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1 |
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
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IIT 2007 |
03:01 min
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2 |
If  , then  a) True b) False
If , then a) True b) False
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IIT 1980 |
04:29 min
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3 |
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
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IIT 1999 |
04:34 min
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4 |
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
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IIT 1985 |
01:35 min
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5 |
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)
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IIT 2003 |
01:32 min
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6 |
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)
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IIT 1998 |
01:15 min
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7 |
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
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IIT 1996 |
02:05 min
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8 |
 is equal to
a) 0 b) 4 c) 6 d) −4
is equal to a) 0 b) 4 c) 6 d) −4
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IIT 2004 |
03:15 min
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9 |
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.
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IIT 1982 |
04:48 min
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10 |
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
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IIT 1988 |
02:59 min
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11 |
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
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12 |
Prove that  is divisible by 25 for any natural number n.
Prove that is divisible by 25 for any natural number n.
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IIT 1982 |
03:55 min
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13 |
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)
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IIT 1981 |
05:47 min
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14 |
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.
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IIT 1988 |
04:37 min
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15 |
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)
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IIT 1995 |
04:45 min
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16 |
 is equal to
a) 0 b)  c)  d) None of these
is equal to a) 0 b) c) d) None of these
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IIT 1984 |
01:15 min
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17 |
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)
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IIT 1983 |
06:17 min
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18 |
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.
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IIT 1991 |
03:25 min
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19 |
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
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IIT 1980 |
01:57 min
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20 |
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
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IIT 1991 |
02:34 min
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21 |
Evaluate  a)  b)  c)  d) 
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IIT 1986 |
05:55 min
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22 |
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
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23 |
a) exists and equals  b) exists and equals  c) does not exist because x – 1 → 0 d) does not exist because the left hand limit is not equal to the right hand limit.
a) exists and equals b) exists and equals c) does not exist because x – 1 → 0 d) does not exist because the left hand limit is not equal to the right hand limit.
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IIT 1998 |
03:32 min
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24 |
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
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IIT 1998 |
03:17 min
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25 |
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
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IIT 1992 |
06:01 min
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