701 |
Find the larger of cos(lnθ) and ln(cosθ) if < θ < . a) cos(lnθ) b) ln(cosθ) c) Neither is larger throughout the interval
Find the larger of cos(lnθ) and ln(cosθ) if < θ < . a) cos(lnθ) b) ln(cosθ) c) Neither is larger throughout the interval
|
IIT 1983 |
|
702 |
If the function f : [ 1, ) → [ 1, ) is defined by f (x) = 2x(x – 1) then f -1(x) is a) b) () c) () d)
|
IIT 1999 |
|
703 |
For three vectors which of the following expressions is not equal to any of the remaining three a) b) c) d)
For three vectors which of the following expressions is not equal to any of the remaining three a) b) c) d)
|
IIT 1998 |
|
704 |
If are in harmonic progression then ………… a) 1 b) c) d)
If are in harmonic progression then ………… a) 1 b) c) d)
|
IIT 1997 |
|
705 |
If then x equals a) b) 1 c) d) –1
If then x equals a) b) 1 c) d) –1
|
IIT 1999 |
|
706 |
Let f ( x ) = , x ≠ 1 then for what value of a is f ( f (x)) = x a) b) c) 1 d) 1
Let f ( x ) = , x ≠ 1 then for what value of a is f ( f (x)) = x a) b) c) 1 d) 1
|
IIT 2001 |
|
707 |
If f : [ 0, ) [ 0, ) and f (x) = 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 f : [ 0, ) [ 0, ) and f (x) = 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 |
|
708 |
A unit vector which is orthogonal to the vectors and coplanar with the vectors and is a) b) c) d)
A unit vector which is orthogonal to the vectors and coplanar with the vectors and is a) b) c) d)
|
IIT 2004 |
|
709 |
Match the following Let (x, y) be such that = Column 1 | Column 2 | i) If a=1 and b=0 then (x, y) | A)Lies on the circle +=1 | ii) If a=1 and b=1 then (x, y) | B)Lies on (−1)(−1) = 0 | iii) If a=1 and b=2 then (x, y) | C)Lies on y = x | iv) If a=2 and b=2 then (x, y) | D)Lies on (−1)(−1) = 0 |
Match the following Let (x, y) be such that = Column 1 | Column 2 | i) If a=1 and b=0 then (x, y) | A)Lies on the circle +=1 | ii) If a=1 and b=1 then (x, y) | B)Lies on (−1)(−1) = 0 | iii) If a=1 and b=2 then (x, y) | C)Lies on y = x | iv) If a=2 and b=2 then (x, y) | D)Lies on (−1)(−1) = 0 |
|
IIT 2007 |
|
710 |
f (x) = and g (x) = a) neither one-one nor onto b) one-one and onto c) one-one and into d) many one and onto
f (x) = and g (x) = a) neither one-one nor onto b) one-one and onto c) one-one and into d) many one and onto
|
IIT 2005 |
|
711 |
One angle of an isosceles triangle is 120 and the radius of its incircle = . Then the area of the triangle in square units is a) b) c) d) 2π
One angle of an isosceles triangle is 120 and the radius of its incircle = . Then the area of the triangle in square units is a) b) c) d) 2π
|
IIT 2006 |
|
712 |
If the vectors b, c, d, are not coplanar then prove that a is parallel to the vector
If the vectors b, c, d, are not coplanar then prove that a is parallel to the vector
|
IIT 1994 |
|
713 |
Prove by vector method or otherwise, that the point of intersection of the diagonals of a trapezium lies on the line passing through the mid points of the parallel sides (you may assume that the trapezium is not a parallelogram)
Prove by vector method or otherwise, that the point of intersection of the diagonals of a trapezium lies on the line passing through the mid points of the parallel sides (you may assume that the trapezium is not a parallelogram)
|
IIT 1998 |
|
714 |
The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Determine the sides of triangle. a) 3, 4, 5 b) 4, 5, 6 c) 4, 5, 7 d) 5, 6, 7
The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Determine the sides of triangle. a) 3, 4, 5 b) 4, 5, 6 c) 4, 5, 7 d) 5, 6, 7
|
IIT 1991 |
|
715 |
True / False Let are unit vectors. Suppose that and the angle between B and then a) True b) False
True / False Let are unit vectors. Suppose that and the angle between B and then a) True b) False
|
IIT 1981 |
|
716 |
A plane which is perpendicular to two planes and passes through (1, −2, 1). The distance of the plane from the point (1, 2, 2) is a) 0 b) 1 c) d)
A plane which is perpendicular to two planes and passes through (1, −2, 1). The distance of the plane from the point (1, 2, 2) is a) 0 b) 1 c) d)
|
IIT 2006 |
|
717 |
Two lines having direction ratios (1, 0, −1) and (1, −1, 0) are parallel to a plane passing through (1, 1, 1). This plane cuts the coordinate axes at A, B, C. Find the value of the tetrahedron OABC.
Two lines having direction ratios (1, 0, −1) and (1, −1, 0) are parallel to a plane passing through (1, 1, 1). This plane cuts the coordinate axes at A, B, C. Find the value of the tetrahedron OABC.
|
IIT 2004 |
|
718 |
If then the two triangles with vertices (x1, y1), (x2, y2), (x3, y3), and (a1, b1), (a2, b2), (a3, b3) must be congruent. a) True b) False
If then the two triangles with vertices (x1, y1), (x2, y2), (x3, y3), and (a1, b1), (a2, b2), (a3, b3) must be congruent. a) True b) False
|
IIT 1985 |
|
719 |
Find the integral solutions of the following system of inequality a) Ø b) x = 1 c) x = 2 d) x = 3
Find the integral solutions of the following system of inequality a) Ø b) x = 1 c) x = 2 d) x = 3
|
IIT 1979 |
|
720 |
Let A = AU1 = , AU2 = and AU3 = a) −1 b) 0 c) 1 d) 3
Let A = AU1 = , AU2 = and AU3 = a) −1 b) 0 c) 1 d) 3
|
IIT 2006 |
|
721 |
Consider the system of linear equations Find the value of θ for which the systems of equations have non-trivial solutions.
|
IIT 1986 |
|
722 |
The set of all solutions of the equation
The set of all solutions of the equation
|
IIT 1997 |
|
723 |
Multiple choices If the first and term of an Arithmetic Progression, a Geometric Progression and a Harmonic Progression are equal and their nth term are a, b, c respectively then a) b) c) d)
Multiple choices If the first and term of an Arithmetic Progression, a Geometric Progression and a Harmonic Progression are equal and their nth term are a, b, c respectively then a) b) c) d)
|
IIT 1988 |
|
724 |
Does there exist a Geometric Progression containing 27, 8 and 12 as three of its terms? If it exists, how many such progressions are possible?
Does there exist a Geometric Progression containing 27, 8 and 12 as three of its terms? If it exists, how many such progressions are possible?
|
IIT 1982 |
|
725 |
The sum of integers from 1 to 100 that are divisible by 2 or 5 is
The sum of integers from 1 to 100 that are divisible by 2 or 5 is
|
IIT 1984 |
|