1126 |
An urn contains two white and two black balls. A ball is drawn at random. If it is white it is not replaced in the urn. Otherwise it is placed along with the other balls of the same colour. The process is repeated. Find the probability that the third ball drawn is black?
An urn contains two white and two black balls. A ball is drawn at random. If it is white it is not replaced in the urn. Otherwise it is placed along with the other balls of the same colour. The process is repeated. Find the probability that the third ball drawn is black?
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IIT 1987 |
|
1127 |
Solve
Solve
|
IIT 1996 |
|
1128 |
The value of a) –1 b) 0 c) 1 d) i e) None of these
The value of a) –1 b) 0 c) 1 d) i e) None of these
|
IIT 1987 |
|
1129 |
Let z and ω be two complex numbers such that |z| ≤ 1, |ω| ≤ 1 and then z equals a) 1 or i b) i or –i c) 1 or –1 d) i or –1
Let z and ω be two complex numbers such that |z| ≤ 1, |ω| ≤ 1 and then z equals a) 1 or i b) i or –i c) 1 or –1 d) i or –1
|
IIT 1995 |
|
1130 |
In ΔABC, D is the midpoint of BC. If AD is perpendicular to AC then . a) True b) False
In ΔABC, D is the midpoint of BC. If AD is perpendicular to AC then . a) True b) False
|
IIT 1980 |
|
1131 |
A function f : R R where R is the set of real numbers is defined by f (x) = . Find the interval of values of α for which f is onto. Is the function one to one for α = 3? Justify your answer. a) 2 ≤ α ≤ 14 b) α ≥ 2 c) α ≤ 14 d) none of the above
A function f : R R where R is the set of real numbers is defined by f (x) = . Find the interval of values of α for which f is onto. Is the function one to one for α = 3? Justify your answer. a) 2 ≤ α ≤ 14 b) α ≥ 2 c) α ≤ 14 d) none of the above
|
IIT 1996 |
|
1132 |
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 |
|
1133 |
In a triangle ABC, D and E are points on and respectively such that and . Let P be the point of intersection of and . Find using vector method. a) b) c) d) 2
|
IIT 1993 |
|
1134 |
The circles and intersect each other in distinct points if a) r < 2 b) r > 8 c) 2 < r < 8 d) 2 ≤ r ≤ 8
The circles and intersect each other in distinct points if a) r < 2 b) r > 8 c) 2 < r < 8 d) 2 ≤ r ≤ 8
|
IIT 1994 |
|
1135 |
Find three dimensional vectors u1, u2, u3 satisfying u1.u1 = 4; u1.u2 = −2; u1.u3 = 6; u2.u2 = 2; u2.u3 = −5; u3.u3 = 29
Find three dimensional vectors u1, u2, u3 satisfying u1.u1 = 4; u1.u2 = −2; u1.u3 = 6; u2.u2 = 2; u2.u3 = −5; u3.u3 = 29
|
IIT 2001 |
|
1136 |
Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and QR intersect at a point x on the circumference of the circle, then 2r equals a) b) c) d)
Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and QR intersect at a point x on the circumference of the circle, then 2r equals a) b) c) d)
|
IIT 2001 |
|
1137 |
|
IIT 2006 |
|
1138 |
A line is perpendicular to and passes through (0, 1, 0). Then the perpendicular distance of this line from the origin is . . .
A line is perpendicular to and passes through (0, 1, 0). Then the perpendicular distance of this line from the origin is . . .
|
IIT 2006 |
|
1139 |
The smallest positive root of the equation tan x – x = 0 lies in a) b) c) d) e) None of these
The smallest positive root of the equation tan x – x = 0 lies in a) b) c) d) e) None of these
|
IIT 1987 |
|
1140 |
Consider a family of circles passing through two fixed points A (3, 7) and B (6, 5). Show that the chords in which the circle cuts the members of the family are concurrent at a point. Find the coordinates of this point.
