Mathematics Tes...

What is \(\lim _{x \rightarrow 0} \frac{\sin x \log (1-x)}{x^{2}}\) equal to?

Find the value of \(\underset{{x \rightarrow 1}}{\lim} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^{2}+x-3}\)

Find the coefficient of \(x^2\)in\(\left(3 x-\frac{1}{x^{2}}\right)^{6}\)

If \(\alpha\) and \(\beta\) are the roots of the equation \(4 x^{2}+2 x-1=0\), then which one of the following is correct?

The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 is:

Let the unit vectors a and \(b\) be perpendicular to each other and the unit vector \(c\) be inclined at an angle \(\theta\) to both a and b. If \(c=x a+y b+z(a \times b)\), then:

If \(\sin ^{-1} \mathrm{x}+\cos ^{-1} \mathrm{y}=\frac{2 \pi}{5}\), then \(\cos ^{-1} \mathrm{x}+\sin ^{-1} \mathrm{y}\) is:

Find the area between the curve \(y=\sin x\) and lines \(x=-\frac{\pi}{3}\) to \(x=\frac{\pi}{3}\).

Find the sum of the series 5 + 55 + 555 + ..... upto n terms.

The cubic equation \(x^{3}-2 x-8=0\), has:

Find the cofactor matrix for the matrix\(A=\left[\begin{array}{ccc}-1 & 2 & 3 \\ -2 & 3 & 5 \\ 4 & -2 & 1\end{array}\right]\)?

Find graphically, the maximum value of \(\mathrm{z}=2 \mathrm{x}+5 \mathrm{y}\), subject to constraints given below:

\(2 \mathrm{x}+4 \mathrm{y} \leq 8 \)

\(3 \mathrm{x}+\mathrm{y} \leq 6 \)

\(\mathrm{x}+\mathrm{y} \leq 4 \)

\(\mathrm{x} \geq 0, \mathrm{y} \geq 0\)

Find the angle between the line \(\frac{x-1}{3}=\frac{y+1}{-1}=\frac{z-3}{2}\) and the plane \(3 x+4 y+z+5=0\).

Find the general solution of given differential equation \(\frac{x d y}{d x}+3 y=4 x^3 ?\)