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

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 ______.

Consider

Statement 1: (p∧∼q) ∧ (∼p ∧ q) is a fallacy.

Statement 2: (p→q) ↔ (∼q→∼p) is a tautology.

The sum of n terms of an AP is 3n² + 5n. The number of term which equals 164 is ______.

If arg(z) < 0, then arg(–z) – arg(z) = ______.

(p ⇒ q) ∩ (q ⇒ r) ⇒ (p ⇒ r) is ______.

If a₁, a₂, a₃, .......... are an A.P. such that a₁ + a₅ + a₁₀ + a₁₅ + a₂₀ + a₂₄ = 225, then a₁ + a₂ + a₃ + ...... + a₂₃ + a₂₄ is equal to ______.

If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is ______.