Mathematics Tes...

A point \(\mathrm{R}\) with \(\mathrm{x}\) -co-ordinate 4 lies on the line segment joining the points \(\mathrm{P}(2,-3,4)\) and \(\mathrm{Q}(8,0,10)\). Find the co-ordinates of thepoint R.

The points \(A, B\) and \(C\) represent the complex numbers \(z_{1}, z_{2},(1-i) z_{1}+i z_{2}\left(\right.\) where \(\left.i^{2}=\sqrt{-1}\right)\) respectively on the complex plane. The triangle \(\mathrm{ABC}\) is :

Let \(f(x)\) be a quadratic expression which is positive for all real \(x\). If \(g(x)=f(x)-f^{\prime}(x)+f^{\prime \prime}(x),\) then for any real \(x\) :

If the area bounded by y=ax² and x=ay², a>0, is 1, then a is equal to :

Tangents to the parabola \(y^{2}=16 x\),which are parallel & perpendicular to the line

Then the coordinates of their points of contact are:

A single letter is selected at random from the word 'PROBABILITY'. The probability that it is a vowel, is :

Find the derivative with respect to \(x\) of the function

\(\left(\log _{\cos x} \sin x\right)\left(\log _{\sin x} \cos x\right)^{-1}+\arcsin \frac{2 x}{1+x^{2}}\) at \(x=\frac{\pi}{4}\)

If ABC be a triangle with$\angle BAC=2\mathrm{\pi }/3$ and AB = x such that (AB) (AC) = 1. If x varies, then the longest possible length of the angle bisector AD is

Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number.

Which of the following statement is a tautology -