If A is a 3x3 non- singular matrix such that AA^T = A^TA, then BB^T is equal to

• l +B
• l

• B^-1

• B^-1

If g is the inverse of a function f and f'(x) =  then g'(x) is equal to 

• 1+ x⁶

• 5x⁴

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• 

If f and ga re differentiable  functions in (0,1) satisfying f(0) =2= g(1), g(0) = 0 and f(1) = 6, then for some c ε] 0,1[

• 2f'(c) = g'(c)

• 2f'(c) = 3g'(c)

• f'(c) = g'(c)

• f'(c) = g'(c)

If f_k(x) = 1/k (sin^k x + cos^k x), where x ε R and k ≥1, then f₄ (x)-f_o (x) equal to 

• 1/6

• 1/3

• 1/4

• 1/4

Let A and B be two events such that  where . Then, the events A and B are

• independent but not equally likely

• independent and equally likely

• mutually exclusive and independent

• mutually exclusive and independent

If =-1 and x =2 are extreme points of f(x) =α log|x| + βx² +x, then

• α = -6, β = 1/2

• α = -6, β = -1/2

• α = 2, β = -1/2

• α = 2, β = -1/2

The integral  dx is equal to 

The Integral  is equal to

• π-4

• 
• 
• 

The area of the region described by A = {(x,y): x² +y² ≤ 1 and y² ≤1-x} is

30.

Let the population of rabbits surviving at a time t be governed by the differential equation. If p(0) = 100 then p(t) is equal to 

• 
• 
• 
•