Mathematics Tes...

If \(A=\left\{x \in \mathbb{C}: x^{4}-1=0\right\}\)

\(B=\left\{x \in \mathbb{C}: x^{2}-1=0\right\}\)

\(C=\left\{x \in \mathbb{C}: x^{2}+1=0\right\}\)

Where \(\mathbb{C}\) is complex plane.

Find the equation of tangent of \(y=x^2\) at \(x=1\)

A unit vector which is perpendicular to the vector \(2 \hat{i}-\hat{j}+2 \hat{k}\) and is coplanar with the vectors \(\hat{i}+\hat{j}-\hat{k}\) and \(2 \hat{i}+2 \hat{j}-\hat{k}\) is:

Let \(A=\left[\begin{array}{cc}1 & \frac{1}{51} \\ 0 & 1\end{array}\right]\). If \(B=\left[\begin{array}{cc}1 & 2 \\ -1 & -1\end{array}\right] A\left[\begin{array}{cc}-1 & -2 \\ 1 & 1\end{array}\right]\), then the sum of all the elements of the matrix \(\sum_{n=1}^{50} B^n\) is equal to:

If \(\left|\begin{array}{ccc}a & a^2 & 1+a^3 \\ b & b^2 & 1+b^3 \\ c & c^2 & 1+c^3\end{array}\right|=0\) and vectors \(\left(1, a, a^2\right),\left(1, b, b^2\right)\) and \(\left(1, c, c^2\right)\) are noncoplanar, then the product abc equals:

Prove the following by using the principle of mathematical induction for all \(\mathrm{n} \in \mathrm{N}: 41^{\mathrm{n}}-14^{\mathrm{n}}\) is:

\(A\) and \(B\) are two events such that \(P(A)=0.3\) and \(P(A \cup B)=0.8\). If \(A\) and \(B\) are independent, then \(p(B)\) is

In a box, 4 coins of ten rupees, 2 coins of five rupees, 2 coins of two rupees and 2 coins of one rupee are put. Now, three coins are taken out randomly. What is the probability that the amount drawn is 12 rupees?

Find the standard deviation of \(15,20,18,22,25\).