Area (in sq. units) of the region outside $\frac{\left|\mathrm{x}\right|}{2} + \frac{\left|\mathrm{y}\right|}{3} = 1$ and inside the ellipse $\frac{{\mathrm{x}}^2}{4} + \frac{{\mathrm{y}}^2}{9} = 1$

• $3\left(\mathrm{\pi } - 2\right)$

• $3\left(4 - \mathrm{\pi }\right)$

• $6\left(\mathrm{\pi } - 2\right)$

• $6\left(4 - \mathrm{\pi }\right)$

412.

If 

• is an empty set

• contains exactly one element.

• contains exactly two elements.

• contains exactly two elements.

For x ε R, f (x)=|log2−sinx| and g(x)=f(f(x)), then :

• g is not differentiable at x=0

• g'(0)=cos(log2)

• g'(0)=-cos(log2)

• g'(0)=-cos(log2)

Let two fair six-faced dice A and B be thrown simultaneously. If E₁ is the event that die A shows up four, E₂ is the event that die B shows up two and E₃ is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?

• E₁ and E₂ are independent

• E₂ and E₃ are independent.

• E₁ and E₃ are independent.

• E₁ and E₃ are independent.

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

• 1+ x⁶

• 5x⁴

• 
• 

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: R →R is a function defined by  where [x] denotes the greatest integer function, then f is

• continuous for every real x

• discontinous only at x = 0

• discontinuous only at non-zero integral values of x

• discontinuous only at non-zero integral values of x

The value of p and q for which the function f(x) =

• p = 1/2. q = -3/2

• p = 5/2, q = 1/2

• p = - 3/2, q = 1/2

• p = - 3/2, q = 1/2

The domain of the function f(x) = 

• (-∞,∞)

• (0,∞)

• (-∞,0)

• (-∞,0)