Mathematics Tes...

Find the points on the curve \(y=x^2\) at which the slope of the tangent is equal to the \(y\)-coordinate of the point.

The integral \(\int \frac{\left(1-\frac{1}{\sqrt{3}}\right)(\cos x-\sin x)}{\left(1+\frac{2}{\sqrt{3}} \sin 2 x\right)} d x\) is equal to :

If \(A =\left[\begin{array}{ccc}1 & -1 & 0 \\ 3 & 2 & -1\end{array}\right]\) and \(B =\left[\begin{array}{l}1 \\ 3 \\ 5\end{array}\right]\), find \(( AB )^{T}\).

Evaluate the integral \(\int_{0}^{\frac{\pi}{4}} \sin ^{3} 2 t \cos 2 t ~d t\).

How many two-digit numbers are divisible by 4?

For any vector \(\alpha\), what is the value of \((\alpha . \hat{i}) \hat{i}+(\alpha . \hat{j}) \hat{j}+(\alpha. \hat{k}) \hat{k}\)

If \(x=\tan ^{-1}(\frac{1}{5})\) then \(\sin 2 x\) is equal to?

In any discrete series (when all values are not same) if \(x\) represent mean deviation about mean and \(y\) represent standard deviation, then which one of the following is correct?

A random variable $X$  takes values $0, 1, 2, 3, x$ , with probability 

$P(X=x)=k(x+1){\left(\frac{1}{5}\right)}^x$ where $P(X = 0)$ is a constant. Then, $P(X = 0)$ is :

If \({ }^{n} C_{15}={ }^{n} C_{8}\), then find the value of \(n\).