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

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

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 ______.

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 ______.

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 ______.

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?

There are ten boys B₁, B₂, ...., B₁₀ and five girls G₁, G₂, ...., G₅ in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B₁ and B₂ together should not be the members of a group is ______.

The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike is ______.

Locus of centroid of the triangle whose vertices are (a cos t, a sin t),(b sin t, – b cos t) and (1, 0), where t is a parameter is ______.

If a variable line drawn through the intersection of the lines `x/3 + y/4` = 1 and `x/4 + y/3` = 1, meets the coordinate axes at A and B, (A ≠ B), then the locus of the midpoint of AB is ______.

For the curve C: (x² + y² – 3) + (x² – y² – 1)⁵ = 0, the value of 3y' – y³ y", at the point (α, α), α < 0, on C, is equal to ______.