Mathematics Tes...

Let A be a \(2 \times 2\) real matrix and I be the identity matrix of order 2 . If the roots of the equation \(|A-x I|=0\) be -1 and 3 , then the sum of the diagonal elements of the matrix \(A^2\) is...............

Let \(X\) be a binomial random variable with mean 1 and variance \(\frac{3}{4}\). The probability that \(X\) takes the value of 3 is:

The acute angle between the lines, whose direction cosines are given by \(2 l-m+2 n=0, l m+m n+n l=0\), is:

Find the multiplicative inverse of 4 - 3i ?

If \(f(x)=x^{3}+3 x^{2}+3 x-7\), then find the value of \(\frac{d f(x)}{d x}\) at \(x=2\).

What is the angle between the two lines whose direction numbers are \((\sqrt{3}-1,-\sqrt{3}-1,4)\) and \((-\sqrt{3}-1, \sqrt{3}-1,4)\)?

The number of common tangents to the circles \(x^2+y^2-4 x-6 x-12=0\) and \(x^2+y^2+6 x+18 y+26=0\), is:

\(f(x)=2 x-\tan ^{-1}x-\log \left\{x+\sqrt{x^{2}+1}\right\}\) is monotonically increasing when:

For positive integers \(\mathrm{r}>1, \mathrm{n}>2\), the coefficient of \((3 \mathrm{r})^{\mathrm{th}}\) and \((\mathrm{r}+2)^{\text {th }}\) terms in the binomial expansion of \((1+\mathrm{x})^{2 \mathrm{n}}\) are equal, then:

If \(\frac{e^{x}}{1-x}=B_{0}+B_{1} x+B_{2} x^{2}+\ldots+B_{n} x^{n}+\ldots\), then the value of \(B_{n}-B_{n-1}\) is: