1026 |
Find the interval in which ‘a’ lies for which the line y + x = 0 bisects the chord drawn from the point to the circle
Find the interval in which ‘a’ lies for which the line y + x = 0 bisects the chord drawn from the point to the circle
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IIT 1996 |
|
1027 |
The points on the curve where the tangent is vertical, is (are) a) b) c) d)
The points on the curve where the tangent is vertical, is (are) a) b) c) d)
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IIT 2002 |
|
1028 |
Let T1, T2 be two tangents drawn from (−2, 0) onto the circle C: x2 + y2 = 1. Determine the circle touching C and having T1, T2 as their pair of tangents. Further find the equation of all possible common tangents to the circles, when taken two at a time.
Let T1, T2 be two tangents drawn from (−2, 0) onto the circle C: x2 + y2 = 1. Determine the circle touching C and having T1, T2 as their pair of tangents. Further find the equation of all possible common tangents to the circles, when taken two at a time.
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IIT 1999 |
|
1029 |
If α, β are roots of and γ, δ are roots of then evaluate in terms of p, q, r, s.
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IIT 1979 |
|
1030 |
For what values of m does the system of equations 3x + my = m, 2x – 5y = 20 have solutions satisfying x > 0, y > 0? a) m ε ( b) m ε ( c) m ε ( ∪ ( d) m ε (
For what values of m does the system of equations 3x + my = m, 2x – 5y = 20 have solutions satisfying x > 0, y > 0? a) m ε ( b) m ε ( c) m ε ( ∪ ( d) m ε (
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IIT 1980 |
|
1031 |
Find the centre and radius of the circle formed by all the points represented by satisfying the relation where α and β are complex numbers given by
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IIT 2004 |
|
1032 |
Three circles of radii 3, 4 and 5 units touch each other externally and tangents drawn at the points of contact intersect at P. Find the distance between P and the point of contact.
Three circles of radii 3, 4 and 5 units touch each other externally and tangents drawn at the points of contact intersect at P. Find the distance between P and the point of contact.
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IIT 2005 |
|
1033 |
a) ln2 b) ln3 c) ln6 d) ln2 ln3
a) ln2 b) ln3 c) ln6 d) ln2 ln3
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IIT 1980 |
|
1034 |
Use the function , x > 0 to determine the bigger of the numbers eπ and πe. a) eπ b) πe
Use the function , x > 0 to determine the bigger of the numbers eπ and πe. a) eπ b) πe
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IIT 1981 |
|
1035 |
Find the area of the region bounded by the X–axis and the curve defined by a) ln2 b) 2ln2 c) d)
Find the area of the region bounded by the X–axis and the curve defined by a) ln2 b) 2ln2 c) d)
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IIT 1984 |
|
1036 |
Let ABCD be a square with side of length 2 units. C2 is the circle through the vertices A, B, C, D and C1 is the circle touching all the sides of the square ABCD. L is a line through A. A circle touching the line L and the circle C1 externally such that both the circles are on the same side of the line, then the locus of the centre of circle is a) Ellipse b) Hyperbola c) Parabola d) Pair of straight lines
Let ABCD be a square with side of length 2 units. C2 is the circle through the vertices A, B, C, D and C1 is the circle touching all the sides of the square ABCD. L is a line through A. A circle touching the line L and the circle C1 externally such that both the circles are on the same side of the line, then the locus of the centre of circle is a) Ellipse b) Hyperbola c) Parabola d) Pair of straight lines
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IIT 2006 |
|
1037 |
Let f(x) = x3 – x2 + x + 1 and Discuss the continuity and differentiability of f(x) in the interval (0, 2) a) Continuous and differentiable in (0, 2) b) Continuous and differentiable in (0, 2)except x = 1 c) Continuous in (0, 2). Differentiable in (0, 2) except x = 1 d) None of the above
Let f(x) = x3 – x2 + x + 1 and Discuss the continuity and differentiability of f(x) in the interval (0, 2) a) Continuous and differentiable in (0, 2) b) Continuous and differentiable in (0, 2)except x = 1 c) Continuous in (0, 2). Differentiable in (0, 2) except x = 1 d) None of the above
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IIT 1985 |
|
1038 |
Find the point on the curve 4x2 + a2y2 = 4a2, 4 < a2 < 8 that is farthest from the point (0, −2). a) (a, 0) b) c) d) (0, - 2)
Find the point on the curve 4x2 + a2y2 = 4a2, 4 < a2 < 8 that is farthest from the point (0, −2). a) (a, 0) b) c) d) (0, - 2)
