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Question(s) from Search: IIT

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426

Let P be a variable point on the ellipse  with foci F1 and F2. . If A is the area of  then the maximum value of A is  . . . . .

Let P be a variable point on the ellipse  with foci F1 and F2. . If A is the area of  then the maximum value of A is  . . . . .

IIT 1994
02:27 min
427

A spherical rain drop evaporates at a rate proportional to its surface area at any instant. The differential equation giving the rate of change of the radius vector of the rain drop is . . . . .

A spherical rain drop evaporates at a rate proportional to its surface area at any instant. The differential equation giving the rate of change of the radius vector of the rain drop is . . . . .

IIT 1997
01:37 min
428

The value of the determinant  is …………

a) 0

b) 1

c) a2 + b2 + c2 – abc

d) a2 + b2 + c2 – 3abc

The value of the determinant  is …………

a) 0

b) 1

c) a2 + b2 + c2 – abc

d) a2 + b2 + c2 – 3abc

IIT 1988
02:49 min
429

The equation  represents

a) An ellipse

b) A hyperbola

c) A circle

d) None of these

The equation  represents

a) An ellipse

b) A hyperbola

c) A circle

d) None of these

IIT 1981
01:03 min
430

Find all the real values of x which satisfy  and  .

Find all the real values of x which satisfy  and  .

IIT 1983
02:29 min
431

For the hyperbola  which of the following remains constant with change in α

a) Abscissae of vertices

b) Abscissae of focii

c) Eccentricity

d) Directrix

For the hyperbola  which of the following remains constant with change in α

a) Abscissae of vertices

b) Abscissae of focii

c) Eccentricity

d) Directrix

IIT 2003
01:32 min
432

The value of  is

a) 0

b) 1

c) 2

d) 4

The value of  is

a) 0

b) 1

c) 2

d) 4

IIT 1997
01:38 min
433

For a ≤ 0, determine all real roots of the equation
 

For a ≤ 0, determine all real roots of the equation
 

IIT 1986
03:49 min
434

If a, b, c, d and p are distinct real numbers such that
 
then a, b, c, d

a) Are in Arithmetic Progression

b) Are in Geometric Progression

c) Are in Harmonic Progression

d) Satisfy ab = cd

e) Satisfy none of these

If a, b, c, d and p are distinct real numbers such that
 
then a, b, c, d

a) Are in Arithmetic Progression

b) Are in Geometric Progression

c) Are in Harmonic Progression

d) Satisfy ab = cd

e) Satisfy none of these

IIT 1987
02:16 min
435

Suppose f(x) is a function satisfying the following conditions

i) f(0) = 2, f(1) = 1

ii) f has a minimum value at x = 5/2 and

iii) for all x

 
where a, b are constants. Determine the constants a and b, and the function f(x).

a)

b)

c)

d)

Suppose f(x) is a function satisfying the following conditions

i) f(0) = 2, f(1) = 1

ii) f has a minimum value at x = 5/2 and

iii) for all x

 
where a, b are constants. Determine the constants a and b, and the function f(x).

a)

b)

c)

d)

IIT 1998
06:16 min
436

Solve  

Solve  

IIT 1988
03:54 min
437

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
438

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
439

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
440

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
441

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
442

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
443

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
444

 =

a)

b)

c)

d)

 =

a)

b)

c)

d)

IIT 1981
00:56 min
445

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
446

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
447

Multiple Choice

For  if
 , then

a)  

b)  

c)  

d)  

Multiple Choice

For  if
 , then

a)  

b)  

c)  

d)  

IIT 1993
06:15 min
448

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
449

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
450

Show that the integral
 =

Show that the integral
 =

IIT 1994
06:09 min

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