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51 |
A box contains two 50 paise coins, 5 twenty five paise coins and a certain number N(≥ 2) of ten and five paise coins. Five coins are taken out of the box at random. Find the probability that the total value of these coins is less than one rupee and 50 paise.
A box contains two 50 paise coins, 5 twenty five paise coins and a certain number N(≥ 2) of ten and five paise coins. Five coins are taken out of the box at random. Find the probability that the total value of these coins is less than one rupee and 50 paise.
|
IIT 1988 |
06:49 min
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|
52 |
 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
|
IIT 2005 |
04:42 min
|
|
53 |
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
|
IIT 1980 |
03:03 min
|
|
54 |
The number of distinct real values of λ for which  are coplanar is a) Zero b) One c) Two d) three
The number of distinct real values of λ for which are coplanar is a) Zero b) One c) Two d) three
|
IIT 2007 |
03:01 min
|
|
55 |
If  , then  a) True b) False
If , then a) True b) False
|
IIT 1980 |
04:29 min
|
|
56 |
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
|
|
57 |
If  then  at x = e is . . . a) 0 b)  c) e d) 1
If then at x = e is . . . a) 0 b) c) e d) 1
|
IIT 1985 |
01:35 min
|
|
58 |
If  then the expression for  in terms of  is a)  b)  c)  d) 
If then the expression for in terms of is a) b) c) d)
|
IIT 2003 |
01:32 min
|
|
59 |
Multiple choice Which of the following expressions are meaningful a)  b)  c)  d) 
Multiple choice Which of the following expressions are meaningful a) b) c) d)
|
IIT 1998 |
01:15 min
|
|
60 |
If  then at x = 0,  is equal to a) 0 b) 1 c) 2 d) 4
If then at x = 0, is equal to a) 0 b) 1 c) 2 d) 4
|
IIT 1996 |
02:05 min
|
|
61 |
 is equal to
a) 0 b) 4 c) 6 d) −4
is equal to a) 0 b) 4 c) 6 d) −4
|
IIT 2004 |
03:15 min
|
|
62 |
Find all values of λ such that  and  where  are unit vectors along the coordinate vectors.
Find all values of λ such that and where are unit vectors along the coordinate vectors.
|
IIT 1982 |
04:48 min
|
|
63 |
The complex numbers sinx + icos2x and cosx – isin2x are conjugate to each other for a) a = nπ b) x = 0 c) x =  d) None of these
The complex numbers sinx + icos2x and cosx – isin2x are conjugate to each other for a) a = nπ b) x = 0 c) x = d) None of these
|
IIT 1988 |
02:59 min
|
|
64 |
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
|
IIT 1981 |
02:56 min
|
|
65 |
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
|
|
66 |
Evaluate  where n is a positive integer and t is a parameter independent of x. a)  b)  c)  d) 
Evaluate where n is a positive integer and t is a parameter independent of x. a) b) c) d)
|
IIT 1981 |
05:47 min
|
|
67 |
Let OABC be a parallelogram with O as the origin and OC a diagonal. Let D be the midpoint of OA. Using vector method, prove that BD and CO intersect in the same ratio.
Let OABC be a parallelogram with O as the origin and OC a diagonal. Let D be the midpoint of OA. Using vector method, prove that BD and CO intersect in the same ratio.
|
IIT 1988 |
04:37 min
|
|
68 |
For positive integers n1 and n2 the value of the expression  where  is real if and only if a)  b)  c)  d) 
For positive integers n1 and n2 the value of the expression where is real if and only if a) b) c) d)
|
IIT 1995 |
04:45 min
|
|
69 |
 is equal to
a) 0 b)  c)  d) None of these
is equal to a) 0 b) c) d) None of these
|
IIT 1984 |
01:15 min
|
|
70 |
Find the area bounded by the X - axis, part of the curve  and the ordinate at x = 2 and x = 4. If the ordinate at x = a divide the area into two equal parts, find a, a)  b)  c)  d) 
Find the area bounded by the X - axis, part of the curve and the ordinate at x = 2 and x = 4. If the ordinate at x = a divide the area into two equal parts, find a, a) b) c) d)
|
IIT 1983 |
06:17 min
|
|
71 |
Determine the value of c so that for all real x the vector cx and  make an obtuse angle with each other.
Determine the value of c so that for all real x the vector cx and make an obtuse angle with each other.
|
IIT 1991 |
03:25 min
|
|
72 |
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
|
|
73 |
The value of  is a) 1 b) – 1 c) 0 d) None of these
The value of is a) 1 b) – 1 c) 0 d) None of these
|
IIT 1991 |
02:34 min
|
|
74 |
Evaluate  a)  b)  c)  d) 
|
IIT 1986 |
05:55 min
|
|
75 |
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
|
IIT 1990 |
01:46 min
|
