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

Let f(x) = `cos(2tan^-1sin(cot^-1sqrt((1 - x)/x))), 0 < x < 1`. Then ______.

If the orthocentre of the triangle formed by (1, 3) (4, –5) and (a, b) is (2, 4), Then the value of 33b + 22a is ______.

If the vertices of a triangle be (0, 0), (6, 0) and (6, 8), then its incentre will be ______.

The orthocentre of the triangle formed by the lines 4x – 7y + 10 = 0, x + y = 5 and 7x + 4y = 15, is ______.

If A = `[(-2, 1),(0, 3)]` Then 2A² – 3A ______.

The ratio in which the segment joining the points (2, 4, 5), (3, 5, –4) is divided by the yz-plane is ______.

The coordinates of the middle points of the sides of a triangle are (4, 2), (3, 3) and (2, 2) then the coordinates of its centroid are ______.

If 3x + y = 0 is a tangent to the circle with centre at the point (2, –1), then the equation of the other tangent to the circle from the origin is ______.

If H is the orthocentre of the triangle ABC, then AH is equal to ______.

If A is a square matrix such that A(adjA) = `[(3, 0, 0),(0, 3, 0),(0, 0, 3)]`, then `(|adj(adjA)|)/|adjA|` is equal to ______.

Two vertices of a triangle are (0, 2) and (4, 3). If its orthocentre is at the origin, then its third vertex lies in which quadrant?

Let C be the centroid of the triangle with vertices (3, –1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y – 1 = 0 and 3x – y + 1 = 0. Then the line passing through the points C and P also passes through the point ______.

The largest interval lying in `((-π)/2, π/2)` for which the function, f(x) = `4^(-x^2) + cos^-1(x/2 - 1) + log(cosx)`, is defined, is ______.

Let A be a 2 × 2 matrix with det (A) = –1 and det ((A + I) (Adj (A) + I)) = 4. Then the sum of the diagonal elements of A can be ______.

If A^T denotes the transpose of the matrix A = `[(0, 0, a),(0, b, c),(d, e, f)]`, where a, b, c, d, e and f are integers such that abd ≠ 0, then the number of such matrices for which A^–1 = A^T is ______.

The sum of the solutions of the equation `|sqrt(x) - 2|+ sqrt(x)(sqrt(x) - 4) + 2, (x > 0)` is equal to ______.

If the orthocentre of the triangle formed by (1, 3) (4, –5) and (a, b) is (2, 4), Then the value of 33b + 22a is ______.

The sum of the series `tan^-1(1/3) + tan^-1(2/9) + ...... + tan^-1[2^(n-1)/(1 + 2^(2n-1))] + ...... ∞` is ..... `(kπ)/4`. Then the value of k is ______.

If the vertices of a triangle be (0, 0), (6, 0) and (6, 8), then its incentre will be ______.

Sum of roots of the equation (x + 3)² – 4 |x + 3| + 3 = 0 is ______.