21.

If P =  is the adjoint of a 3 x3 matrix A and |A| = 4, then α is equal to 

• 4

• 11

• 5

• 5

If y  = sec (tan^-1 x), then dy/dx at x = 1 is equal to 

• 
• 

• 1

• 1

Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

• 3/2

• 5/2

• 7/2

• 7/2

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to the additional number of workers x is given by . If the firm employs 25 more workers, then
the new level of production of items is

• 2500

• 3000

• 3500

• 3500

If the lines


are coplanar, then k can have

• any value

• exactly one value

• exactly two values

• exactly two values

If the vectors AB = 3î + 4k̂ and AC = 5î - 2ĵ + 4k̂ are the sides of a Δ ABC, then the length of the median through A is 

• √18

• √72

• √33

• √45

If ∫f x dx =Ψ (x),then ∫x⁵ f(x³)dx is equal to

Statement I - The value of the integral  is equal to π/6.
Statement II-

• Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

• Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I

• Statement -I is True; Statement -II is False.

• Statement -I is True; Statement -II is False.

The area (in square units) bounded by the curves y =  2y-x+3 =0, X -axis and lying in the first quadrant is 

• 9

• 36

• 18

• 18

The intercepts on X- axis made by tangents to the curve,  which are parallel to the line y =2x, are equal to

• ±1

• ±2

• ±3

• ±3