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

In triangle ABC, a = 4, b = 3 and ∠A = 60°. If ' c' is a root of the equation c² – 3c – k = 0. Then k = ______. (with usual notations)

Let x = `(sin^3θ)/(cos^2θ)`, y = `(cos^3θ)/(sin^2θ)` and sinθ + cosθ = `1/2`. If x + y = `p/q` where p and q are coprime then (p + q) is equal to ______.

If y = `x^((sinx)^(x^((sinx)^(x^(...∞)`, then `(dy)/(dx)` at x = `π/2` is equal to ______.

Let λ₁λ₂ ∈[0, π] are the solutions of the equation `"cosec"(π/4 + x) + "cosec"(π/4 - x) = 2sqrt(2)`, then 8(sin²λ₁ + sin²λ₂) is equal to ______.

`int (dx)/sqrt(5x - 6 - x^2)` equals ______.

The sum of the last eight coefficients in the expansion of (1 + x)¹⁶ is equal to ______.

Let 2cos 2x + 3cos x – 2 > 0 and x² + x – 2 < 0 (x is measured in radians), then number of integral values of x satisfying both the inequations is ______.

In ΔABC with usual notations, if ∠A = 30° and a = 5, then `s/(sumsinA)` is equal to ______.

The number of solutions of the equation sin 2x – 2 cosx + 4 sinx = 4 in the interval [0, 5π] is ______.

Number of values of x which satisfy then relation `12tan^2x + 24/sqrt(3)tanx + 12sin^2x - 12sinx + 7` in (–2π, 4π) ______.

If the coefficients of (2r + 4)^th, (r – 2)^th terms in the expansion of (1 + x)¹⁸ are equal, then r is ______.

Let `(5 + 2sqrt(6))^n` = p + f where n∈N and p∈N and 0 < f < 1 then the value of f² – f + pf – p is ______. 

The general solution of x satisfying `cot(π/4 - x/3) = sqrt(3)/3` is ______.

Let ABC be a triangle such that ∠A = 45°, ∠B = 75° then `"a" + "c"sqrt(2)` is equal to ______. (in usual notation)

If `(tan2θ + tanθ)/(1 - tanθtan2θ)` = 0, then the general value of θ is ______.

In a triangle ABC, in usual notation, (a + b + c)(b + c – a) = λbc will be true if ______.

If sum of all the solutions of the equation `8cosx.(cos(π/6 + x).cos(π/6 - x) - 1/2)` = 1 in [0, π] is kπ, then k is equal to ______.

Consider the statement: “P(n) : n² – n + 41 is prime." Then which one of the following is true?

The positive integer just greater than (1 + 0.0001)¹⁰⁰⁰⁰ is ______.

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is ______.