Let  be three unit vectors such that  then the angle between  is

• 3π/4

• π/2

• 2π/3

• 5π/6

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

• 3a²−26a+55=0

• 3a²−32a+84=0

• 3a²−34a+91=0

• 3a²−34a+91=0

Let y(x) be the solution of the differential equation  (x  ≥1). Then, y (e) is equal to 

• e

• 0

• 2

• 2

If  is equal to

• 4/3

• 1/3

• -2/3

• -2/3

Let In ∫tan x dx,(n> 1) . I⁴ + I⁶ = a tan⁵x + bx⁵ + C, where C is a constant of integration, then the ordered pair (a, b) is equal to

How many real solutions does the equation x⁷+ 14x⁵+ 16x³+ 30x – 560 = 0 have?

• 7

• 1

• 3

• 3

Let the orthocentre and centroid of a triangle be A(–3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is

• $\frac{3\sqrt{5}}{2}$

• $\sqrt{10}$

• $2\sqrt{10}$

• $3\sqrt{\frac{5}{2}}$

8.

Consider the non-constant differentiable function f of one variable which obeys the relation $\frac{\mathrm{f}\left(\mathrm{x}\right)}{\mathrm{f}\left(\mathrm{y}\right)}$ f(x - y ). If f'(0)= p and f(y) . f'(5) = q, then f'(- 5) is

• $\frac{{\mathrm{p}}^2}{\mathrm{q}}$

• $\frac{\mathrm{q}}{\mathrm{p}}$

• $\frac{\mathrm{p}}{\mathrm{q}}$

• q

If f(x)=log₅(log₃(x)), then f'(e) is equal to

• e log_e(5)

• e log_e(3)

• $\frac{1}{{\mathrm{elog}}_{\mathrm{e}}\left(5\right)}$

• $\frac{1}{{\mathrm{elog}}_{\mathrm{e}}\left(3\right)}$

Let F(x)=e^x, G(x)=e^{- x} and H(x) = G(F(x)), where x is a real variable. Then, $\frac{\mathrm{dH}}{\mathrm{dx}}$ at x= 0 is

• 1

• - 1

• $- \frac{1}{\mathrm{e}}$

• $\text{- e}$