Mathematics Tes...

The equation of the lines through \((1,1)\) and making angles of \(45^{\circ}\) with the line \(x+y=0\) are:

Differentiate \(f(x)=e^{a x+b}\) from first principles.

Let \(L\) be the line of intersection of the planes \(2 x+3 y+z=1\) and \(x+3 y+2 z=2\). If \(L\) makes an angle \(\alpha\) with the positive \(x\) -axis, then \(\cos \alpha\) is equal to:

Question 8 was solved by 67 examinees in an examination. Question 9 is 46 and Question 10 is 40. 28 examinees had solved both questions 8 and 9, 8 answered both questions 9 and 10, 26 both questions 8 and 10 and 2 solved all three questions, then how many had solved question 8, but questions 9 and not 10?

If$\alpha$ and$\beta$ are the roots of the equation$a{x}^2+2bx+c=0$ then find the value of$\frac{\alpha }{\beta }+\frac{\beta }{\alpha }$

The distance between the pair of lines represented by the equation \(x^{2}-6 x y+9 y^{2}+3 x-9 y-4=0\) is:

The radius of the circle passing through the foci of the ellipse \(\frac{x^{2}}{16}+\frac{y^{2}}{9}=1\) and having its centre \((0,3)\) is:

\(A=\left[\begin{array}{cc}x & -7 \\ 7 & y\end{array}\right]\) is a skew-symmetric matrix, then \((x, y)=?\)

If \(e^{\theta \phi}=c+4 \theta \phi,\) where \(c\) is an arbitrary constant and \(\phi\) is a function of \(\theta,\) then what is \(\phi \mathrm{d} \theta\) equal to?