Mathematics Tes...

For the equations \(x+2 y+3 z=1,2 x+y+3 z=2\) and \(5 x+5 y+9 z=4\).

If the roots of the quadratic equation \(x^{2}-4 x-\log _{3} a=0\) are real, then the least value of \(a\) isequal to

The sum to \(n\) terms of the series \(\frac{1}{(\sqrt{1}+\sqrt{3})}+\frac{1}{(\sqrt{3}+\sqrt{5})}+\frac{1}{(\sqrt{5}+\sqrt{7})}+\ldots\) is:

If \(\mathrm{X}\) and \(\mathrm{Y}\) are two sets such that \(\mathrm{X}\) has \(40\) elements, \(\mathrm{X} \cup \mathrm{Y}\) has \(60\) elements and \(\mathrm{X} \cap \mathrm{Y}\) has \(10\) elements, how many elements does \(\mathrm{Y}\) have?

Range of the function \(f(x)=\frac{x^{2}+x+2}{x^{2}+x+1} ; x \in R\) is

The area bounded by the coordinate axes and the curve \(\sqrt{ x }+\sqrt{ y }=1\), is:

The probability that \(A\) speaks truth is \(\frac{4}{5}\), while this probability for \(\mathrm{B}\) is \(\frac{3}{4}\). The probability that they contradict each other when asked to speak on a fact is

The value of \(\sec \left(\tan ^{-1} \frac{ y }{2}\right)\) is:

If \(\sin ^{2} x+\sin x=1\), then what is the value of \(\cos ^{12} x+3 \cos ^{10} x+3 \cos ^{8} x+\cos ^{6} x\) ?

What is the equation of the ellipse having foci \((\pm 2,0)\) and the eccentricity \(\frac{1}{2}\)?

A vector is perpendicular to both the vectors \(\hat{ i }+\hat{ j }\) and \(\hat{ j }+\hat{ k }\) is:

Find the equation of line passing through \((h, 0)\) and \((0, k)\) and divided by the point \((1,2)\) in the ratio \(2: 3\).

If the system of linear equations

\(x+y+z=5 \)

\(x+2 y+2 z=6 \)

\(x+3 y+\lambda z=\mu\)

\((\lambda, \mu \in R)\), has infinitely many solutions, then the value of \(\lambda+\mu\) is:

If \(f(x)=\log x+3 x-10\) and \(g(x)=\tan x\) then find \(f^{\prime}(x)\)