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Question(s) from Search: IIT

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826

The minimum value of the expression  where  are real numbers satisfying  is

a) Positive

b) Zero

c) Negative

d) –3

The minimum value of the expression  where  are real numbers satisfying  is

a) Positive

b) Zero

c) Negative

d) –3

IIT 1995
827

Using the relation , or otherwise prove that

a) True

b) False

Using the relation , or otherwise prove that

a) True

b) False

IIT 2003
828

If A > 0, B > 0 and A + B = , then the maximum value of tan A tanB is ……….

a)

b)

c)

d)

If A > 0, B > 0 and A + B = , then the maximum value of tan A tanB is ……….

a)

b)

c)

d)

IIT 1993
829

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

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

IIT 1997
830

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

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

IIT 2005
831

True / False

For any three vectors a, b and c
 

a) True

b) False

True / False

For any three vectors a, b and c
 

a) True

b) False

IIT 1989
832

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

a)

b)

c)

d)

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

a)

b)

c)

d)

IIT 1999
833

For all ,

a) True

b) False

For all ,

a) True

b) False

IIT 1981
834

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 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

IIT 1983
835

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.

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.

IIT 2007
836

Find the smallest possible value of p for which the equation
 

a)

b)

c)

d)

Find the smallest possible value of p for which the equation
 

a)

b)

c)

d)

IIT 1995
837

If f (x) =  for every real x then the minimum value of f

a) does not exist because f is unbounded

b) is not attained even though f is bounded

c) is equal to 1

d) is equal to −1

If f (x) =  for every real x then the minimum value of f

a) does not exist because f is unbounded

b) is not attained even though f is bounded

c) is equal to 1

d) is equal to −1

IIT 1998
838

Suppose f (x) = (x + 1)2 for x ≥ . If g (x) is the function whose graph is the reflection of the graph of f (x) with respect to the line y = x then g (x) equals

a) ,  0

b)

c)

d)

Suppose f (x) = (x + 1)2 for x ≥ . If g (x) is the function whose graph is the reflection of the graph of f (x) with respect to the line y = x then g (x) equals

a) ,  0

b)

c)

d)

IIT 2000
839

Let a, b, c be three positive real numbers and
 
Then tan θ = ………..

a) 0

b) 1

c) 2

d) 3

Let a, b, c be three positive real numbers and
 
Then tan θ = ………..

a) 0

b) 1

c) 2

d) 3

IIT 1981
840

If X and Y are two sets and f : X  Y
If { f (c) = y, c ⊂ x, y ⊂ Y } then the true statement is

a)

b)

c) , a ⊂ X

d)

If X and Y are two sets and f : X  Y
If { f (c) = y, c ⊂ x, y ⊂ Y } then the true statement is

a)

b)

c) , a ⊂ X

d)

IIT 2005
841

Let O (0, 0), P (3, 4), Q (6, 0) be the vertices of the triangle OPQ. The point inside the triangle OPQ is such that OPR, PQR, OQR are of equal area. The coordinates of R are

a)

b)

c)

d)

Let O (0, 0), P (3, 4), Q (6, 0) be the vertices of the triangle OPQ. The point inside the triangle OPQ is such that OPR, PQR, OQR are of equal area. The coordinates of R are

a)

b)

c)

d)

IIT 2006
842

 If f be a one–one function with domain { x, y, z}and range { 1, 2, 3}. It is given that exactly one of the following statements is true and the remaining statements are false. Determine (1)

1. f(x) = 1

2. f(y) ≠ 1

3. f(z) ≠ 2

a) {0}

b) {1}

c) {y}

d) none of the above

 If f be a one–one function with domain { x, y, z}and range { 1, 2, 3}. It is given that exactly one of the following statements is true and the remaining statements are false. Determine (1)

1. f(x) = 1

2. f(y) ≠ 1

3. f(z) ≠ 2

a) {0}

b) {1}

c) {y}

d) none of the above

IIT 1982
843

One or more correct answers
In triangle ABC the internal angle bisector of ∠A meets the side BC in D. DE is a perpendicular to AD which meets AC in E and AB in F. Then

a) AE is harmonic mean of b and c

b) AD

c)

d) Δ AEF is isosceles

One or more correct answers
In triangle ABC the internal angle bisector of ∠A meets the side BC in D. DE is a perpendicular to AD which meets AC in E and AB in F. Then

a) AE is harmonic mean of b and c

b) AD

c)

d) Δ AEF is isosceles

IIT 2006
844

For a triangle ABC it is given that  , then Δ ABC is equilateral.

a) True

b) False

For a triangle ABC it is given that  , then Δ ABC is equilateral.

a) True

b) False

IIT 1984
845

True / False

The function f (x) =  is not one to one.

a) True

b) False

True / False

The function f (x) =  is not one to one.

a) True

b) False

IIT 1983
846

Find the set of all values of a such that  are sides of a triangle.

a) (0, 3)

b) (3, ∞)

c) (0, 5)

d) (5, ∞)

Find the set of all values of a such that  are sides of a triangle.

a) (0, 3)

b) (3, ∞)

c) (0, 5)

d) (5, ∞)

IIT 1985
847

Fill in the blank

Let A be the set of n distinct elements then the total number of distinct functions from A to A is ……… and out of these …… are onto

a) n!, 1

b) nn, n!

c) nn, 1

d) none of the above

Fill in the blank

Let A be the set of n distinct elements then the total number of distinct functions from A to A is ……… and out of these …… are onto

a) n!, 1

b) nn, n!

c) nn, 1

d) none of the above

IIT 1985
848

In a triangle of base a the ratio of the other two sides is  r (< 1). Then the altitude of the triangle is less than or equal to  .

a) True

b) False

In a triangle of base a the ratio of the other two sides is  r (< 1). Then the altitude of the triangle is less than or equal to  .

a) True

b) False

IIT 1991
849

The value of k such that  lies in the plane
  is

a) 7

b) – 7

c) No real value

d) 4

The value of k such that  lies in the plane
  is

a) 7

b) – 7

c) No real value

d) 4

IIT 2003
850

If ABCD are four points in a space, prove that

If ABCD are four points in a space, prove that

IIT 1987

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