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Question(s) from Search: IIT

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1

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
2

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
3

Show that   =
 

Show that   =
 

IIT 1999
09:29 min
4

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
5

(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
6

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
7

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
8

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
9

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
10

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
11

The fourth power of the common difference of an arithmetic progression with integer entries is added to the product of four consecutive terms of it, prove that the resulting sum is square of an integer.

The fourth power of the common difference of an arithmetic progression with integer entries is added to the product of four consecutive terms of it, prove that the resulting sum is square of an integer.

IIT 2000
02:57 min
12

If a  are linearly dependent and |c|  then

a)

b)

c)

d)

If a  are linearly dependent and |c|  then

a)

b)

c)

d)

IIT 1998
04:11 min
13

Six boys and six girls sit in a row at random. Find the probability that the girls and the boys sit alternately.

Six boys and six girls sit in a row at random. Find the probability that the girls and the boys sit alternately.

IIT 1978
05:30 min
14

 is equal to

a)

b)

c)

d)

 is equal to

a)

b)

c)

d)

IIT 1984
03:04 min
15

If a, b, c are positive real numbers then prove that
 

If a, b, c are positive real numbers then prove that
 

IIT 2004
02:42 min
16

Let f(x) be a quadratic expression which is positive for all values of x. If g(x) =  then for any real x

a) g (x) < 0

b) g (x) > 0

c) g (x) = 0

d) g (x) ≥ 0

Let f(x) be a quadratic expression which is positive for all values of x. If g(x) =  then for any real x

a) g (x) < 0

b) g (x) > 0

c) g (x) = 0

d) g (x) ≥ 0

IIT 1990
02:54 min
17

If  and , then constants A and B are

a)

b)

c)

d)

If  and , then constants A and B are

a)

b)

c)

d)

IIT 1995
02:11 min
18

If the vectors  form sides BC, CA and AB respectively of a triangle ABC then

a)

b)

c)

d)

If the vectors  form sides BC, CA and AB respectively of a triangle ABC then

a)

b)

c)

d)

IIT 2000
02:48 min
19

Cards are drawn one by one at random from a well shuffled pack of 52 playing cards until 2 aces are drawn for the first time. If N is the number of cards required to be drawn show that
 where 2 < n ≤ 50

Cards are drawn one by one at random from a well shuffled pack of 52 playing cards until 2 aces are drawn for the first time. If N is the number of cards required to be drawn show that
 where 2 < n ≤ 50

IIT 1983
07:44 min
20

If the lengths of the sides of a triangle are 3, 5, 7 then the largest angle of the triangle is

a)

b)

c)

d)

If the lengths of the sides of a triangle are 3, 5, 7 then the largest angle of the triangle is

a)

b)

c)

d)

IIT 1994
01:44 min
21

If y = y (x) and it follows the relation xcosy + ycosx = π then  is

a) – 1

b) π

c) – π

d) 1

If y = y (x) and it follows the relation xcosy + ycosx = π then  is

a) – 1

b) π

c) – π

d) 1

IIT 2005
03:40 min
22

Let f be a positive function. Let
 
 where
2k – 1 > 0 then  is

a) 2

b) k

c)

d) 1

Let f be a positive function. Let
 
 where
2k – 1 > 0 then  is

a) 2

b) k

c)

d) 1

IIT 1997
02:23 min
23

Let
,
then  depends on

a) Only x

b) Only y

c) Neither x nor y

d) Both x and y

Let
,
then  depends on

a) Only x

b) Only y

c) Neither x nor y

d) Both x and y

IIT 2001
01:20 min
24

In a multiple choice question there are four alternative answers out of which one or more is correct. A candidate will get full marks in the question only if he ticks the correct answers. If he is allowed up to three chances to answer the question, find the probability that he will get marks in the question?

In a multiple choice question there are four alternative answers out of which one or more is correct. A candidate will get full marks in the question only if he ticks the correct answers. If he is allowed up to three chances to answer the question, find the probability that he will get marks in the question?

IIT 1985
05:36 min
25

Let the Harmonic Mean and Geometric Mean of two positive numbers be in the ratio of 4:5. Then the two numbers are in the ratio .  .  .  .  .

Let the Harmonic Mean and Geometric Mean of two positive numbers be in the ratio of 4:5. Then the two numbers are in the ratio .  .  .  .  .

IIT 1992
02:26 min

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