1 |
and where α, β ε [π, π]. Values of α, β which satisfy both the equations is/are a) 0 b) 1 c) 2 d) 4
and where α, β ε [π, π]. Values of α, β which satisfy both the equations is/are a) 0 b) 1 c) 2 d) 4
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IIT 2005 |
04:42 min
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2 |
Given positive integers r > 1, n > 2 and the coefficients of (3r)th term and (r + 2)th terms in the binomial expansion of (1 + x)2n are equal then a) n = 2r b) n = 2r + 1 c) n = 3r d) none of these
Given positive integers r > 1, n > 2 and the coefficients of (3r)th term and (r + 2)th terms in the binomial expansion of (1 + x)2n are equal then a) n = 2r b) n = 2r + 1 c) n = 3r d) none of these
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IIT 1980 |
03:03 min
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3 |
Let E be the ellipse and C be the circle . Let P and Q be the points (1, 2) and (2, 1) respectively. Then a) Q lies inside C but outside E b) Q lies outside both C and E c) P lies inside both C and E d) P lies inside C but outside E
Let E be the ellipse and C be the circle . Let P and Q be the points (1, 2) and (2, 1) respectively. Then a) Q lies inside C but outside E b) Q lies outside both C and E c) P lies inside both C and E d) P lies inside C but outside E
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IIT 1994 |
04:15 min
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4 |
If , then a) True b) False
If , then a) True b) False
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IIT 1980 |
04:29 min
|
5 |
If in the expansion of (1 + x)m (1 – x)n, the coefficients of x and x2 are 3 and –6 respectively. then m is a) 6 b) 9 c) 12 d) 24
If in the expansion of (1 + x)m (1 – x)n, the coefficients of x and x2 are 3 and –6 respectively. then m is a) 6 b) 9 c) 12 d) 24
|
IIT 1999 |
04:34 min
|
6 |
If tangents are drawn to the ellipse then the locus of the mid-points of the intercepts made by the tangents between the coordinate axes is a) b) c) d)
If tangents are drawn to the ellipse then the locus of the mid-points of the intercepts made by the tangents between the coordinate axes is a) b) c) d)
|
IIT 2004 |
03:11 min
|
7 |
Suppose is an identity in x where are constants and . Then the value of n = ………. a) 4 b) 5 c) 6 d) 7
Suppose is an identity in x where are constants and . Then the value of n = ………. a) 4 b) 5 c) 6 d) 7
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IIT 1981 |
02:56 min
|
8 |
Prove that is divisible by 25 for any natural number n.
Prove that is divisible by 25 for any natural number n.
|
IIT 1982 |
03:55 min
|
9 |
Let P be a variable point on the ellipse with foci F1 and F2. . If A is the area of then the maximum value of A is . . . . .
Let P be a variable point on the ellipse with foci F1 and F2. . If A is the area of then the maximum value of A is . . . . .
