851 |
The real roots of the equation x + = 1 in the interval (−π, π) are …........... a) x = 0 b) x = ± c) x = 0 , x = ±
The real roots of the equation x + = 1 in the interval (−π, π) are …........... a) x = 0 b) x = ± c) x = 0 , x = ±
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IIT 1997 |
|
852 |
The domain of the derivative of the function f (x) = a) R { 0 } b) R c) R d) R
The domain of the derivative of the function f (x) = a) R { 0 } b) R c) R d) R
|
IIT 2002 |
|
853 |
The greater of the two angles and is a) A b) B c) Both are equal
The greater of the two angles and is a) A b) B c) Both are equal
|
IIT 1989 |
|
854 |
If f (x) = sinx + cosx, g (x) = x2 – 1 then g ( f (x)) is invertible in the domain a) b) c) d)
If f (x) = sinx + cosx, g (x) = x2 – 1 then g ( f (x)) is invertible in the domain a) b) c) d)
|
IIT 2004 |
|
855 |
One or more correct answers In a triangle the length of the two larger sides are 10 and 9 respectively. If the angles are in arithmetic progression then the length of the third side can be a) b) c) 5 d) e) None of these
One or more correct answers In a triangle the length of the two larger sides are 10 and 9 respectively. If the angles are in arithmetic progression then the length of the third side can be a) b) c) 5 d) e) None of these
|
IIT 1987 |
|
856 |
Let f (x) = Ax2 + Bx + C where A, B , C are real numbers. Prove that if f (x) is an integer then the numbers 2A, A + B and C are all integers. Conversely prove that if the numbers 2A, A + B and C are all integers then f ( x ) is an integer whenever x is an integer.
Let f (x) = Ax2 + Bx + C where A, B , C are real numbers. Prove that if f (x) is an integer then the numbers 2A, A + B and C are all integers. Conversely prove that if the numbers 2A, A + B and C are all integers then f ( x ) is an integer whenever x is an integer.
|
IIT 1998 |
|
857 |
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 |
|
858 |
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 |
|
859 |
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 |
|
860 |
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 |
|
861 |
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 |
|
862 |
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 |
|
863 |
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 |
|
864 |
The unit vector perpendicular to the plane determined by is.
The unit vector perpendicular to the plane determined by is.
|
IIT 1983 |
|
865 |
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 |
|
866 |
Show that =
Show that =
|
IIT 1985 |
|
867 |
For all A, B, C, P, Q, R show that = 0
For all A, B, C, P, Q, R show that = 0
|
IIT 1996 |
|
868 |
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 |
|
869 |
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
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IIT 1979 |
|
870 |
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 |
|
871 |
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
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IIT 2006 |
|
872 |
Let a, b, c, ε R and α, β be roots of such that and then show that .
|
IIT 1995 |
|
873 |
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 |
|
874 |
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 |
|
875 |
If three complex numbers are in Arithmetic Progression, then they lie on a circle in a complex plane. a) True b) False
If three complex numbers are in Arithmetic Progression, then they lie on a circle in a complex plane. a) True b) False
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IIT 1985 |
|