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)

Find the centre of the circle passing through (0, 0) and (1, 0) and touching the circle .

The number of integral values of k for which the equation  has a solution is

a) 4

b) 8

c) 10

d) 12

Evaluate if sin |x| - |x| is differentiable at x = 0.

a) Yes

b) No

Prove that  Hence or otherwise evaluate the integral .

Fill in the blank

Let A, B, C be three vectors of length 3, 4, 5 respectively. Let A is perpendicular to B + C, B is perpendicular to C + A, and C is perpendicular to A + B then the length of the vector  is equal to  . . . .

The number of common tangents to the circles  and  is

a) 0

b) 1

c) 3

d) 4

Use mathematical induction to show that (25)^{n + 1} – 24n + 5735 is divisible by (24)² for all n = 1, 2, .  .  .

given that  and

a) does not exist

b) is equal to

c) is equal to

d) is equal to 3