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IIT 1994 |
02:27 min
|
10 |
The equation represents a) An ellipse b) A hyperbola c) A circle d) None of these
The equation represents a) An ellipse b) A hyperbola c) A circle d) None of these
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IIT 1981 |
01:03 min
|
11 |
The equation has a) No solution b) One solution c) More than one real solution d) Cannot be said
The equation has a) No solution b) One solution c) More than one real solution d) Cannot be said
|
IIT 1980 |
01:57 min
|
12 |
For the hyperbola which of the following remains constant with change in α a) Abscissae of vertices b) Abscissae of focii c) Eccentricity d) Directrix
For the hyperbola which of the following remains constant with change in α a) Abscissae of vertices b) Abscissae of focii c) Eccentricity d) Directrix
|
IIT 2003 |
01:32 min
|
13 |
The number of solutions of the equation a) 0 b) 1 c) 2 d) Infinitely many
The number of solutions of the equation a) 0 b) 1 c) 2 d) Infinitely many
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IIT 1990 |
01:46 min
|
14 |
The number of values of x in the interval (0, 5π) satisfying the equation is a) 0 b) 5 c) 6 d) 10
The number of values of x in the interval (0, 5π) satisfying the equation is a) 0 b) 5 c) 6 d) 10
|
IIT 1998 |
03:17 min
|
15 |
Find the natural number a for which where the function f satisfies the relation f (x + y) = f (x).f(y)for all natural numbers x and y and further f (1) = 2
Find the natural number a for which where the function f satisfies the relation f (x + y) = f (x).f(y)for all natural numbers x and y and further f (1) = 2
|
IIT 1992 |
06:01 min
|
16 |
India played two matches each with Australia and West indies. In any match the probability of India getting the points 0, 1, and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least seven points is a) 0.8730 b) 0.0875 c) 0.0625 d) 0.0250
India played two matches each with Australia and West indies. In any match the probability of India getting the points 0, 1, and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least seven points is a) 0.8730 b) 0.0875 c) 0.0625 d) 0.0250
|
IIT 1992 |
03:03 min
|
17 |
If α + β = and β + γ = α, then tanα equals a) 2(tanβ + tanγ) b) tanβ + tanγ c) tanβ + 2tanγ d) 2tanβ + tanγ
If α + β = and β + γ = α, then tanα equals a) 2(tanβ + tanγ) b) tanβ + tanγ c) tanβ + 2tanγ d) 2tanβ + tanγ
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IIT 2001 |
02:03 min
|
18 |
Let n be a positive integer and (1 + x + x2)n = a0 + a1x + a2x + a2x2 + . . . + a2nx2n then prove that
Let n be a positive integer and (1 + x + x2)n = a0 + a1x + a2x + a2x2 + . . . + a2nx2n then prove that
|
IIT 1994 |
06:48 min
|
19 |
Three of the vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equals a) b) c) d)
Three of the vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equals a) b) c) d)
|
IIT 1995 |
02:30 min
|
20 |
If are complementary events E and F respectively and if 0 < p(E) < 1, then a) b) c) d)
If are complementary events E and F respectively and if 0 < p(E) < 1, then a) b) c) d)
|
IIT 1998 |
01:47 min
|
21 |
The larger of 9950 + 10050 and 10150 is
The larger of 9950 + 10050 and 10150 is
|
IIT 1982 |
04:38 min
|
22 |
The numbers are selected from the set S = {1, 2, 3, 4, 5, 6} without replacement one by one. Probability that the minimum of the two numbers is less than 4 is a) b) c) d)
The numbers are selected from the set S = {1, 2, 3, 4, 5, 6} without replacement one by one. Probability that the minimum of the two numbers is less than 4 is a) b) c) d)
|
IIT 2003 |
03:06 min
|
23 |
One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is a) b) c) d)
One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is a) b) c) d)
|
IIT 2007 |
09:20 min
|
24 |
Find all solutions of in a) b) c) d)
Find all solutions of in a) b) c) d)
|
IIT 1984 |
03:20 min
|
25 |
Let f (x) = sin x and g (x) = ln|x|. If the range of the composition functions fog and gof are R1 and R2 respectively, then a) R1 = [ u : −1 ≤ u < 1], R2 = [ v : − < v < 0 ] b) R1 = [ u : − < u < 0 ], R2 = [ v : −1 ≤ v ≤ 0] c) R1 = [ u : −1 < u < 1], R2 = [ v : − < v < 0 ] d) R1 = [ u : −1 ≤ u ≤ 1], R2 = [ v : − < v ≤ 0 ]
Let f (x) = sin x and g (x) = ln|x|. If the range of the composition functions fog and gof are R1 and R2 respectively, then a) R1 = [ u : −1 ≤ u < 1], R2 = [ v : − < v < 0 ] b) R1 = [ u : − < u < 0 ], R2 = [ v : −1 ≤ v ≤ 0] c) R1 = [ u : −1 < u < 1], R2 = [ v : − < v < 0 ] d) R1 = [ u : −1 ≤ u ≤ 1], R2 = [ v : − < v ≤ 0 ]
|
IIT 1994 |
03:03 min
|