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

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 ______.

`cot^-1(sqrt(cos α)) - tan^-1 (sqrt(cos α))` = x, then sin x = ______.

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 ______.

The differential equation representing the family of ellipse having foci either on the x-axis or on the y-axis centre at the origin and passing through the point (0, 3) is ______.

If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is ______.

The sides of a triangle are 3x + 4y, 4x + 3y and 5x + 5y where x, y > 0 then the triangle is ______.

Let Δ ∈ {∧, ∨, ⇒, ⇔}be such that (p ∧ q)Δ((p ∨ q) ⇒ q) is a tautology. Then Δ is equal to ______.

`50tan(3tan^-1(1/2) + 2cos^-1(1/sqrt(5))) + 4sqrt(2) tan(1/2tan^-1(2sqrt(2)))` is equal to ______.

Let P₁: `vecr.(2hati + hatj - 3hatk)` = 4 be a plane. Let P₂ be another plane which passes through the points (2, –3, 2), (2, –2, –3) and (1, –4, 2). If the direction ratios of the line of intersection of P₁ and P₂ be 16, α, β, then the value of α + β is equal to ______.

Negation of the Boolean statement (p ∨ q) ⇒ ((∼r) ∨ p) is equivalent to ______.

Let 3, 6, 9, 12 ....... upto 78 terms and 5, 9, 13, 17 ...... upto 59 be two series. Then, the sum of the terms common to both the series is equal to ______.

The statement among the following that is a tautology is ______.

Which of the following Boolean expression is a tautology?

The curve passing through (0, 1) and satisfying `sin(dy/dx) = 1/2` is ______.

If the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8^th terms is ______.

The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is ______.

If n AM's are inserted between 1 and 31 and ratio of 7^th and (n – 1)^th A.M. is 5:9, then n equals ______.