If the function g(x) = is differntiable, then the value of k+m is

• 2

• 16/5

• 10/3

• 10/3

The normal to the curve x² + 2xy-3y² =0 at (1,1)

• does not meet the curve again

• meets the curve again in the second quadrant

• meets the curve again in the third quadrant

• meets the curve again in the third quadrant

The number of common tangent to the circles x²+y²-4x-6y-12=0 and x²+y²+6x+18y+26 = 0 is

• 1

• 2

• 3

• 3

A =  is a matrix satisfying the equation AA^T = 9I, Where I is 3 x 3 identity matrix, then the ordered pair (a,b) is equal to

• (2,-1)

• (-2,1)

• (2,1)

• (2,1)

The set of all values of λ for which the system of linear equations 

2x₁-2x₂+x₃ = λx₁
2x₁- 3x₂ + 2x₃ = λx₂
-x₁ + 2x₂ = λx₃
a non- trivial solution.

• is an empty set

• is a singleton set

• contains two elements

• contains two elements

• 4

• 3

• 2

• 2

17.

Let  where .Then, a value of y is

• 
• 
• 
• 

Let f (x) be a polynomial of degree four having extreme values at x =1 an x =2. If  then f(2) is equal to 

• -8

• -4

• 0

• 0

If 12 identical balls are to be placed in 3 identical boxes, then the probability that  one of the boxes contains exactly 3 balls, is

The integral