JEE Main entrance exam Question Bank Solutions

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?

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 ______.