21.

The area (in sq. units) of the region
{(x, y} : x  ≥ 0, x + y ≤ 3, x2 ≥ 4y and y ≤ 1 +√x}

• 5/2

• 59/12

• 3/2

• 3/2

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends,3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is

• 484

• 485

• 468

• 468

The normal to the curve y(x – 2)(x – 3) = x + 6 at the point where the curve intersects the y-axis passes through the point

• 1/8

• 25/8

• 2

• 2

The integral  is equal to

• -1

• -2

• 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

If the image of the point P(1, –2, 3) in the plane, 2x + 3y – 4z + 22 = 0 measured parallel to line, x/1 = y/4= z/5 is Q, then PQ is equal to

The distance of the point (1, 3, –7) from the plane passing through the point (1, –1, –1), having normal perpendicular to both the lines is

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one–by–one, with replacement, then the variance of the number of green balls drawn is

• 6/25

• 12/5

• 6

• 6