Question(s) from Search: IIT

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
 

For x ε R,  is equal to

a) e

b)

c)

d)

True/False

If  for some non zero vector X then  

a) True

b) False

If  then  

a) True

b) False

Let  and  where O, A and B are non-collinear points. Let p denote the area of the quadrilateral OABC and let q denote the area of the quadrilateral with OA and OC as adjacent sides. If p = kq then k = .  .  .  .  .

Prove that  = 2[cosx + cos3x + cos5x + … + cos(2k−1)x] for any positive integer k. Hence prove that  =

The function
f(x) =|px – q| + r |x|, x ε (−, )
where p > 0, q > 0, r > 0 assumes minimum value on one point if

a) p ≠ q

b) r = q

c) r ≠ p

d) r = p = q

Let f : R → R be any function defined g : R → R by g (x) = |f (x)| for all x. Then g is

a) onto if f is onto

b) one to one if f is one to one

c) continuous if f is continuous

d) differentiable if f is differentiable

If f : [ 1,  → [ 2, ] is given by f (x) = x +  then ( x ) is given by

a)

b)

c)

d) 1 +

The function of f : R → R be defined by f (x) = 2x + sinx for x ε R . Then f is

a) one-one and onto

b) one-one but not onto

c) onto but not one-one

d) neither one-one nor onto