Mathematics Tes...

The length of the normal from origin to the plane \(x+2 y-2 z=9\) is equal to:

Consider the following in respect of the function \({f}({x})=|{x}-3|\):

1. \(f(x)\) is continuous at \(x=3\)

2. \(f(x)\) is differentiable at \(x=0\)

Which of the above statements is/are correct?

If \(f(x)=2 x-x^{2}\), then what is the value of \(f(x+2)+f(x-2)\) when \(x=0\) ?

If \(\sec \theta, \tan \theta\) are the roots of the equation \(a x^{2}+b x+c=0\) then \((\sec \theta-\tan \theta) \sec \theta \tan \theta\) is?

For all \(\mathbf{n} \in \mathbf{N},\left(1+\frac{3}{1}\right)\left(1+\frac{5}{4}\right)\left(1+\frac{7}{9}\right) \ldots \ldots\left(1+\left(\frac{2 n+1)}{n^{2}}\right)\right)\) is equal to:

In how many different ways the letters of the word 'MENHIR' be arranged so that the vowel never comes together?

Consider the expansion of \((1+x)^{2 n+1}\), the average of the coefficients of the two middle terms in the expansion is:

If \(x\) increases at the rate of \(2 \mathrm{~m} / \mathrm{sec}\) at the instant when \(x=3 \mathrm{~m}, y=1 \mathrm{~m}\), at what rate must \(y\) be changing in order that the function \(2 x y-3 x^{2} y\) shall be neither increasing nor decreasing?