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 
|
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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