEXD in terms of a, b, and c.

Which of the following statements is necessarily true?

How many times the total number of students in all the three schools A, B and C together was exactly equal among the given years?

Seven villages A, B, C, D E, F and G are situated as follows:

E is 2 km to the west of B

F is 2 km to the north of A

C is 1 km to the west of A

D is 2 km to the south of G

G is 2 km to the east of C

D is exactly in the middle of B and E.

Q69. How far is E and F (in km) as crow flies?

Q97. Consider the following pairs: Union Territory

High Court Jurisdiction

1. Lakshadweep : Kerala HC

2. Daman & Diu : Gujarat HC

3. Puducherry : Madras HC

4. Andaman & Nicobar Islands : Calcutta HC

5. Dadra & Nagar Haveli : Gujarat HC

Which of the pairs given above is/are correctly matched?

If the processes can take place simultaneously, what is the minimum time (In hours) required to get one unit of the final product?
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A positive integer is called "Panache” if it can be written as a sum of distinct positive powers of 4, and "Elan" if it can be written as a sum of distinct positive powers of 6. From the given number, which of the following can we write as a sum of a "Panache” number and an "Elan" number?

P, Q and R enter into a business. P put Rs. 2000 for 6 months, Q puts Rs. 2400 for 8 months and R puts Rs. 2800 for 10 months. After one year their gain was Rs. 1332. Find out the share of P.

Consider the non-decreasing sequence of positive integers:

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5.... in which $n^{th}$ positive number appears n times. Find the remainder when the 2000th term is divided by 4.

Which of the following is a valid max heap?

Find the sum to n terms of the series $\frac{3}{1^2\times 2^2}+\frac{5}{2^2\times 3^3}+\frac{7}{3^2\times 4^2}......$ is

The sum of the first 100 odd numbers is divisible by:

Q89. Consider the following Statements regarding National Flag:

1. The ratio of the length to the height (width) of the Flag shall be 1:1

2. The design of the National Flag was adopted by the Constituent Assembly of India before independence.

3. It was designed by Pingali Venkayya.

Which of the above statement(s) is/are correct?

On a certain assembly line, the rejection rate for Monday's production was $4\%$, for Tuesday it was $8\%$ and for the two days combined $7\%$. What was the ratio of Tuesday's production to Monday's production?

What is Samarth's rank from the top in the class of 40 students?

I. Samarth's rank is 10 rank below Nisha who is 35th from the ending.

II. Samarth's rank is 10 rank above Satwik who is 24th from the beginning.

Let $A,B\text{and}C$ be three events, which are pair-wise independent and $\overline{E}$ denotes the complement of an event $E$. If $P(A\cap B\cap C)=0$, then $P\left[\right(\overline{A}\cap \overline{B}\left)|C\right]$ is equal to: