851 |
Range of ; x ℝ is a) (1, ∞) b) c) d)
Range of ; x ℝ is a) (1, ∞) b) c) d)
|
IIT 2003 |
|
852 |
If where . Given F(5) = 5, then f(10) is equal to a) 5 b) 10 c) 0 d) 15
If where . Given F(5) = 5, then f(10) is equal to a) 5 b) 10 c) 0 d) 15
|
IIT 2006 |
|
853 |
Subjective problems Let . Find all real values of x for which y takes real values. a) [− 1, 2) b) [3, ∞) c) [− 1, 2) ∪ [3, ∞) d) None of the above
Subjective problems Let . Find all real values of x for which y takes real values. a) [− 1, 2) b) [3, ∞) c) [− 1, 2) ∪ [3, ∞) d) None of the above
|
IIT 1980 |
|
854 |
Let R be the set of real numbers and f : R → R be such that for all x and y in R, . Prove that f(x) is constant.
Let R be the set of real numbers and f : R → R be such that for all x and y in R, . Prove that f(x) is constant.
|
IIT 1988 |
|
855 |
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 |
|
856 |
If f1(x) and f2(x) are defined by domains D1 and D2 respectively then f1(x) + f2(x) is defined as on D1 ⋂ D2 a) True b) False
If f1(x) and f2(x) are defined by domains D1 and D2 respectively then f1(x) + f2(x) is defined as on D1 ⋂ D2 a) True b) False
|
IIT 1988 |
|
857 |
If then the domain of f(x) is
If then the domain of f(x) is
|
IIT 1985 |
|
858 |
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 |
|
859 |
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 |
|
860 |
Let f(x) be a non constant differentiable function defined on (−∞, ∞) such that f(x) = f(1 – x) and then a) vanishes at twice an (0, 1) b) c) d)
Let f(x) be a non constant differentiable function defined on (−∞, ∞) such that f(x) = f(1 – x) and then a) vanishes at twice an (0, 1) b) c) d)
|
IIT 2008 |
|
861 |
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 |
|
862 |
A ladder rests against a wall at an angle α to the horizontal. If its foot is pulled away from the wall through a distance a, so that it slides a distance b down the wall making an angle β with the horizontal, then . a) True b) False
A ladder rests against a wall at an angle α to the horizontal. If its foot is pulled away from the wall through a distance a, so that it slides a distance b down the wall making an angle β with the horizontal, then . a) True b) False
|
IIT 1985 |
|
863 |
Let be the vertices of an n sided regular polygon such that . Then find n. a) 5 b) 6 c) 7 d) 8
Let be the vertices of an n sided regular polygon such that . Then find n. a) 5 b) 6 c) 7 d) 8
|
IIT 1994 |
|
864 |
A variable plane at a distance of one unit from the origin cuts the coordinate axes at A, B and C. If the centroid D(x, y, z) of triangle ABC satisfies the relation then the value of k is a) 9 b) c) 1 d) 3
A variable plane at a distance of one unit from the origin cuts the coordinate axes at A, B and C. If the centroid D(x, y, z) of triangle ABC satisfies the relation then the value of k is a) 9 b) c) 1 d) 3
|
IIT 2005 |
|
865 |
Find the equation of the plane passing through the points (2, 1, 0), (4, 1, 1), (5, 0, 1). Find the point Q such that its distance from the plane is equal to the point P(2, 1, 6) from the plane and the line joining P and Q is perpendicular to the plane.
Find the equation of the plane passing through the points (2, 1, 0), (4, 1, 1), (5, 0, 1). Find the point Q such that its distance from the plane is equal to the point P(2, 1, 6) from the plane and the line joining P and Q is perpendicular to the plane.
|
IIT 2003 |
|
866 |
The unit vector perpendicular to the plane determined by is.
The unit vector perpendicular to the plane determined by is.
|
IIT 1983 |
|
867 |
Show that =
Show that =
|
IIT 1985 |
|
868 |
For all A, B, C, P, Q, R show that = 0
For all A, B, C, P, Q, R show that = 0
|
IIT 1996 |
|
869 |
Let a, b, c be real numbers with a2 + b2 + c2 = 1. Show that the equation represents a straight line = 0
Let a, b, c be real numbers with a2 + b2 + c2 = 1. Show that the equation represents a straight line = 0
|
IIT 2001 |
|
870 |
Find the integral solutions of the following system of inequality a) x = 1 b) x = 2 c) x = 3 d) x = 4
Find the integral solutions of the following system of inequality a) x = 1 b) x = 2 c) x = 3 d) x = 4
|
IIT 1979 |
|
871 |
mn squares of equal size are arranged to form a rectangle of dimension m by n, where m and n are natural numbers. Two squares will be called neighbours if they have exactly one common side. A natural number is written in each square such that the number written in any square is the arithmetic mean of the numbers written in the neighbouring squares. Show that this is possible only if all the numbers used are equal.
mn squares of equal size are arranged to form a rectangle of dimension m by n, where m and n are natural numbers. Two squares will be called neighbours if they have exactly one common side. A natural number is written in each square such that the number written in any square is the arithmetic mean of the numbers written in the neighbouring squares. Show that this is possible only if all the numbers used are equal.
|
IIT 1982 |
|
872 |
Let A = AU1 = , AU2 = and AU3 = a) 3 b) −3 c) d) 2
Let A = AU1 = , AU2 = and AU3 = a) 3 b) −3 c) d) 2
|
IIT 2006 |
|
873 |
Let a, b, c, ε R and α, β be roots of such that and then show that .
|
IIT 1995 |
|
874 |
The real numbers x1, x2, x3 satisfying the equation x3 – x2 + βx + γ = 0 are in Arithmetic Progression. Find the interval in which β and γ lie.
The real numbers x1, x2, x3 satisfying the equation x3 – x2 + βx + γ = 0 are in Arithmetic Progression. Find the interval in which β and γ lie.
|
IIT 1996 |
|
875 |
Number of solutions of lying in the interval is a) 0 b) 1 c) 2 d) 3
Number of solutions of lying in the interval is a) 0 b) 1 c) 2 d) 3
|
IIT 1993 |
|