Mathematics Tes...

\(A\) fires \(5\) shots to \(B\)'s \(3\) but A kills only once in \(3\) shots while \(B\) kills once in \(2\) shots. When \(B\) has missed \(27\) times, \(A\) has killed

Find the asymptotes to the hyperbola \(9 x^{2}-16 y^{2}=144\).

Find the sum of the series \(3+\frac{9}{2}+6+\frac{15}{2}+\ldots\) upto \(25^{\text {th }}\) term.

Solve the following L.P.P. by graphical method:

Minimize: \(Z=6 x+2 y\) subject to \(x+2 y \geq 3, x+4 y \geq 4,3 x+y \geq 3, x \geq 0, y \geq 0\).

Find the conjugate of \(\frac{1+i}{1-i}\).

If the latus rectum of an ellipse is equal to half of the minor axis, then what is its eccentricity?

Consider the following statements in respect of f(x) = |x| - 1

1. f(x) is continuous at x = 1.

2. f(x) is differentiable at x = 0.

Which of the above statements is/are correct?

Find the Cartesian equations of the lines that pass through the origin and (1, −3, 4).

The vectors î - 2xĵ - 3yk̂ and î + 3xĵ + 2yk̂ are orthogonal to each other. Then the locus of the point (x, y) is-

In an examination, a candidate has to pass in each of the 5 subjects. In how many ways he can fail?