101 |
If a, b, c are in Geometric Progression then the equations have a common root if are in a) Arithmetic Progression b) Geometric Progression c) Harmonic Progression d) None of these
If a, b, c are in Geometric Progression then the equations have a common root if are in a) Arithmetic Progression b) Geometric Progression c) Harmonic Progression d) None of these
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IIT 1985 |
03:08 min
|
102 |
The circle intersects hyperbola in four points then a)  b)  c)  d) 
The circle intersects hyperbola in four points then a)  b)  c)  d) 
|
IIT 1998 |
02:27 min
|
103 |
Solve for x in the following equation
Solve for x in the following equation
|
IIT 1987 |
07:03 min
|
104 |
Let Tr be the rth term of an Arithmetic Progression for If for some positive integers m, n we have and then Tmn equals a)  b)  c)  d) 
Let Tr be the rth term of an Arithmetic Progression for If for some positive integers m, n we have and then Tmn equals a)  b)  c)  d) 
|
IIT 1998 |
01:51 min
|
105 |
The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2 then is a) 0.4 b) 0.8 c) 1.2 d) 1.4
The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2 then is a) 0.4 b) 0.8 c) 1.2 d) 1.4
|
IIT 1987 |
02:39 min
|
106 |
Consider an infinite geometric series with first term a and common ratio r. If its sum is four and the second term is then a)  b)  c)  d) 
Consider an infinite geometric series with first term a and common ratio r. If its sum is four and the second term is then a)  b)  c)  d) 
|
IIT 2000 |
01:48 min
|
107 |
The probability of India winning a test match against West Indies is ½. Assuming independence of outcomes in each match, the probability that in a 5 test match series India’s second win will occur in the third test is a)  b)  c)  d) 
The probability of India winning a test match against West Indies is ½. Assuming independence of outcomes in each match, the probability that in a 5 test match series India’s second win will occur in the third test is a)  b)  c)  d) 
|
IIT 1995 |
02:40 min
|
108 |
For every positive integer n, prove that Hence or otherwise prove that Where [ ] denotes greatest integer not exceeding x.
For every positive integer n, prove that Hence or otherwise prove that Where [ ] denotes greatest integer not exceeding x.
|
IIT 2000 |
03:07 min
|
109 |
If are positive real numbers whose product is a fixed number c then the minimum value of is a)  b)  c)  d) 
If are positive real numbers whose product is a fixed number c then the minimum value of is a)  b)  c)  d) 
|
IIT 2002 |
01:19 min
|
110 |
If from each of the three boxes containing 3 white and one black; 2 white and 2 black; 1 white and 3 black balls, one ball is drawn at random then the probability that 2 white and 1 black ball will be drawn is a)  b)  c)  d) 
If from each of the three boxes containing 3 white and one black; 2 white and 2 black; 1 white and 3 black balls, one ball is drawn at random then the probability that 2 white and 1 black ball will be drawn is a)  b)  c)  d) 
|
IIT 1998 |
02:35 min
|
111 |
Let a and b the roots of the equation and those of are c and d, then find the value of a + b + c + d when a ≠ b ≠ c ≠ d.
Let a and b the roots of the equation and those of are c and d, then find the value of a + b + c + d when a ≠ b ≠ c ≠ d.
|
IIT 2006 |
06:39 min
|
112 |
=  a) True b) False
=  a) True b) False
|
IIT 1985 |
04:05 min
|
113 |
The scalar equals a) 0 b)  c)  d) None of these
The scalar equals a) 0 b)  c)  d) None of these
|
IIT 1981 |
02:30 min
|
114 |
Fill in the blanks If is a root of the equation where p and q are real then (p, q) …………
Fill in the blanks If is a root of the equation where p and q are real then (p, q) …………
|
IIT 1982 |
02:44 min
|
115 |
If the mth, nth and pth term of an Arithmetic Progression and a Geometric Progression are equal and are x, y, z then prove that 
If the mth, nth and pth term of an Arithmetic Progression and a Geometric Progression are equal and are x, y, z then prove that 
|
IIT 1979 |
06:24 min
|
116 |
A fair die is rolled. The probability that 1 occurs at the even number of trail is a)  b)  c)  d) 
A fair die is rolled. The probability that 1 occurs at the even number of trail is a)  b)  c)  d) 
|
IIT 2005 |
05:00 min
|
117 |
Fill in the blank If the quadratic equation and have a common root then the numerical value of a + b is …………
Fill in the blank If the quadratic equation and have a common root then the numerical value of a + b is …………
|
IIT 1986 |
01:36 min
|
118 |
Show that = 
Show that = 
|
IIT 1999 |
09:29 min
|
119 |
Let a, b, c be distinct non-negative numbers. If the vectors lie in a plane then c is a) Arithmetic mean of a and b b) Geometric mean of a and b c) Harmonic mean of a and b d) Equal to zero
Let a, b, c be distinct non-negative numbers. If the vectors lie in a plane then c is a) Arithmetic mean of a and b b) Geometric mean of a and b c) Harmonic mean of a and b d) Equal to zero
|
IIT 1993 |
01:42 min
|
120 |
(One or more correct answers) For two given events A and B, P (A ∩ B) is a) Not less than P (A) + P (B) − 1 b) Not greater than P (A) + P (B) c) Equal to P (A) + P (B) − P (A ∪ B) d) Equal to P (A) + P (B) + P (A ∪ B)
(One or more correct answers) For two given events A and B, P (A ∩ B) is a) Not less than P (A) + P (B) − 1 b) Not greater than P (A) + P (B) c) Equal to P (A) + P (B) − P (A ∪ B) d) Equal to P (A) + P (B) + P (A ∪ B)
|
IIT 1988 |
01:39 min
|
121 |
Fill in the blank The sum of the real roots of the equation is ………..
Fill in the blank The sum of the real roots of the equation is ………..
|
IIT 1997 |
03:01 min
|
122 |
If are in Arithmetic Progression, determine the value of x.
If are in Arithmetic Progression, determine the value of x.
|
IIT 1990 |
02:49 min
|
123 |
Let F(x) be an indefinite integral of sin2x Statement 1: The function F(x) satisfies F(x + π) = F(x) for all real x because Statement 2: sin2(x + π) = sin2x for all real x Then which one of the following statements is true? a) Statement 1 and 2 are true statements and Statement 2 is a correct explanation of Statement 1 b) Statement 1 and 2 are true statements and statement 2 is not a correct explanation of statement 1 c) Statement 1 is true, Statement 2 is false d) Statement 1 is false, Statement 2 is true
Let F(x) be an indefinite integral of sin2x Statement 1: The function F(x) satisfies F(x + π) = F(x) for all real x because Statement 2: sin2(x + π) = sin2x for all real x Then which one of the following statements is true? a) Statement 1 and 2 are true statements and Statement 2 is a correct explanation of Statement 1 b) Statement 1 and 2 are true statements and statement 2 is not a correct explanation of statement 1 c) Statement 1 is true, Statement 2 is false d) Statement 1 is false, Statement 2 is true
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IIT 2007 |
02:04 min
|
124 |
Let are non–coplanar unit vectors such that then the angle between a and b is a)  b)  c)  d) π
Let are non–coplanar unit vectors such that then the angle between a and b is a)  b)  c)  d) π
|
IIT 1995 |
02:20 min
|
125 |
The number is a) an integer b) a rational number c) an irrational number d) a prime number
The number is a) an integer b) a rational number c) an irrational number d) a prime number
|
IIT 1992 |
00:47 min
|