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IIT 1987 |
|
1039 |
The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix a) x = −a b) c) d)
The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix a) x = −a b) c) d)
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IIT 2002 |
|
1040 |
Match the following Let Column 1 | Column 2 | i) If then f (x) satisfies | A) | ii) If then f (x) satisfies | B) | iii) If then f (x) satisfies | C) | iv) If then f (x) satisfies | D) |
Match the following Let Column 1 | Column 2 | i) If then f (x) satisfies | A) | ii) If then f (x) satisfies | B) | iii) If then f (x) satisfies | C) | iv) If then f (x) satisfies | D) |
|
IIT 2007 |
|
1041 |
Let p be the first of the n Arithmetic Means between two numbers and q be the first of n Harmonic Means between the same numbers. Then show that q does not lie between p and
Let p be the first of the n Arithmetic Means between two numbers and q be the first of n Harmonic Means between the same numbers. Then show that q does not lie between p and
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IIT 1991 |
|
1042 |
Find all maximum and minimum of the curve y = x(x – 1)2, 0 ≤ x ≤ 2. Also find the area bounded by the curve y = x(x – 2)2, the Y–axis and the line y = 2. a) Local minimum at x = 1, Local maximum at x = , Area = b) Local minimum at x = , Local maximum at x =1, Area = c) Local minimum at x = 2, Local maximum at x = , Area = d) Local minimum at x = , Local maximum at x =2, Area =
Find all maximum and minimum of the curve y = x(x – 1)2, 0 ≤ x ≤ 2. Also find the area bounded by the curve y = x(x – 2)2, the Y–axis and the line y = 2. a) Local minimum at x = 1, Local maximum at x = , Area = b) Local minimum at x = , Local maximum at x =1, Area = c) Local minimum at x = 2, Local maximum at x = , Area = d) Local minimum at x = , Local maximum at x =2, Area =
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IIT 1989 |
|
1043 |
The curve y = ax3 + bx2 + cx + 5 touches the X – axis at (− 2, 0) and cuts the Y–axis at a point Q where the gradient is 3. Find a, b, c. a) b) c) d)
The curve y = ax3 + bx2 + cx + 5 touches the X – axis at (− 2, 0) and cuts the Y–axis at a point Q where the gradient is 3. Find a, b, c. a) b) c) d)
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IIT 1994 |
|
1044 |
Points A, B, C lie on the parabola . The tangents to the parabola at A, B, C taken in pair intersect at the points P, Q, R. Determine the ratios of the areas of ΔABC and ΔPQR.
Points A, B, C lie on the parabola . The tangents to the parabola at A, B, C taken in pair intersect at the points P, Q, R. Determine the ratios of the areas of ΔABC and ΔPQR.
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IIT 1996 |
|
1045 |
Let a line passing through the fixed point (h, k) cut the X–axis at P and Y–axis at Q. Then find the minimum area of ΔOPQ. a) hk b) h2/k c) k2/h d) 2hk
Let a line passing through the fixed point (h, k) cut the X–axis at P and Y–axis at Q. Then find the minimum area of ΔOPQ. a) hk b) h2/k c) k2/h d) 2hk
|
IIT 1995 |
|
1046 |
Let An be the area bounded by the curve y = (tanx)n and the line x = 0, y = 0 and . Prove that for . Hence deduce that
|
IIT 1996 |
|
1047 |
If the curve y = f(x) passes through the point (1, −1) and satisfies the differential equation y(1 + xy) dx = xdy then is equal to a) b) c) d)
If the curve y = f(x) passes through the point (1, −1) and satisfies the differential equation y(1 + xy) dx = xdy then is equal to a) b) c) d)
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IIT 2016 |
|
1048 |
One or more than one correct options Let f : (0, ∞) → ℝ be a differentiable function such that for all x ∈ (0, ∞) and f(1) ≠ 1. Then a) b) c) d)
One or more than one correct options Let f : (0, ∞) → ℝ be a differentiable function such that for all x ∈ (0, ∞) and f(1) ≠ 1. Then a) b) c) d)
|
IIT 2016 |
|
1049 |
A curve passes through the point . Let the slope of the curve at each point (x, y) is , x > 0. Then the equation of the curve is a) b) c) d)
A curve passes through the point . Let the slope of the curve at each point (x, y) is , x > 0. Then the equation of the curve is a) b) c) d)
|
IIT 2013 |
|
1050 |
Let f:[0, 1] → ℝ (the set all real numbers)be a function. Suppose the function is twice differentiable, f(0) = f(1) = 0 and satisfiesf′′(x) – 2f′(x) + f(x) ≥ ex, x ∈ [0, 1]Which of the following is true? a) b) c) d)
Let f:[0, 1] → ℝ (the set all real numbers)be a function. Suppose the function is twice differentiable, f(0) = f(1) = 0 and satisfiesf′′(x) – 2f′(x) + f(x) ≥ ex, x ∈ [0, 1]Which of the following is true? a) b) c) d)
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IIT 2013 |
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