JEE Main entrance exam Question Bank Solutions

The locus of a point, which moves such that the sum of squares of its distances from the points (0, 0), (1, 0), (0, 1), (1, 1) is 18 units, is a circle of diameter d. Then d² is equal to ______.

Let O(0, 0) and A(0, 1) be two fixed points. Then the locus of a point P such that the perimeter of ΔAOP is 4, is ______.

All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is ______.

The sum of the series 2.²⁰C₀ + 5.²⁰C₁ + 8.²⁰C₂ + 11.²⁰C₃ + .... + 62.²⁰C₂₀ is equal to ______.

If D, E, F are the mid points of the sides BC, CA and AB respectively of a triangle ABC and 'O' is any point, then, `|vec(AD) + vec(BE) + vec(CF)|`, is ______.

The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.

Number of values of x where the function

f(x) = `{{:((tanxlog(x - 2))/(x^2 - 4x + 3); x∈(2, 4) - {3, π}),(1/6tanx; x = 3","  π):}`

is discontinuous, is ______.

If θ = `sin^-1((2x)/(1 + x^2)) + cos^-1((1 - x^2)/(1 + x^2))`, for `x ≥ 3/2` then the absolute value of `((cosθ + tanθ + 4)/secθ)` is ______.

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 ______.