751 |
Let f(x) = , x ≠ then for what value of α, f(f(x)) = x a) b) c) d)
Let f(x) = , x ≠ then for what value of α, f(f(x)) = x a) b) c) d)
|
IIT 2001 |
|
752 |
If and then f is a) One-one and onto b) One-one but not onto c) Onto but not one-one d) Neither one-one nor onto
If and then f is a) One-one and onto b) One-one but not onto c) Onto but not one-one d) Neither one-one nor onto
|
IIT 2003 |
|
753 |
Multiple choice Let be three vectors. A vector in the plane of b and c whose projection on a is of magnitude is a) b) c) d)
Multiple choice Let be three vectors. A vector in the plane of b and c whose projection on a is of magnitude is a) b) c) d)
|
IIT 1993 |
|
754 |
If and Then f – g is a) Neither one to one nor onto b) One to one and onto c) One to one and into d) Many one and onto
If and Then f – g is a) Neither one to one nor onto b) One to one and onto c) One to one and into d) Many one and onto
|
IIT 2005 |
|
755 |
Let A be vector parallel to the line of intersection of planes P1 and P2. Plane P1 is parallel to the vectors and and that P2 is parallel to and , then the angle between vector A and a given vector is a) b) c) d)
|
IIT 2006 |
|
756 |
A vector A has components A1, A2, A3 in a right handed rectangular cartesian coordinate system OXYZ. The coordinate system is rotated about the X–axis through an angle . Find the components of A in the new co-ordinate system in terms of A1, A2, A3.
A vector A has components A1, A2, A3 in a right handed rectangular cartesian coordinate system OXYZ. The coordinate system is rotated about the X–axis through an angle . Find the components of A in the new co-ordinate system in terms of A1, A2, A3.
|
IIT 1983 |
|
757 |
Subjective Problems Let f (x + y) = f (x) . f (y) for all x, y. Suppose f (5) = 2 and = 3. Find f (5).
Subjective Problems Let f (x + y) = f (x) . f (y) for all x, y. Suppose f (5) = 2 and = 3. Find f (5).
|
IIT 1981 |
|
758 |
In a triangle OAB, E is the midpoint of BO and D is a point on AB such that AD : DB = 2 : 1. If OD and AE intercept at P determine the ratio OP : PD using vector methods.
In a triangle OAB, E is the midpoint of BO and D is a point on AB such that AD : DB = 2 : 1. If OD and AE intercept at P determine the ratio OP : PD using vector methods.
|
IIT 1989 |
|
759 |
Find the natural number a for which where the function f satisfies the relation f(x + y) = f(x) f(y) for all natural numbers x and y and further f(1) = 2.
Find the natural number a for which where the function f satisfies the relation f(x + y) = f(x) f(y) for all natural numbers x and y and further f(1) = 2.
|
IIT 1992 |
|
760 |
The position vectors of the vertices A, B, C of a tetrahedron are respectively. The altitude from the vertex D to the opposite face ABC meets the median line through A of the triangle ABC at E. If the length of the side AD is 4 and the volume of the tetrahedron is . Find the position vector of E or all possible positions.
The position vectors of the vertices A, B, C of a tetrahedron are respectively. The altitude from the vertex D to the opposite face ABC meets the median line through A of the triangle ABC at E. If the length of the side AD is 4 and the volume of the tetrahedron is . Find the position vector of E or all possible positions.
|
IIT 1996 |
|
761 |
If where a > 0 and n is a positive integer then f(f(x)) = x. a) True b) False
If where a > 0 and n is a positive integer then f(f(x)) = x. a) True b) False
|
IIT 1983 |
|
762 |
For any two vectors u and v prove that i) ii)
For any two vectors u and v prove that i) ii)
|
IIT 1998 |
|
763 |
The domain of the function is
The domain of the function is
|
IIT 1984 |
|
764 |
If f is an even function defined on (−5, 5) then the four real values of x satisfying the equation are
If f is an even function defined on (−5, 5) then the four real values of x satisfying the equation are
|
IIT 1996 |
|
765 |
True/False If for some non zero vector X then a) True b) False
True/False If for some non zero vector X then a) True b) False
|
IIT 1983 |
|
766 |
Let , 0 < x < 2 are integers m ≠ 0, n > 0 and let p be the left hand derivative of |x − 1| at x = 1. If , then a) n = −1, m = 1 b) n = 1, m = −1 c) n = 2, m = 2 d) n > 2, n = m
Let , 0 < x < 2 are integers m ≠ 0, n > 0 and let p be the left hand derivative of |x − 1| at x = 1. If , then a) n = −1, m = 1 b) n = 1, m = −1 c) n = 2, m = 2 d) n > 2, n = m
|
IIT 2008 |
|
767 |
Let and where O, A and B are non-collinear points. Let p denote the area of the quadrilateral OABC and let q denote the area of the quadrilateral with OA and OC as adjacent sides. If p = kq then k = . . . . .
Let and where O, A and B are non-collinear points. Let p denote the area of the quadrilateral OABC and let q denote the area of the quadrilateral with OA and OC as adjacent sides. If p = kq then k = . . . . .
|
IIT 1997 |
|
768 |
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 |
|
769 |
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 |
|
770 |
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 |
|
771 |
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 |
|
772 |
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 |
|
773 |
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 |
|
774 |
If ABCD are four points in a space, prove that
If ABCD are four points in a space, prove that
|
IIT 1987 |
|
775 |
If a, b, c are distinct positive numbers then the expression ( b + c – a ) ( c + a – b ) ( a + b – c ) –abc is a) Positive b) Negative c) Non–positive d) None of these
If a, b, c are distinct positive numbers then the expression ( b + c – a ) ( c + a – b ) ( a + b – c ) –abc is a) Positive b) Negative c) Non–positive d) None of these
|
IIT 1986 |
|