The domain of the function f(x) = 

• (-∞,∞)

• (0,∞)

• (-∞,0)

• (-∞,0)

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

• √3/4

• 3√2 /8

• 8/3√2

• 8/3√2

If dy/dx = y + 3 > 0 and y(0) = 2, then y(ln2) is equal to:

• 7

• 5

• 13

• 13

Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3, 1) and has eccentricity  is

• 3x² + 5y² -32 = 0

• 5x² + 3y² - 48 = 0

• 3x² + 5y² - 15 = 0 

• 3x² + 5y² - 15 = 0 

• does not exist

• equal 

• equal 

• equal 

16.

The two circles x² + y² = ax and x² + y² = c²(c > 0) touch each other if

• 2|a| = c

• |a| = c

• a = 2c

• a = 2c

Let A and B be two symmetric matrices of order 3.
Statement-1: A(BA) and (AB)A are symmetric matrices.
Statement-2: AB is symmetric matrix if matrix multiplication of A with B is commutative.

• 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 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. 

If A = sin² x + cos⁴ x, then for all real x

• 3/4 ≤ A ≤ 1

• 31/16 ≤ A ≤ 1

• 1≤ A ≤2

• 1≤ A ≤2

The number of values of k for which the linear equations
4x + ky + 2z = 0
kx + 4y + z = 0
2x + 2y + z = 0
posses a non-zero solution is:

• 3

• 2

• 1

• 1

The value of  is

• 
• 

• log 2

• log 2