Consider a family of circles passing through two fixed points A (3, 7) and B (6, 5). Show that the chords in which the circle cuts the members of the family are concurrent at a point. Find the coordinates of this point.
|
IIT 1993 |
|
1141 |
Find the equation of the circle touching the line 2x + 3y + 1 = 0 at the point (1, −1) and is orthogonal to the circle which has the line segment having end points (0, −1) and (−2, 3) as diameter.
Find the equation of the circle touching the line 2x + 3y + 1 = 0 at the point (1, −1) and is orthogonal to the circle which has the line segment having end points (0, −1) and (−2, 3) as diameter.
|
IIT 2004 |
|
1142 |
The area bounded by the curve y = f(x), the X–axis and the ordinates x = 1, x = b is (b – 1) sin (3b + 4). Then f(x) is a) (x – 1) cos (3x + b) b) sin (3x + 4) c) sin (3x + 4) + 3 (x – 1) cos (3x + 4) d) none of these
The area bounded by the curve y = f(x), the X–axis and the ordinates x = 1, x = b is (b – 1) sin (3b + 4). Then f(x) is a) (x – 1) cos (3x + b) b) sin (3x + 4) c) sin (3x + 4) + 3 (x – 1) cos (3x + 4) d) none of these
|
IIT 2005 |
|
1143 |
Find the area bounded by the curve x2 = 4y and the straight line x = 4y – 2. a) 3/2 b) 3/4 c) 9/4 d) 9/8
Find the area bounded by the curve x2 = 4y and the straight line x = 4y – 2. a) 3/2 b) 3/4 c) 9/4 d) 9/8
|
IIT 1981 |
|
1144 |
If f(x) and g(x) are differentiable functions for 0 ≤ x ≤ 1 such that f(0) = 2, g(0) = 0, f(1) = 6, g(1) = 2 then show that there exists c satisfying 0 < c < 1 and . a) 0 < c < 1 and b) 0 < c < 1 and c) 0 < c < 1 and d) 0 < c < 1 and
If f(x) and g(x) are differentiable functions for 0 ≤ x ≤ 1 such that f(0) = 2, g(0) = 0, f(1) = 6, g(1) = 2 then show that there exists c satisfying 0 < c < 1 and . a) 0 < c < 1 and b) 0 < c < 1 and c) 0 < c < 1 and d) 0 < c < 1 and
|
IIT 1982 |
|
1145 |
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 line M is drawn through A parallel to BD. Point S moves such that the distance from the line BD and the vertex A are equal. If the locus of S cuts M at T2 and T3 and AC at T1, then find the area of △T1T2T3.
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 line M is drawn through A parallel to BD. Point S moves such that the distance from the line BD and the vertex A are equal. If the locus of S cuts M at T2 and T3 and AC at T1, then find the area of △T1T2T3.
|
IIT 2006 |
|
1146 |
Fill in the blank The system of equations will have a non-zero solution if real value of λ is given by …………
Fill in the blank The system of equations will have a non-zero solution if real value of λ is given by …………
|
IIT 1982 |
|
1147 |
Find the area bounded by the curves a) 1/6 b) 1/3 c) π d)
Find the area bounded by the curves a) 1/6 b) 1/3 c) π d)
|
IIT 1986 |
|
1148 |
If the line x – 1 = 0 is the directrix of the parabola y2 – kx + 8 = 0, then one of the values of k is a) b) 8 c) 4 d)
If the line x – 1 = 0 is the directrix of the parabola y2 – kx + 8 = 0, then one of the values of k is a) b) 8 c) 4 d)
|
IIT 2000 |
|
1149 |
Find the area bounded by the curves x2 + y2 = 25, 4y = |4 – x2| and x = 0 above the X–axis. a) b) c) d)
Find the area bounded by the curves x2 + y2 = 25, 4y = |4 – x2| and x = 0 above the X–axis. a) b) c) d)
|
IIT 1987 |
|
1150 |
Compute the area of the region bounded by the curves y = exlnx and a) b) c) d)
Compute the area of the region bounded by the curves y = exlnx and a) b) c) d)
|
IIT 1990 |
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