JEE Main entrance exam Question Bank Solutions for Mathematics (JEE Main)

If number of arrangements of letters of the word "DHARAMSHALA" taken all at a time so that no two alike letters appear together is (4^a.5^b.6^c.7^d), (where a, b, c, d ∈ N), then a + b + c + d is equal to ______.

If `""^mC_3 + ""^mC_4 > ""^(m+1)C_3`, then least value of m is ______.

Consider f(x) = sin^–1[2x] + cos^–1([x] – 1) (where [.] denotes greatest integer function.) If domain of f(x) is [a, b) and the range of f(x) is {c, d} then `a + b + (2d)/c` is equal to ______. (where c < d) 

If sum of the coefficient of second and fourth terms in the expansion of `(2x - 1/(3x^2))^5`, in descending powers of x, is S, Then the value `|81/40"S"|` of is ______.

Unit vector perpendicular to the plane of the triangle ABC with position vectors `veca, vecb, vecc` of the vertices A, B, C is ______.

Let x = sin^–1(sin8) + cos^–1(cos11) + tan^–1(tan7), and x = k(π – 2.4) for an integer k, then the value of k is ______.

Number of selections of at least one letter from the letters of MATHEMATICS, is ______.

A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be ______.

There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are with numbers in ascending or descending order is equal to ______.

Number of values of x satisfying the system of equations `sin^-1sqrt(2 + e^(-2x) - 2e^-x) + sec^-1sqrt(1 - x^2 + x^4) = π/2` and `5^(1+tan^-1x)` = 4 + [cos^–1x] is ______ (where [.] denotes greatest integer function)

There are (n + 1) white and (n + 1) black balls each set numbered 1 to (n + 1). The number of ways in which the balls can be arranged in row so that the adjacent balls are of different colours is ______.

If Q(x) is the quotient when P(x) = 1111x¹¹¹¹ – 111x¹¹¹ + 11x¹¹ – 1011 is divided by x – 1, then sum of the digits in the sum of coefficients of Q(x) is ______.

There are 12 persons seated in a line. Number of ways in which 3 persons can be selected such that atleast two of them are consecutive, is ______.

cos^–1(cos10) is equal to ______.

The no. of different ways, the letters of the word KUMARI can be placed in the 8 boxes of the given figure so that no row remains empty will be ______.

If f(x) = `{{:(1 if x  "is rational"),(-1 if x  "is rational"):}` is continuous on ______.

Let S(K) = 1 + 3 + 5 ... + (2K – 1) = 3 + K². Then which of the following is true?

If a_n = `sqrt(7 + sqrt(7  + sqrt(7 + ......)` having n radical signs then by methods of mathematical induction which is true?

Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.

The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4, (repetition of digits is not allowed) and are multiple of 3 is?