21.

The population p(t) at time t of a certain mouse species satisfies the differential equation . if p (0) = 850, then the  time at which the population becomes zero is

• 2 log 18

• log 9

• 
• 

Let a, b ∈ R be such that the function f given by f(x) = ln |x| + bx
2+ ax, x ≠ 0 has extreme values at x = –1 and x = 2.
Statement 1: f has local maximum at x = –1 and at x = 2.
Statement 2: 

• Statement 1 is false, statement 2 is true

• 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 true; statement 2 is not a correct explanation for statement 1

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

Let P and Q be 3 × 3 matrices with P ≠ Q. If P³= Q³ and P²Q = Q²P, then determinant of(P²+ Q²) is equal to

• -2

• 1

• 0

• 0

Consider the function f(x) = |x – 2| + |x – 5|, x ∈ R.
Statement 1: f′(4) = 0
Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and f(2) = f(5).

• Statement 1 is false, statement 2 is true

• 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 true; statement 2 is not a correct explanation for statement 1

Let  be  two unit vectors. If the vectors  and  are perpendicular to each other, then the angle between  is 

• π/6

• π/2

• π/3

• π/3

If the integral   then an equal to 

• -1

• -2

• 1

• 1

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is

• 880

• 629

• 630

• 630

If g(x) =  then g(x +π) equals

• g(x)/g(π)

• g(x) +g(π)

• g (x) - g(π)

• g (x) - g(π)

Let ABCD be a parallelogram such that  and ∠BAD be an acute angle. If   is the vector that coincides with the altitude directed from the vertex B the side AD, then  is given byLet ABCD be a parallelogram such that AB = q,AD = p and ∠BAD be an acute angle. If r is the vector that coincides with the altitude directed from the vertex B to the side AD, then r is given by (1)