Question(s) from Search: IIT

If and , then find  

The integral  equals

a)

b)

c) 1

d)

The inequality |z – 4| < |z – 2| represents the region given by

a) Re(z) ≥ 0

b) Re(z) < 0

c) Re(z) > 0

d) None of these

a) True

b) False

Coefficient of t²⁴ in (1 + t²)¹² (1 + t¹²) (1 + t²⁴) is

a)

b)

c)

d)

If f (x) = |x – 2| and g (x) =  then  for x > 20

a) 0

b) 1

c) 2

d) 4

The value of the integral  is

a)

b)

c)

d)

If tan A  then

a) True

b) False

For a real y, let [y] denote the greatest integer less than or equal to y. Then the function  is

a) Discontinuous at some x

b) Continuous at all x but the derivative  does not exist for some x

c)  exists for all x but the derivative  does not exist for some x

d)  exists for all x

Show that

The position vectors of the point A, B, C, D are  respectively. If the points A, B, C and D lie in a plane, find the value of λ.

If k =  then the numerical value of k is ……….

a)

b)

c)

d)

If f (a) =  then the value of  is

a) – 5

b)

c) 5

d) None of these

Evaluate

a)

b)

c)

d)

Let A = . Determine a vector R satisfying  and .

If a, b, c are in Arithmetic Progression then the straight line
 will pass through a fixed point whose coordinates are  . . . . .

If  then

tan

a) True

b) False

Let  be non–coplanar unit vectors equally inclined to one another at an angle θ. If find p, q, r in terms of θ

If  is the unit vector along the incident ray,  is a unit vector along the reflected ray and is a unit vector along the outward drawn normal to the plane mirror at the point of incidence. Find  in terms of  and

True / False

For any three vectors a, b and c
 

a) True

b) False

Multiple choices
For a positive integer n, let
 
.  .  . then

a)

b)

c)

d)

For all ,

a) True

b) False

Let f (x) = |x – 1| then

a) f (x²) = |f (x)|²

b) f (x + y) = f (x) + f (y)

c) f () = |f (x)|

d) None of these

Let the vectors represent the edges of a regular hexagon

Statement 1 -  because

Statement 2 -

a) Statement 1 and 2 are true and Statement 2 is a correct explanation of statement 1.

b) Statement 1 and 2 are true and Statement 2 is not a correct explanation of statement 1.

c) Statement 1 is true. Statement 2 is false.

d) Statement 1 is false. Statement 2 is true.

Find the smallest possible value of p for which the equation
 

a)

b)

c)

d)