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Question(s) from Search: IIT

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601

 =

a)

b)

c)

d)

 =

a)

b)

c)

d)

IIT 1983
02:26 min
602

If a < b < c < d then the roots of the equation
  
are real and distinct.

a) True

b) False

If a < b < c < d then the roots of the equation
  
are real and distinct.

a) True

b) False

IIT 1984
03:45 min
603

The volume of the parallelopiped whose sides are given by
 

a)

b) 4

c)

d) None of these

The volume of the parallelopiped whose sides are given by
 

a)

b) 4

c)

d) None of these

IIT 1983
02:22 min
604

If three distinct numbers are chosen randomly from the first 100 natural numbers then the probability that all three of them are divisible by 2 and 3 is

a)

b)

c)

d)

If three distinct numbers are chosen randomly from the first 100 natural numbers then the probability that all three of them are divisible by 2 and 3 is

a)

b)

c)

d)

IIT 2003
03:45 min
605

The angles of a triangle are in Arithmetic Progression and let . Find the angle A.

The angles of a triangle are in Arithmetic Progression and let . Find the angle A.

IIT 1981
03:20 min
606

Show that
 =   where y =

Show that
 =   where y =

IIT 1996
04:40 min
607

The number of unit vectors perpendicular to the vectors  and  is

a) 1

b) 2

c) 3

d) Infinitely many

e) None of these

The number of unit vectors perpendicular to the vectors  and  is

a) 1

b) 2

c) 3

d) Infinitely many

e) None of these

IIT 1987
03:26 min
608

If α, β, γ are the cube roots of P, P < 0, then for any x, y, z,
………..

If α, β, γ are the cube roots of P, P < 0, then for any x, y, z,
………..

IIT 1989
07:21 min
609

If n is a natural number such that  and  are distinct primes, then show that
 

If n is a natural number such that  and  are distinct primes, then show that
 

IIT 1983
03:00 min
610

For any natural number m, show that
 

For any natural number m, show that
 

IIT 2002
04:12 min
611

Let α, β, γ be distinct real numbers. The points with position vectors
 

a) Are collinear

b) Form an equilateral triangle

c) Form a scalene triangle

d) Form a right angled triangle

Let α, β, γ be distinct real numbers. The points with position vectors
 

a) Are collinear

b) Form an equilateral triangle

c) Form a scalene triangle

d) Form a right angled triangle

IIT 1994
03:45 min
612

The least value of the expression  for x > 1 is

a) 10

b) 2

c) −0.01

d) none of these

The least value of the expression  for x > 1 is

a) 10

b) 2

c) −0.01

d) none of these

IIT 1980
02:59 min
613

The probability that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively. Of these subjects, the student has 75% chances of passing in at least one, a 50% chance of passing in at least two and 40% chance of passing in exactly two. Which of the following relations is true?

a)

b)

c)

d)

The probability that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively. Of these subjects, the student has 75% chances of passing in at least one, a 50% chance of passing in at least two and 40% chance of passing in exactly two. Which of the following relations is true?

a)

b)

c)

d)

IIT 1998
08:20 min
614

If  satisfies ,
find the value of

If  satisfies ,
find the value of

IIT 1991
04:16 min
615

Let f : ℝ → ℝ and g : ℝ → ℝ be continuous functions. Then the value of integral  is

a) π

b) 1

c) – 1

d) 0

Let f : ℝ → ℝ and g : ℝ → ℝ be continuous functions. Then the value of integral  is

a) π

b) 1

c) – 1

d) 0

IIT 1990
01:59 min
616

Let  If c is a vector such that  and the angle between  and c is 30° then  is equal to

a)

b)

c) 2

d) 3

Let  If c is a vector such that  and the angle between  and c is 30° then  is equal to

a)

b)

c) 2

d) 3

IIT 1999
03:56 min
617

An anti–aircraft gun can take a maximum of 4 shots at an enemy plane moving away from it. The probability of hitting the plane at the first shot, 2nd, 3rd and 4th shots are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?

An anti–aircraft gun can take a maximum of 4 shots at an enemy plane moving away from it. The probability of hitting the plane at the first shot, 2nd, 3rd and 4th shots are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?

IIT 1981
02:45 min
618

The value of the expression  is equal to

a) 2

b)

c) 4

d)

The value of the expression  is equal to

a) 2

b)

c) 4

d)

IIT 1988
02:02 min
619

Let f(x) =  where p is a constant

Then  at x = 0 is

a) p

b)

c)

d) Independent of p

Let f(x) =  where p is a constant

Then  at x = 0 is

a) p

b)

c)

d) Independent of p

IIT 1997
04:22 min
620

 

a)

b)

c)

d)

 

a)

b)

c)

d)

IIT 1997
02:03 min
621

A and B are independent events. The probability that both A and B occur is  and probability that neither of them occur is . Find the probability of the occurrence of A.

A and B are independent events. The probability that both A and B occur is  and probability that neither of them occur is . Find the probability of the occurrence of A.

IIT 1984
04:43 min
622

Let  then  equals

a) tan

b) tan

c) tan

d) tan2

Let  then  equals

a) tan

b) tan

c) tan

d) tan2

IIT 1994
02:33 min
623

 equals

a)

b)

c)

d)

 equals

a)

b)

c)

d)

IIT 2007
01:21 min
624

If  f(x) = x – [x] for every real number x, where [x] is the integral part of x, then  is

a) 1

b) 2

c) 0

d)

If  f(x) = x – [x] for every real number x, where [x] is the integral part of x, then  is

a) 1

b) 2

c) 0

d)

IIT 1998
02:21 min
625

If a and b are two unit vectors such that  are perpendicular to each other then the angle between a and b is

a) 45°

b) 60°

c)

d)

If a and b are two unit vectors such that  are perpendicular to each other then the angle between a and b is

a) 45°

b) 60°

c)

d)

IIT 2003
01:56 min

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