Mathematics Tes...

If \(\mathrm{f}(\mathrm{x})=\frac{\sin ^{2} \mathrm{x}+4 \sin \mathrm{x}+5}{2 \sin ^{2} \mathrm{x}+8 \sin \mathrm{x}+8},\) then range of \(\mathrm{f}(\mathrm{x})\) is \(-\)

If statement (P →q) → (q →r) is false, then truth values of statements p,q and r respectively can be

The greatest value of λ ≥ 0 for which both the equations 2x² + ( λ − 1)x + 8 = 0 and x² − 8x + λ + 4 = 0 have real roots is

Let a₁, a₂, a₃, .... be terms of an A.P.If \(\frac{a_{1}+a_{2}+\ldots+a_{p}}{a_{1}+a_{2}+\ldots a_{q}}=\frac{p^{2}}{q^{2}} p \neq q,\) then \(\frac{a_{6}}{a_{21}}\) equals

The equation of the bisector of the acute angle between the lines 3x − 4y + 7 = 0 and 12x + 5y − 2 = 0 is

The foci of a hyperbola coincide with the foci of the ellipse \(\frac{x^{2}}{25}+\frac{y^{2}}{9}=1\). The equation of the hyperbola if its eccentricity is 2, is

If \(z\) and \(\omega\) are two non-zero complex numbers such that \(|z \omega|=1\) and \(\arg (z)-\arg (\omega)=\pi / 2,\) the \(\bar{Z} \omega\) is equal to