Mathematics Tes...

The value of K, for which the equation (K–2)x² + 8x + K + 4 = 0 has both the roots real distinct and negative is:

Number of real solutions of the equation (tan x + 1)(tan x + 3)(tan x + 5)(tan x + 7) = 33

If A and B are two square matrices such that B = –A^–1 BA, then (A+B)² is equal to

A hyperbola has focus at origin, its eccentricity is √2 and corresponding directrix is x + y + 1 = 0. The equation(s) of its asymptotes is/are

The number of distinct integral factor pairs of 10,500 whose product is 10,500 is

The coefficient of the term independent of x in the expansion of${\left(\sqrt{\frac{x}{3}}+\frac{\sqrt{3}}{x^2}\right)}^{10}$is-

If a, b, are in GP and $\log \left(\frac{a}{2b}\right),\log \left(\frac{3b}{3c}\right)\log \left(\frac{3c}{a}\right)$ are in AP, then a, b, c are the lengths of the sides of a triangle which is

The altitude of a cone is 20cm and its semi-vertical angle is 30°. If the semi-vertical angle is increasing at the rate of 2° per second, then the radius of the base is increasing at the rate of

Directions: The following question has four choices, out of which ONE or MORE are correct.

Let the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be reciprocal to that of the ellipse $x^2+4y^2=4$ If the hyperbola passes through a focus of the ellipse, then

If the roots of ax² + 2bx + c = 0 (a ≠ 0) are non-real complex and a + c < 2b, then

Find the 5 th term form the end in the expansion of \(\left(x-\frac{1}{x}\right)^{12}\) ?