The mean proportional between 24and 54 is:

2𝑛 + 2𝑛 − 1 / 2𝑛+1 − 2𝑛

The sum of the squares of two consecutive positive integers exceeds their product by 91. Find the integers?

If the ratio of two numbers is 7: 11. If 7 is added to each number, then the new
ratio will be 2: 3 then the number are.

An examination paper consists of 12 questions divided into parts A and B Part A contains 7 questions and part B contains 5 questions. A candidate is required to attempt 8 questions selecting at least 3 from each part. In how many maximum ways can the candidate select the question? 

Code word is to consist of two English alphabets followed by two distinct numbers between 1 and 9. How many such code words are there? 

The common difference of an A.P. is 3 and the 15th term is 37. Find the first term.

Geometric mean G between two numbers a and b id

If A and G are arithmetic and geometric mean respectively between two positive numbers a and b, then A (AM) < G (GM) is correct?

Find the sum of the AP: 11, 17, 23, and 29… of first 10 terms.

Find the G. M. between 𝟑/2 and 𝟐𝟕/2

If 4, 36, 324 are in G.P. insert two more numbers in this progression so that it again forms a G.P.

The distance travelled (in cm) by a simple pendulum in consecutive seconds are 16, 12,

9,…. How much distance will it travel before coming to rest?

Which term of the G.P.: 5, -10, 20, -40,… is 320?

The sum of infinity of the progression 9-3+1- 𝟏/3+ … is

The product (32) (32)1/6(32)1/36 …..To∞ is.

Obtain the sum of all positive integers up to 1000, which are divisible by 5 and not divisible by 2.

m men and n women are to be seated in a row so that no two women sit together. If m>n, them then the number of ways in which can be seated is

The number of times the digit 3 will be written when listing the integers from 1 to 1000 is:

Ten persons, amongst whom are A, B, and c to speak at a function. The number of ways in which it can be done. If A wants to speak before B and B wants to speak before C is 

How many words can be made out from the letters of the word INDEPENDENCE, in which vowels always come together?

The exponent of 3 in 100! Is

If A has 4 elements B has 8 elements, then the minimum and maximum number of
elements in A Ս B are respectively

The number of triangle that can be formed by choosing the vertices from a set of 12 points, seven of which lie on the same straight line, is:

A bag contains 4 red, 3 black, and 2 white balls. In how many ways 3 balls can be drawn from his bag so that they include at least one black ball?

At a certain conference of 100 people there are 29 Indians women and 23 Indian men,
out of these Indian people 4 are doctors and 24 are either men or doctor. There are no
foreign doctors. The numbers of women doctors attending the conference is:

The relation ‘’Is parallel to ‘’ over the set of straight line in a given plane is:

Let N be the set of all natural numbers; E be the set of all even natural numbers then the
function
F: N = E defined as f(x) = 2x – VxEN is =

Let F. R → R be defined by

The value of f(-1) + f(2) + f(4) is

In how many different ways, can the letters of the word ‘DETAIL’ be arranged in such a way that the vowels occupy only the odd numbered position?

A business house wishes to simultaneously elevate two of its six branch heads. In how many ways these elevations can take place? 

Let A = R – {3} and B = R – {1}. Let f A→B defined by f (x) = 𝐱−𝟐 / 𝐱−𝟑 what is value of 𝐟−𝟏 (𝟏 / 𝟐)?

If f (x) = x2 -1 and g (x) = |2x + 3|, then fog (3) – gof (-3) =

Out of group of 20 teachers in a school, 10 teach mathematics, 9 teach Physics and 7 teach
Chemistry. 4 teach Mathematics and Physics but none teach both mathematics and
chemistry. How many teach chemistry and Physics; how many teach only Physics?

If a related to b if and only if the difference in a and b is an even integer. This relation is

f (x) = {(2, 2) ; (3, 3) ; (4, 4) ; (5, 5) ; (6, 6)} be a relation of set A = {2,3,4,5,6}
It is a:

If f(y) = 𝒚−𝟏 / 𝒚 , find f 1 (x)

Two finite sets have x and y number of elements. The total number of subsets of first is 56
more than the total number of subsets of second. The value of x and y is:

Eight guests have to be seated 4 on each side of a long rectangular table. 2 particular guests desire to sit on one side of the table and 3 on the other side. The number of ways in which the sitting arrangements can be made is:

Let x = at3, y= 𝒂÷𝒕𝟐. Then 𝒅𝒚÷𝒅𝒙 =

If the cost of function of a commodity is given by C = 150x-5x2+ 𝒙𝟑 ÷ 𝟔, where C stands for cost and x stands for output. If the average cost is equal to the marginal cost then the output x = _______ 

Differentiate x^x w.r.t x. 

The value of ∫^𝟐_−𝟐 𝐟(𝐱) dx, where f(x) = 1+1, x ≤ 0; f(x) = 1-2x, x ≥ 0 is

The cost of producing x units is 500-20x2 + x3 / 3. The marginal cost is minimum at x = _______.

If y- 𝒙 4÷𝒆 𝒙 𝒕𝒉𝒆𝒏 𝒅𝒚÷𝒅𝒙 is equal to:

The speed of a train at a distance x (from the starting point) is given by 3x2-5x+4. What is the rate of change (of distance) at x=1?