JEE Main entrance exam Question Bank Solutions

If the normal to the curve y(x) = `int_0^x(2t^2 - 15t + 10)dt` at a point (a, b) is parallel to the line x + 3y = –5, a > 1, then the value of |a + 6b| is equal to ______.

If in a triangle ABC, AB = 5 units, AB = 5 units, ∠B = `cos^-1 (3/5)` and radius of circumcircle of ΔABC is 5 units, then the area (in sq.units) of ΔABC is  ______.

If α = `cos^-1(3/5)`, β = `tan^-1(1/3)`, where 0 < α, β < `π/2`, then α – β is equal to ______.

If the sum of all solutions of equation sinx + 2cosx = `1 + sqrt(3)cosx` in [0, 2π] is `(kπ)/6`. The value of k is ______.

If the number of five-digit numbers with distinct digits and 2 at the 10^th place is 336 k, then k is equal to ______.

`d/(dx)x^(logx)` = ______.

Let y = sin²θ + cos²θ + tan²θ + sec²θ + cosec²θ + cot²θ attains its least value (where θ ∈ [0, 4π]), then number of such possible values of θ is ______.

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 ______.