Question(s) from Search: IIT

Let  be unit vectors such that . Which one of the following is correct

a)

b)

c)

d)  are mutually perpendicular

The complex number z = x + iy which satisfies the equation  lies on

a) The real axis

b) The straight line y = 5

c) Circle passing through origin

d) None of these

In the binomial expansion of  the sum of the 5^th term and 6^th term is zero, then  equals

a)

b)

c)

d)

Multiple choice

Let a and b be two non-collinear unit vectors. If  and  then  is

a) ||

b)

c)

d)

Let F(x) = f (x) g (x) h (x) for all real x, where f (x), g (x) and h (x) are differentiable functions. At some point x₀

 and

 then k is equal to

a) 12

b) 20

c) 24

d) 28

If  then f

a)

b)

c) 3

d) None

If c be a given non-zero scalar and A and B be given non-zero vectors such that A is perpendicular to B, find the vector X which satisfies the equations

The set of all values of x in the interval (0, π) for which
 is

a) (0, )

b) {  }

c) ( , π)

d) (0,   ) U {  } U ( , π)

If G(x) then  is

a)

b)

c)

d)

Show that

If a, b, c are coplanar, show that
  

 is the reflexion of in the line whose equation is . .

Use mathematical induction to prove that  is divisible by 24 for all n > 0.

If

Where [x] denotes the greatest integer less than or equal to x then  equals

a) 1

b) 0

c) – 1

d) None of these

Evaluate

a)

b)

c)

d)

Given the points A (0, 4) and B (0, - 4) the equation of the locus of the point P (x, y) such that |AP – BP| = 6 is . . . . .

The solution of is

a)

b)

c)

d) None of these

Let [.] denotes the greatest integer function and

f(x) =  then

a)  does not exist

b) f (x) is continuous at x = 0

c) f (x) is not differentiable at x = 0

d)

Evaluate

a)

b)

c)

d)

Two circles  and  are given. Then the equation of the circle through their points of intersection and the point (1, 1) is

a)

b)

c)

d) None of these

If n be a positive integer such that
 then

a)

b)

c)

d)

 is

a) 2

b) – 2

c)

d)

Evaluate

a)

b)

c)

d)

Which of the following are rational?

a)

b)

c)

d)

Using mathematical induction prove that