Mathematics Tes...

Find the value of \(k\) for which the line through the points (2, 4, 8) and (1, 2, 4) is parallel to the line through the points (3, 6, k) and (1, 2, 1)?

The function f : [0, 3] → [1, 29], defined by $f\left(x\right)=2x^3–15x^2+36x+1$, is

The locus of the mid–point of the chord of contact of tangents drawn from points lying on the straight line $4x–5y=20$to the circle $x^2+y^2=9$ is

In a triangle PQR, P is the largest angle and cos P = 1/3. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)

Let f : [0, 1] → R (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0) = f(1) = 0 and satisfies f "(x) - 2f '(x) + f(x) >= e^x, x ∈ [0, 1].Which of the following is true for 0 < x < 1 ?

Let a-n denote the number of all n–digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let b-n = the number of such n–digit integers ending with digit 1 and c-n = the number of such n–digit integers ending with digit 0. Which of the following is correct?