The slope of the normal to the curve y = x² - $\frac{1}{{\mathrm{x}}^2}$ at (- 1, 0) is

• $\frac{1}{4}$

• $- \frac{1}{4}$

• 4

• - 4

The minimum value of sin(x) + cos(x) is

• $\sqrt{2}$

• $- \sqrt{2}$

• $\frac{1}{\sqrt{2}}$

• $- \frac{1}{\sqrt{2}}$

The slope of the tangent to the curve y = 3x² - 5x + 6 at (1, 4) is

• - 2

• 1

• 0

• - 1

The chord joining the points (5, 5) and (11, 227) on the curve y = 3x² - 11x - 15 is parallel to tangent at a point on the curve. Then, the abscissa of the point is

• - 4

• 4

• - 8

• 8

The function f(x) = sin(x) - kx - c, where k and c are constants, decreases always when

• k > 1

• $\mathrm{k} \ge 1$

• k < 1

• $\mathrm{k} \le 1$

If y = mlog(x) + nx² + x has its extreme values at x = 2 and x = 1, then 2m + 10n is equal to

• - 1

• - 4

• - 2

• - 3

If s = 2t³ - 6t² + at + 5 is the distance travelled by a particle at time t and if the velocity is - 3 when its acceleration is zero, then the value of a is

• - 3

• 3

• 4

• - 4

Let f(x) = [3 sin²(10x + 11) - 7]² for x $\in$ R. Then, the maximum value of the function f is

• 9

• 16

• 49

• 100

549.

If a circular plate is heated uniformly, its area expands 3c times as fast as its radius, then the value of c when the radius is 6 units, is

• $4\mathrm{\pi }$

• $2\mathrm{\pi }$

• $6\mathrm{\pi }$

• $3\mathrm{\pi }$

The minimum valuje of 2x³ - 9x² + 12x + 4 is

• 4

• 5

• 6

• 8