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Question(s) from Search: IIT

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576

Multiple choices

For real x, the function  will assume all real values provided

a)

b)

c)

d)

Multiple choices

For real x, the function  will assume all real values provided

a)

b)

c)

d)

IIT 1984
05:06 min
577

If the matrix A is equal to where a, b, c are real positive numbers, abc = 1 and ATA = I then find the value of a3 + b3 + c3.

a) 1

b) 2

c) 3

d) 4

If the matrix A is equal to where a, b, c are real positive numbers, abc = 1 and ATA = I then find the value of a3 + b3 + c3.

a) 1

b) 2

c) 3

d) 4

IIT 2003
04:04 min
578

Prove if α, β are roots of the equation  and γ, δ are roots of  then show that
 

Prove if α, β are roots of the equation  and γ, δ are roots of  then show that
 

IIT 1978
03:39 min
579

If the function f: [0, 4] → ℝ is differentiable, then for a, b ε [0, 4]

a) 8 f (a) f (b)

b) 8 f (a) f '(b)

c) 8 f '(a) f (b)

d) 8 f '(a) f '(b)

If the function f: [0, 4] → ℝ is differentiable, then for a, b ε [0, 4]

a) 8 f (a) f (b)

b) 8 f (a) f '(b)

c) 8 f '(a) f (b)

d) 8 f '(a) f '(b)

IIT 2003
01:57 min
580

Find the equation of the common tangent in the first quadrant to the circle  and the ellipse   . Also find the length of the intercept of the tangent between the coordinate axis.

Find the equation of the common tangent in the first quadrant to the circle  and the ellipse   . Also find the length of the intercept of the tangent between the coordinate axis.

IIT 2005
06:45 min
581

A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the value of the determinant chosen is positive is

a)

b)

c)

d)

A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the value of the determinant chosen is positive is

a)

b)

c)

d)

IIT 1982
03:18 min
582

If one root of  is equal to the power of the other then show that
 

If one root of  is equal to the power of the other then show that
 

IIT 1983
02:26 min
583

For 0 < a < x the minimum value of the function logax + logxa is 2.

a) True

b) False

For 0 < a < x the minimum value of the function logax + logxa is 2.

a) True

b) False

IIT 1984
01:26 min
584

The curve described parametrically by   ,  represents

a) A pair of straight lines

b) An ellipse

c) A parabola

d) A hyperbola

The curve described parametrically by   ,  represents

a) A pair of straight lines

b) An ellipse

c) A parabola

d) A hyperbola

IIT 1999
01:59 min
585

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
586

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
587

Solve for x in the following equation

 

Solve for x in the following equation

 

IIT 1987
07:03 min
588

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
589

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
590

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
591

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
592

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
593

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
594

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
595

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
596

 =

a) True

b) False

 =

a) True

b) False

IIT 1985
04:05 min
597

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
598

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
599

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
600

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

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