Question(s) from Search: IIT

If n is a natural number such that  and  are distinct primes, then show that
 

The equation of the common tangent to the curves  and  is

a)

b)

c)

d)

The least value of the expression  for x > 1 is

a) 10

b) 2

c) −0.01

d) none of these

(Multiple choice)

The equation of common tangent to the parabolas  and  is/are

a)

b)

c)

d)

If  satisfies ,
find the value of

Three normals are drawn from the point (c, 0) to the curve . Show that c must be greater than. One normal is always the X-axis. Find c for which the other two normals are perpendicular.

The value of the expression  is equal to

a) 2

b)

c) 4

d)

Let  then  equals

a) tan

b) tan

c) tan

d) tan²

Match the following

Normals are drawn at the points P, Q and R lying on the parabola  which intersect at (3, 0) then

The length of longest interval in which the function  is increasing is

a)

b)

c)

d)

Let p, q be the roots of the equation , and r and s are roots of the equation . If  are in arithmetic progression then A = .  .  .  .  . , B = .  .  .  .  .

If  is a solution of  and  then  is equal to

a)

b)

c) 1

d)

Let  then one of the possible value of k is

a) 1

b) 2

c) 4

d) 16

The value of the integral  

a)

b)

c) 3

d) 5

If and , then find  

The integral  equals

a)

b)

c) 1

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)

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

If f (a) =  then the value of  is

a) – 5

b)

c) 5

d) None of these

Evaluate

a)

b)

c)

d)

Evaluate

a)

b)

c)

d)

Show that

Determine a positive integer n ≤ 5 such that .

a) 1

b) 2

c) 3

d) 4