21.

Let A be a 2 × 2 matrix
Statement 1 : adj (adj A) = A
Statement 2 : |adj A| = |A|

• Statement–1 is true, Statement–2 is true, Statement–2 is a correct explanation for statement–1

• Statement–1 is true, Statement–2 is true; Statement–2 is not a correct explanation for statement–1.

• Statement–1 is true, statement–2 is false.

• Statement–1 is true, statement–2 is false.

The lines p(p²+ 1) x – y + q = 0 and (p²+ 1)2x + (p²+ 1) y + 2q = 0 are
perpendicular to a common line for

• no value of p

• exactly one value of p

• exactly two values of p

• exactly two values of p

If  are non–coplanar vectors and p, q are real numbers, then the equality  holds for

• exactly one value of (p, q)

• exactly two values of (p, q)

• more than two but not all values of (p, q)

• more than two but not all values of (p, q)

Let the line  lie in the plane x + 3y – αz + β = 0. Then (α, β) equals

• (6, – 17)

• (–6, 7)

• (5, –15)

• (5, –15)

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is

• less than 500

• at least 500 but less than 750

• at least 750 but less than 1000

• at least 750 but less than 1000

In a binomial distribution B(n, n= 1/4) , if the probability of at least one success is greater than or equal to 9/10 , then n is greater than 

If P and Q are the points of intersection of the circles x²+ y²+ 3x + 7y + 2p – 5 = 0 and x²+ y²+ 2x + 2y – p² = 0, then there is a circle passing through P, Q and (1, 1) for

• all values of p

• all except one value of p

• all except two values of p

• all except two values of p

If , then the maximum value of |Z| is equal to

• 
• 

• 2

• 2

The area of the region bounded by the parabola (y – 2)2 = x – 1, the tangent to the parabola at the point (2, 3) and the x-axis is 

• 3

• 6

• 9

• 9

The shortest distance between the line y – x = 1and the curve x = y² is