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Question(s) from Search: IIT

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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

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

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

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