Maths

Let f : R -> R be defined as f(x) = x – 1 and g : R – {1, -1} ® R be defined as g(x) = $\frac{x^2}{x^2-1}.$  Then the function fog is:

Let S be the set of all the natural numbers, for which the line $\frac{x}{a}+\frac{y}{b}=2$  is a tangent to the curve ${\left(\frac{x}{a}\right)}^n+{\left(\frac{y}{b}\right)}^n=2$  at the point (a, b), ab  Then

The sum of the absolute minimum and the absolute maximum values of the friction f(x) = $\left|3x-x^2+2\right|-x$ in the interval [1, 2] is

Let f, g : R → R be two real valued function defined as f(x) =   $\{\begin{array}{cc}\hfill -\left|x+3\right|,\hfill & \hfill x<0\hfill \\ \hfill e^x,\hfill & \hfill x\ge 0\hfill \end{array}$ and $g\left(x\right)=\{\begin{array}{cc}\hfill x^2+k_{1}x,\hfill & \hfill x<0\hfill \\ \hfill 4x+k_2,\hfill & \hfill x\ge 0\hfill \end{array}$ , where k₁ and k₂ are real constants. If (gof) is differentiable at x = 0, then (gof)(-4) is equal to

 $\underset{x\to \frac{1}{\sqrt[]{2}}}{lim}\frac{sin\left(co{s}^{-1}x\right)-x}{1-tan\left(co{s}^{-1}x\right)}$ is equal to

The remainder when (2021)²⁰²³ is divided by 7 is

The ordered pair (a, b), for which the system of linear equations

3x – 2y + z = b

5x – 8y + 9z = 3

2x + y + az = -1

has no solution, is

Let A be a 3 * 3 invertible matrix. If $\left|adj\left(24A\right)\right|=\left|adj\left(3adj\left(2A\right)\right)\right|,then{\left|A\right|}^2$ is equal to

Let A = $\left\{Z\in C:\left|\frac{z+1}{z-1}\right|<1\right\}$and B = $\left\{z\in C:arg\left(\frac{z-1}{z+1}\right)=\frac{2\pi }{3}\right\}.$Then $A\cup B$ is

Let A = $\left\{Z\in C:\left|\frac{z+1}{z-1}\right|<1\right\}$and B = $\left\{z\in C:arg\left(\frac{z-1}{z+1}\right)=\frac{2\pi }{3}\right\}.$Then $A\cup B$ is