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) 
|
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
|