A curve y = me^mx where m > 0 intersects y-axis at a point P. What is the equation of tangent to the curve at P ?

• y = mx + m

• y = - mx + 2m

• y = m²x + 2m

• y = m²x + m

A curve y = me^mx where m > 0 intersects y-axis at a point P. How much angle does the tangent at P make with y-axis ?

• ${\tan }^{-1}\left({\mathrm{m}}^2\right)$

• ${\cot }^{-1}\left(1 + {\mathrm{m}}^2\right)$

• ${\sin }^{-1}\left(\frac{{\mathrm{m}}^2}{\sqrt{1 +\hspace{0.17em}{\mathrm{m}}^4}}\right)$

• ${\sec }^{-1}\left(\sqrt{1 + {\mathrm{m}}^4}\right)$

A curve y = me^mx where m > 0 intersects y-axis at a point P. What is the slope of the curve at the point of intersection P ?

• m

• m²

• 2m

• 2m²

74.

If 3x - 4y - 5 = 0 and 3x - 4y + 15 = 0 are the equations of a pair of opposite sides of a square, then what is the area of the square ?

• 4 square units

• 9 square units

• 16 square units

• 25 square units

What is the obtuse angle between the lines whose slopes are 2 - $\sqrt{3}$ and 2 + $\sqrt{3}$ ?

• $105°$

• $120°$

• $135°$

• $150°$

If the foot of the perpendicular drawn from the point (0, k) to the line 3x – 4y – 5 = 0 is (3, 1), then what is the value of k ?

• 3

• 4

• 5

• 6 

Let ABC be a triangle. If D(2, 5) and E(5, 9) are the mid-points of the AB and AC respectively, then what is the length of the side BC ?

• 8

• 10

• 12

• 14

If the circumcentre of the triangle formed by the lines x + 2 = 0, y + 2 = 0 and kx + y + 2 = 0 is (- 1, - 1), then what is the value of k ?

•  - 1

• - 2

• 1

• 2

The point (1, - 1) is one of the vertices of a square. If 3x + 2y = 5 is the equation of one diagonal of the square, then what is the equation of the other diagonal ?

• 3x - 2y = 5

• 2x - 3y = 1

• 2x - 3y = 5

• 2x + 3y = - 1

What is the area of the region enclosed between the curve y² = 2x and the straight line y = x ? 

• $\frac{1}{2}$

• 1

• $\frac{2}{3}$

• 2