If \(\int \frac{(\cos x-\sin x)}{8-\sin 2 x} d x=\frac{1}{p} \log \left[\frac{3+\sin x+\cos x}{3-\sin x-\cos x}\right]+c\), then \(\mathrm{p}=(\) Where \(\mathrm{c}\) is a constant of integration)

The equation of a plane containing the lines \(\overline{\mathrm{r}}=(\hat{\imath}+2 \hat{\jmath}-4 \hat{\mathrm{k}})+\lambda(2 \hat{\imath}+3 \hat{\jmath}+6 \hat{\mathrm{k}})\) and
\(\overline{\mathbf{r}}=(\hat{\imath}+3 \hat{\jmath}+4 \hat{\mathrm{k}})+\mu(\hat{\imath}+\hat{\jmath}-\hat{\mathrm{k}})\) is

The graphical solution set of the system of in equations \(\mathrm{x}+\mathrm{y} \leq 70, \mathrm{x}+2 \mathrm{y} \leq 100,2 \mathrm{x}+\mathrm{y} \leq 120, \mathrm{x} \geq 0, \mathrm{y} \geq 0\) is given by

The equation of the plane containing the line \(\frac{x+1}{2}=\frac{y+2}{1}=\frac{z-2}{3}\) and the point \((1,-1,3)\) is

A coin is tossed until one head appears or a tail appears 4 times in succession. The probability distribution of the number of tosses is

If \(\mathrm{B}\) is end point of minor axis of the ellipse \(b^{2} x^{2}+a^{2} y^{2}=a^{2} b^{2}(a>b)\) and \(\mathrm{S}\) and S' are foci of ellipse such that \(\Delta \mathrm{SBS}^{\prime}\) is an equilateral triangle, then eccentricity \(\mathrm{e}=\)

The velocity of a particle at time \(t\) is given by the relation \(v=6 t-\frac{t^{2}}{6}\). The distance traveled in \(3 \mathrm{~s}\) is, if \(s=0\) at \(t=0\)

If \(\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}, \overrightarrow{\mathbf{c}}\) are three non coplanar vectors and \(\overrightarrow{\mathbf{p}}, \overrightarrow{\mathbf{q}}, \overrightarrow{\mathbf{r}}\) are defined by the relations
\(\overrightarrow{\mathbf{p}}=\frac{\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}}}{[\overrightarrow{\mathbf{a}} \overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{c}}]}, \quad \overrightarrow{\mathbf{q}}=\frac{\overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{a}}}{[\overrightarrow{\mathbf{a}} \overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{c}}]}\) and \(\overrightarrow{\mathbf{r}}=\frac{\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{a}}}{[\overrightarrow{\mathbf{a}} \overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{c}}]}\)
then \(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{p}}+\overrightarrow{\mathbf{b}} \cdot \overrightarrow{\mathbf{q}}+\overrightarrow{\mathbf{c}} \cdot \overrightarrow{\mathbf{r}}\) is equal to

If \(x=3 \tan \mathrm{t}\) and \(y=3 \sec \mathrm{t}\), then the value of \(\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}\) at \(\mathrm{t}=\frac{\pi}{4}\) is

Fundamental frequency of sonometer wire is ' n '. If the tension and length are increased 3 times and diameter is increased twice, the new frequency will be

A coil has an area \(0.06 \mathrm{~m}^2\) and it has 600 turns. After placing the coil in a magnetic field of strength \(5 \times 10^{-5} \mathrm{Wbm}^{-2}\), it is rotated through \(90^{\circ}\) in 0.2 second. The magnitude of average e.m.f induced in the coil is

Which among the following statement is true for Galvanic cell?

Which of following salt's solubility increases appreciably with increase in temperature?