JEE Main entrance exam Question Bank Solutions

The sum of solutions of the equation `cosx/(1 + sinx) = |tan2x|, x∈(-π/2, π/2) - {π/4, -π/4}` is ______.

Let X = {x ∈ N: 1 ≤ x ≤ 17} and Y = {ax + b: x ∈ X and a, b ∈ R, a > 0}. If mean and variance of elements of Y are 17 and 216 respectively then a + b is equal to ______.

The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the product of the remaining two observations is ______.

The value of the determinant `|(1, cos(β - α), cos(γ - α)),(cos(α - β), 1, cos(γ - β)),(cos(α - γ), cos(β - γ), 1)|` is equal to ______.

Let f(x) = `x + x^2/2 + x^3/3 + x^4/4 + x^5/5` and g(x) = f^–1(x), then |g''(0)| is ______.

If the vector `vecb` is collinear with the vector `veca = (2sqrt(2), -1, 4)` and `|vecb|` = 10, then ______.

If A, B and C are the angles of a triangle ABC, then `|(sin2"A", sin"C", sin"B"),(sin"C", sin2"B", sin"A"),(sin"B", sin"A", sin2"C")|` = ______.

In a triangle the length of the two larger sides are 10 and 9, respectively. If the angles are in A.P., then the length of the third side can be ______.

The possible values of θ ∈ (0, π) such that sin (θ) + sin (4θ) + sin (7θ) = 0 are ______.

Let a, b, c be such that b(a + c) ≠ 0 if

`|(a, a + 1, a - 1),(-b, b + 1, b - 1),(c, c - 1, c + 1)| + |(a + 1, b + 1, c - 1),(a - 1, b - 1, c + 1),((-1)^(n + 2)a, (-1)^(n + 1)b, (-1)^n c)|` = 0, then the value of n is ______.

The line segment joining the points (1, 2) and (−2, 1) is divided by the line 3x + 4y = 7 in the ratio ______.

`int (dx)/(e^x + e^(-x))` is equal to ______.

`int_0^5 cos(π(x - [x/2]))dx` where [t] denotes greatest integer less than or equal to t, is equal to ______.

Let f be a real valued continuous function on [0, 1] and f(x) = `x + int_0^1 (x - t)f(t)dt`. Then, which of the following points (x, y) lies on the curve y = f(x)?

If `int_0^1(sqrt(2x) - sqrt(2x - x^2))dx = int_0^1(1 - sqrt(1 - y^2) - y^2/2)dy + int_1^2(2 - y^2/2)dy` + I then I equal.

If `int_(-a)^a(|x| + |x - 2|)dx` = 22, (a > 2) and [x] denotes the greatest integer ≤ x, then `int_a^(-a)(x + [x])dx` is equal to ______.

Let the functions f: R→R and g: R→R be defined as:

f(x) = `[((x + 2",", x < 0)),((x^2",", x ≥ 0))]` and

g(x) = `{{:(x^3",", x < 1),(3x - 2",", x ≥ 1):}`

Then, the number of points in R where (fog)(x) is NOT differentiable is equal to ______.

The value of the integral `int_(-1)^1log_e(sqrt(1 - x) + sqrt(1 + x))dx` is equal to ______.

The number of real roots of the equation `tan^-1sqrt(x(x + 1)) + sin^-1sqrt(x^2 + x + 1) = π/4` is ______.

Let a be a positive real number such that `int_0^ae^(x-[x])dx` = 10e – 9 where [x] is the greatest integer less than or equal to x. Then, a is equal to ______.