276 |
The axis of the parabola is along the line and the distance of the vertex and focus from origin are and respectively. If vertex and focus both lie in the first quadrant, then the equation of the parabola is a) b) c) d)
The axis of the parabola is along the line and the distance of the vertex and focus from origin are and respectively. If vertex and focus both lie in the first quadrant, then the equation of the parabola is a) b) c) d)
|
IIT 2006 |
05:21 min
|
277 |
(Subjective problem) Solve where a > 0, b = a2x.
(Subjective problem) Solve where a > 0, b = a2x.
|
IIT 1978 |
04:27 min
|
278 |
Sketch the region bounded by the curves y = x2 and . Find the area. a) b) c) d)
Sketch the region bounded by the curves y = x2 and . Find the area. a) b) c) d)
|
IIT 1992 |
06:17 min
|
279 |
Find the equation of the normal to the curve which passes through the point (1, 2).
Find the equation of the normal to the curve which passes through the point (1, 2).
|
IIT 1984 |
03:23 min
|
280 |
The expression is equal to a) 0 b) 1 c) 3 d) sin4α + cosα
The expression is equal to a) 0 b) 1 c) 3 d) sin4α + cosα
|
IIT 1986 |
04:12 min
|
281 |
If ω be the cube root of unity then the value of is a) b) c) d)
If ω be the cube root of unity then the value of is a) b) c) d)
|
IIT 1994 |
02:00 min
|
282 |
At any point P on the parabola , a tangent is drawn which meets the directrix at Q. Find the locus of the point R which divides QP externally in the ratio .
At any point P on the parabola , a tangent is drawn which meets the directrix at Q. Find the locus of the point R which divides QP externally in the ratio .
|
IIT 2004 |
06:48 min
|
283 |
is true if a) x + y= 0 b) x = y, x ≠ 0 c) x = y d) x ≠ 0, y ≠ 0
is true if a) x + y= 0 b) x = y, x ≠ 0 c) x = y d) x ≠ 0, y ≠ 0
|
IIT 1996 |
01:49 min
|
284 |
Find the value of the expression 1.(2−ω)(2−+ 2.(3−ω)(3−+ … (n−1).(n−ω)(n− where ω is an imaginary cube root of unity. a) n(n−1)(+3n+4) b) n(n+1)(+3n+4) c) n(n−1)(+n+1) d) n(n+1)(+n+1)
|
IIT 1996 |
05:00 min
|
285 |
A solution of the differential equation is a) y = 2 b) y = 2x c) d) 2
A solution of the differential equation is a) y = 2 b) y = 2x c) d) 2
|
IIT 1999 |
01:47 min
|
286 |
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
|
287 |
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
|
288 |
Let y = Find a) b) c) d) 0
Let y = Find a) b) c) d) 0
|
IIT 1984 |
02:52 min
|
289 |
If Then = a) 0 b) 1 c) 2 d) 3
If Then = a) 0 b) 1 c) 2 d) 3
|
IIT 2000 |
02:01 min
|
290 |
The derivative of an even function is always an odd function. a) False b) True
The derivative of an even function is always an odd function. a) False b) True
|
IIT 1983 |
01:33 min
|
291 |
The derivative of with respect to at x = is a) 0 b) 1 c) 2 d) 4
The derivative of with respect to at x = is a) 0 b) 1 c) 2 d) 4
|
IIT 1986 |
04:19 min
|
292 |
If f (x) is differentiable and , then equals a) b) c) d)
If f (x) is differentiable and , then equals a) b) c) d)
|
IIT 2004 |
01:33 min
|
293 |
equals a) b) c) d) 4 f (2)
equals a) b) c) d) 4 f (2)
|
IIT 2007 |
03:41 min
|
294 |
The function is not defined at x = 0. The value which should be assigned to f at x = 0 so that it is continuous at x = 0 is a) a – b b) a + b c) lna – lnb d) None of these
The function is not defined at x = 0. The value which should be assigned to f at x = 0 so that it is continuous at x = 0 is a) a – b b) a + b c) lna – lnb d) None of these
|
IIT 1983 |
02:48 min
|
295 |
Find the value of a) b) c) d)
Find the value of a) b) c) d)
|
IIT 1982 |
07:35 min
|
296 |
The set of all points where the function is differentiable is a) b) [0, ∞) c) d) (0, ∞) e) None of these
The set of all points where the function is differentiable is a) b) [0, ∞) c) d) (0, ∞) e) None of these
|
IIT 1987 |
04:36 min
|
297 |
Given a function f (x) such that i) it is integrable over every interval on the real axis and ii) f (t + x) = f (x) for every x and a real t, then show that the integral is independent of a.
Given a function f (x) such that i) it is integrable over every interval on the real axis and ii) f (t + x) = f (x) for every x and a real t, then show that the integral is independent of a.
|
IIT 1984 |
02:15 min
|
298 |
The function f(x) = denotes the greatest integer function is discontinuous at a) All x b) All integer points c) No x d) x which is not an integer
The function f(x) = denotes the greatest integer function is discontinuous at a) All x b) All integer points c) No x d) x which is not an integer
|
IIT 1993 |
03:16 min
|
299 |
If f (x) and g (x) are continuous functions on (0, a) satisfying f (x) = f (a – x) and g (x) + g (a – x) = 2 then show that
If f (x) and g (x) are continuous functions on (0, a) satisfying f (x) = f (a – x) and g (x) + g (a – x) = 2 then show that
|
IIT 1989 |
02:36 min
|
300 |
A cubic f (x) vanishes at x = −2 and has a relative minimum/maximum at x = −1 and . If , find the cube f (x). a) x3 + x2 + x + 1 b) x3 + x2 − x + 1 c) x3 − x2 + x + 2 d) x3 + x2 − x + 2
A cubic f (x) vanishes at x = −2 and has a relative minimum/maximum at x = −1 and . If , find the cube f (x). a) x3 + x2 + x + 1 b) x3 + x2 − x + 1 c) x3 − x2 + x + 2 d) x3 + x2 − x + 2
|
IIT 1992 |
05:24 min
|