The area bounded by the curve y = sin(x) between the ordinates x = 0, x = $\mathrm{\pi }$ and tht x-axis is :

• 2 sq unit

• 4 sq unit

• 1 sq unit

• 3 sq unit

42.

The degree of the differential equation $\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} + {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^3 + 6\mathrm{y} = 0$ is :

• 1

• 3

• 2

• 5

The solution of the equation (2y - 1)dx - (2x + 3)dy = 0 is  :

• $\frac{2\mathrm{x} - 1}{2\mathrm{y} + 3} = \mathrm{c}$

• $\frac{2\mathrm{x} + 3}{2\mathrm{y} - 1} = \mathrm{c}$

• $\frac{2\mathrm{x} - 1}{2\mathrm{y} - 1} = \mathrm{c}$

• $\frac{2\mathrm{y} + 1}{2\mathrm{x} - 3} = \mathrm{c}$

$\int \frac{\sin \left(\mathrm{x}\right)}{\sin \left(\mathrm{x} - \mathrm{\alpha }\right)}\mathrm{dx}$ is equal to

• $\left(\mathrm{x} - \mathrm{\alpha }\right)\cos \left(\mathrm{\alpha }\right) + \sin \left(\mathrm{\alpha }\right)\log \left(\sin \left(\mathrm{x} - \mathrm{\alpha }\right)\right) + \mathrm{c}$

• $\sin \left(\mathrm{x} - \mathrm{\alpha }\right) + \sin \left(\mathrm{x}\right) + \mathrm{c}$

• $\left(\mathrm{x} - \mathrm{\alpha }\right)\cos \left(\mathrm{\alpha }\right) + \log \left(\sin \left(\mathrm{x} - \mathrm{\alpha }\right)\right) + \mathrm{c}$

• $\cos \left(\mathrm{x} - \mathrm{\alpha }\right) + \cos \left(\mathrm{x}\right) + \mathrm{c}$

$\int {13}^{\mathrm{x}}\mathrm{dx}$ is :

• $\frac{{13}^{\mathrm{x}}}{\log \left(13\right)} + \mathrm{c}$

• ${13}^{\mathrm{x} + 1} + \mathrm{c}$

• 14x + c

• 14^{x + 1} + c

${\int }_0^{\frac{\mathrm{\pi }}{2}}\sin \left(2\mathrm{x}\right)\log \left(\tan \left(\mathrm{x}\right)\right)d\mathrm{x}$

• $\mathrm{\pi }$

• $\frac{\mathrm{\pi }}{2}$

• 1

• 0

${\int }_0^{\frac{\mathrm{\pi }}{2}}\mathrm{xsin}\left(\mathrm{x}\right)\mathrm{dx}$ is equal to :

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{2}$

• $\mathrm{\pi }$

• 1

The inclination of the straight line passing through the point (- 3, 6) and the mid point of the line joining the points ( 4, - 5) and (- 2, 9) is:

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{3\mathrm{\pi }}{4}$

A point moves such that the area of the triangle formed by it with the points (1, 5) and (3, - 7) is 21 sq unit Then locus of the point is :

• 6x + y - 32 = 0

• 6x - y + 32 = 0

• x + 6y - 32 = 0

• 6x - y - 32 = 0

The line $\frac{\mathrm{x}}{\mathrm{a}} - \frac{\mathrm{y}}{\mathrm{b}}$ = 1 cuts the x-axis at P. The equation of the line through P perpendicular to the given line is :

• x + y = ab

• x + y = a + b

• ax + by = a²

• bx + ay = b²