826 |
The value of . Given that a, x, y, z, b are in Arithmetic Progression while the value of . If a, x, y, z, b are in Harmonic Progression then find a and b.
The value of . Given that a, x, y, z, b are in Arithmetic Progression while the value of . If a, x, y, z, b are in Harmonic Progression then find a and b.
|
IIT 1978 |
|
827 |
If S1, S2, . . . .,Sn are the sums of infinite geometric series whose first terms are 1, 2, 3, . . ., n and whose common ratios are respectively, then find the value of
If S1, S2, . . . .,Sn are the sums of infinite geometric series whose first terms are 1, 2, 3, . . ., n and whose common ratios are respectively, then find the value of
|
IIT 1991 |
|
828 |
Let a, b are real positive numbers. If a, A1, A2, b are in Arithmetic Progression, a, G1, G2, b are in Geometric Progression and a, H1, H2, b are in Harmonic Progression show that
Let a, b are real positive numbers. If a, A1, A2, b are in Arithmetic Progression, a, G1, G2, b are in Geometric Progression and a, H1, H2, b are in Harmonic Progression show that
|
IIT 2002 |
|
829 |
Consider the lines ; The unit vector perpendicular to both L1 and L2 is a) b) c) d)
Consider the lines ; The unit vector perpendicular to both L1 and L2 is a) b) c) d)
|
IIT 2008 |
|
830 |
The differential equation determines a family of circles with a) Variable radii and a fixed centre ( 0, 1) b) Variable radii and a fixed centre ( 0, -1) c) Fixed radius and a variable centre along the X-axis d) Fixed radius and a variable centre along the Y-axis
The differential equation determines a family of circles with a) Variable radii and a fixed centre ( 0, 1) b) Variable radii and a fixed centre ( 0, -1) c) Fixed radius and a variable centre along the X-axis d) Fixed radius and a variable centre along the Y-axis
|
IIT 2007 |
|
831 |
If and , then show that
|
IIT 1989 |
|
832 |
Let u (x) and v (x) satisfy the differential equations and where p (x), f (x) and g (x) are continuous functions. If u (x1) > v (x1) for some x1 and f (x) > g (x) for all x > x1, prove that at any point (x, y) where x > x1 does not satisfy the equations y = u (x) and y = v (x)
|
IIT 1997 |
|
833 |
is
is
|
IIT 2006 |
|
834 |
Let f(x) = |x – 1|, then a) b) c) d) None of these
Let f(x) = |x – 1|, then a) b) c) d) None of these
|
IIT 1983 |
|
835 |
Let , then the set is a) b) c) d) ϕ
Let , then the set is a) b) c) d) ϕ
|
IIT 1995 |
|
836 |
If f(x) = 3x – 5 then a) is given by b) is given by c) does not exist because f is not one-one d) does not exist because f is not onto
If f(x) = 3x – 5 then a) is given by b) is given by c) does not exist because f is not one-one d) does not exist because f is not onto
|
IIT 1998 |
|
837 |
The domain of definition of is a) b) c) d)
The domain of definition of is a) b) c) d)
|
IIT 2001 |
|
838 |
Let f : ℝ → ℝ be defined by f(x) = 2x + sinx for all x ℝ. Then f is a) One to one and onto b) One to one but not onto c) Onto but not one to one d) Neither one to one nor onto
Let f : ℝ → ℝ be defined by f(x) = 2x + sinx for all x ℝ. Then f is a) One to one and onto b) One to one but not onto c) Onto but not one to one d) Neither one to one nor onto
|
IIT 2002 |
|
839 |
Range of ; x ℝ is a) (1, ∞) b) c) d)
Range of ; x ℝ is a) (1, ∞) b) c) d)
|
IIT 2003 |
|
840 |
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 |
|
841 |
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 |
|
842 |
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 |
|
843 |
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 |
|
844 |
If then the domain of f(x) is
If then the domain of f(x) is
|
IIT 1985 |
|
845 |
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 |
|
846 |
Let n be an odd integer. If sin nθ = for every value of θ, then a) = 1, = 3 b) = 0, = n c) = −1, = n d) = 1, =
|
IIT 1998 |
|
847 |
Multiple choices Let and (x is measured in radians) then x lies in the interval a) b) c) d)
Multiple choices Let and (x is measured in radians) then x lies in the interval a) b) c) d)
|
IIT 1994 |
|
848 |
lies between –4 and 10. a) True b) False
lies between –4 and 10. a) True b) False
|
IIT 1979 |
|
849 |
Let and be three non-zero vectors such that c is a unit vector perpendicular to both the vectors a and b and the angle between the vectors a and b is then is equal to a) 1 b) c) d) None of these
Let and be three non-zero vectors such that c is a unit vector perpendicular to both the vectors a and b and the angle between the vectors a and b is then is equal to a) 1 b) c) d) None of these
|
IIT 1986 |
|
850 |
Determine the smallest positive value of x (in degrees) for which a) 30° b) 50° c) 55° d) 60°
Determine the smallest positive value of x (in degrees) for which a) 30° b) 50° c) 55° d) 60°
|
IIT 1993 |
|