226 |
The value of where [.] represents the greatest integer function is a) b) c) d)
The value of where [.] represents the greatest integer function is a) b) c) d)
|
IIT 1995 |
07:03 min
|
227 |
If the vectors are coplanar then the value of . . . . . .
If the vectors are coplanar then the value of . . . . . .
|
IIT 1987 |
04:15 min
|
228 |
If then the value of f(1) is a) b) 0 c) 1 d)
If then the value of f(1) is a) b) 0 c) 1 d)
|
IIT 1998 |
01:09 min
|
229 |
A unit vector coplanar with and and perpendicular to is . . . . .
|
IIT 1992 |
04:49 min
|
230 |
Given find
Given find
|
IIT 1980 |
03:52 min
|
231 |
The centre of the circle inscribed in the square formed by the lines and a) (4, 7) b) (7, 4) c) (9, 4) d) (4, 9)
The centre of the circle inscribed in the square formed by the lines and a) (4, 7) b) (7, 4) c) (9, 4) d) (4, 9)
|
IIT 2003 |
02:21 min
|
232 |
Let , where f is such that and then g(2) satisfies the inequality a) b) c) d)
Let , where f is such that and then g(2) satisfies the inequality a) b) c) d)
|
IIT 2000 |
02:05 min
|
233 |
If y = Prove that
If y = Prove that
|
IIT 1998 |
03:49 min
|
234 |
The value of is a) π b) aπ c) d) 2π
The value of is a) π b) aπ c) d) 2π
|
IIT 2001 |
04:30 min
|
235 |
Let a, b, c be non-zero real numbers such that Then the quadratic function has a) no root in (0, 2) b) at least one root in (1, 2) c) a double root in (0, 2) d) two imaginary roots
Let a, b, c be non-zero real numbers such that Then the quadratic function has a) no root in (0, 2) b) at least one root in (1, 2) c) a double root in (0, 2) d) two imaginary roots
|
IIT 1981 |
04:42 min
|
236 |
Let be a polynomial in a real variable x with 0< then the function p(x) has a) neither maximum nor minimum b) only one maximum c) only one minimum d) only one maximum and only one minimum e) none of these
Let be a polynomial in a real variable x with 0< then the function p(x) has a) neither maximum nor minimum b) only one maximum c) only one minimum d) only one maximum and only one minimum e) none of these
|
IIT 1986 |
02:37 min
|
237 |
Let F(x) = f (x) g (x) h (x) for all real x, where f (x), g (x) and h (x) are differentiable functions. At some point x0 and then k is equal to a) 12 b) 20 c) 24 d) 28
Let F(x) = f (x) g (x) h (x) for all real x, where f (x), g (x) and h (x) are differentiable functions. At some point x0 and then k is equal to a) 12 b) 20 c) 24 d) 28
|
IIT 1997 |
01:17 min
|
238 |
Let a given line L1 intersect the X-axis and Y-axis at P and Q respectively. Let another line L2 perpendicular to L1 cut the X and Y axis at R and S respectively. Show that the locus of the point of intersection of the lines PS and QR is a circle passing through the origin.
Let a given line L1 intersect the X-axis and Y-axis at P and Q respectively. Let another line L2 perpendicular to L1 cut the X and Y axis at R and S respectively. Show that the locus of the point of intersection of the lines PS and QR is a circle passing through the origin.
|
IIT 1987 |
07:55 min
|
239 |
If then f a) b) c) 3 d) None
If then f a) b) c) 3 d) None
|
IIT 2005 |
02:29 min
|
240 |
The function defined by is a) Decreasing for all x b) Decreasing in and increasing in c) Increasing for all x d) Decreasing in and increasing in
The function defined by is a) Decreasing for all x b) Decreasing in and increasing in c) Increasing for all x d) Decreasing in and increasing in
|
IIT 1994 |
01:20 min
|
241 |
If G(x) then is a) b) c) d)
If G(x) then is a) b) c) d)
|
IIT 1983 |
01:40 min
|
242 |
Show that
Show that
|
IIT 1982 |
01:38 min
|
243 |
If Where [x] denotes the greatest integer less than or equal to x then equals a) 1 b) 0 c) – 1 d) None of these
If Where [x] denotes the greatest integer less than or equal to x then equals a) 1 b) 0 c) – 1 d) None of these
|
IIT 1985 |
02:39 min
|
244 |
Let a circle be given by . Find the condition on a and b if two chords each bisected by the X–axis can be drawn from .
Let a circle be given by . Find the condition on a and b if two chords each bisected by the X–axis can be drawn from .
|
IIT 1992 |
06:10 min
|
245 |
Evaluate a) b) c) d)
|
IIT 1984 |
03:38 min
|
246 |
Consider the following Statement (S) and Reason (R) S: Both sinx, cosx are decreasing functions in the interval R: If a differentiable function decreases in an interval (a, b) then the derivative also decreases in (a, b) Which of the following is true? a) Both S and R are wrong b) Both S and R are correct but R is not the correct explanation of S c) S is correct and R is the correct explanation of S d) S is correct and R is wrong
Consider the following Statement (S) and Reason (R) S: Both sinx, cosx are decreasing functions in the interval R: If a differentiable function decreases in an interval (a, b) then the derivative also decreases in (a, b) Which of the following is true? a) Both S and R are wrong b) Both S and R are correct but R is not the correct explanation of S c) S is correct and R is the correct explanation of S d) S is correct and R is wrong
|
IIT 2000 |
02:40 min
|
247 |
Let [.] denotes the greatest integer function and f(x) = then a) does not exist b) f (x) is continuous at x = 0 c) f (x) is not differentiable at x = 0 d)
Let [.] denotes the greatest integer function and f(x) = then a) does not exist b) f (x) is continuous at x = 0 c) f (x) is not differentiable at x = 0 d)
|
IIT 1993 |
01:28 min
|
248 |
Evaluate a) b) c) d)
|
IIT 1988 |
06:04 min
|
249 |
is a) 2 b) – 2 c) d)
|
IIT 1999 |
03:16 min
|
250 |
Evaluate a) b) c) d)
|
IIT 1991 |
09:59 min
|