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Question(s) from Search: IIT

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601

Solve  

Solve  

IIT 1988
03:54 min
602

If  are in Geometric Progression then
 are in

a) Arithmetic Progression

b) Geometric Progression

c) Harmonic Progression

d) None of these

If  are in Geometric Progression then
 are in

a) Arithmetic Progression

b) Geometric Progression

c) Harmonic Progression

d) None of these

IIT 1998
02:25 min
603

Let  for n ≥ 2 and
 

Then equals

a)

b)

c)

d)

Let  for n ≥ 2 and
 

Then equals

a)

b)

c)

d)

IIT 2007
08:22 min
604

India played two matches each with Australia and West indies. In any match the probability of India getting the points 0, 1, and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least seven points is

a) 0.8730

b) 0.0875

c) 0.0625

d) 0.0250

India played two matches each with Australia and West indies. In any match the probability of India getting the points 0, 1, and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least seven points is

a) 0.8730

b) 0.0875

c) 0.0625

d) 0.0250

IIT 1992
03:03 min
605

Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If  then n equals

a) 5

b) 7

c) 6

d) 4

Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If  then n equals

a) 5

b) 7

c) 6

d) 4

IIT 2001
02:30 min
606

Three of the vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equals

a)

b)

c)

d)

Three of the vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equals

a)

b)

c)

d)

IIT 1995
02:30 min
607

Let a, b, c be real numbers with a ≠ 0 and let α, β be roots of the equation . Express the roots of  in terms of α, β.

Let a, b, c be real numbers with a ≠ 0 and let α, β be roots of the equation . Express the roots of  in terms of α, β.

IIT 2001
04:00 min
608

Suppose a, b, c are in Arithmetic Progression and  are in Geometric Progression. If  then the value of a is

a)

b)

c)

d)

Suppose a, b, c are in Arithmetic Progression and  are in Geometric Progression. If  then the value of a is

a)

b)

c)

d)

IIT 2002
05:17 min
609

 =

a)

b)

c)

d)

 =

a)

b)

c)

d)

IIT 1981
00:56 min
610

If  are complementary events E and F respectively and if 0 < p(E) < 1, then

a)

b)

c)

d)

If  are complementary events E and F respectively and if 0 < p(E) < 1, then

a)

b)

c)

d)

IIT 1998
01:47 min
611

The equation  has an irrational root.

a) False

b) True

The equation  has an irrational root.

a) False

b) True

IIT 1983
00:48 min
612

Multiple Choice

For  if
 , then

a)  

b)  

c)  

d)  

Multiple Choice

For  if
 , then

a)  

b)  

c)  

d)  

IIT 1993
06:15 min
613

The numbers are selected from the set S = {1, 2, 3, 4, 5, 6} without replacement one by one. Probability that the minimum of the two numbers is less than 4 is

a)

b)

c)

d)

The numbers are selected from the set S = {1, 2, 3, 4, 5, 6} without replacement one by one. Probability that the minimum of the two numbers is less than 4 is

a)

b)

c)

d)

IIT 2003
03:06 min
614

Fill in the blank

If the product of the roots of the equation
  is 7
Then the roots are real for  ………….

Fill in the blank

If the product of the roots of the equation
  is 7
Then the roots are real for  ………….

IIT 1984
01:40 min
615

Show that the integral
 =

Show that the integral
 =

IIT 1994
06:09 min
616

One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is

a)

b)

c)

d)

One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is

a)

b)

c)

d)

IIT 2007
09:20 min
617

Fill in the blank

There are exactly two distinct linear functions ………. and ………. which map {−1, 1} onto {0, 2}.

Fill in the blank

There are exactly two distinct linear functions ………. and ………. which map {−1, 1} onto {0, 2}.

IIT 1989
02:15 min
618

Find three numbers a, b, c between 2 and 18 such that (i) their sum is 25 (ii) 2, a, b are consecutive terms of an Arithmetic Progression and (iii) the numbers b, c, 18 are consecutive terms of a Geometric Progression

Find three numbers a, b, c between 2 and 18 such that (i) their sum is 25 (ii) 2, a, b are consecutive terms of an Arithmetic Progression and (iii) the numbers b, c, 18 are consecutive terms of a Geometric Progression

IIT 1983
04:09 min
619

Show that  =

Show that  =

IIT 2001
06:38 min
620

Let p and q be the position vectors of P and Q respectively with respect to O and . The points R and S divide PQ internally and externally in the ratio 2:3 respectively. If OR and OS are perpendicular then

a)

b)

c)

d)

Let p and q be the position vectors of P and Q respectively with respect to O and . The points R and S divide PQ internally and externally in the ratio 2:3 respectively. If OR and OS are perpendicular then

a)

b)

c)

d)

IIT 1994
02:26 min
621

Let u, v and w be vectors such that  . If  then  is equal to

a) 47

b) –25

c) 0

d) 25

Let u, v and w be vectors such that  . If  then  is equal to

a) 47

b) –25

c) 0

d) 25

IIT 1995
05:00 min
622

(One or more correct answers)
There are four machines and it is known that exactly two of them are faulty. They are tested one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed

a)

b)

c)

d)

(One or more correct answers)
There are four machines and it is known that exactly two of them are faulty. They are tested one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed

a)

b)

c)

d)

IIT 1998
04:38 min
623

(Subjective problem)

Solve  
where a > 0, b = a2x.

(Subjective problem)

Solve  
where a > 0, b = a2x.

IIT 1978
04:27 min
624

Let f : ℝ → ℝ be a differentiable function and f (1) = 4. Then show that the value of   =

Let f : ℝ → ℝ be a differentiable function and f (1) = 4. Then show that the value of   =

IIT 1990
02:32 min
625

A box contains 2 black, 4 white and 3 red balls. One ball is drawn at random from the box and kept aside from the remaining balls in the box. Another ball is drawn at random and kept besides the first. This process is repeated till all the balls are drawn from the box. Find the probability that the balls drawn are in the sequence of 2 black, 4 white and 3 red.

A box contains 2 black, 4 white and 3 red balls. One ball is drawn at random from the box and kept aside from the remaining balls in the box. Another ball is drawn at random and kept besides the first. This process is repeated till all the balls are drawn from the box. Find the probability that the balls drawn are in the sequence of 2 black, 4 white and 3 red.

IIT 1979
03:42 min

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