426 |
The area bounded by the curves and the X–axis in the first quadrant is a) 9 b) c) 36 d) 18
The area bounded by the curves and the X–axis in the first quadrant is a) 9 b) c) 36 d) 18
|
IIT 2003 |
04:28 min
|
427 |
Find the point on which is nearest to the line
Find the point on which is nearest to the line
|
IIT 2003 |
04:09 min
|
428 |
The equation has a) no real solutions b) one real solution c) two real solutions d) infinite real solutions
The equation has a) no real solutions b) one real solution c) two real solutions d) infinite real solutions
|
IIT 1982 |
03:09 min
|
429 |
For positive numbers x, y and z the numerical value of the determinant is ……….. a) 1 b) –1 c) ±1 d) 0
For positive numbers x, y and z the numerical value of the determinant is ……….. a) 1 b) –1 c) ±1 d) 0
|
IIT 1993 |
02:04 min
|
430 |
If f(x) = xa lnx and f(0) = 0 then the value of a for which Rolle’s theorem can be applied in [0, 1] is a) – 2 b) – 1 c) 0 d)
If f(x) = xa lnx and f(0) = 0 then the value of a for which Rolle’s theorem can be applied in [0, 1] is a) – 2 b) – 1 c) 0 d)
|
IIT 2004 |
02:30 min
|
431 |
If a > 0, b > 0, c > 0, prove that
If a > 0, b > 0, c > 0, prove that
|
IIT 1984 |
02:45 min
|
432 |
The third term of Geometric Progression is 4. The product of the five terms is a) b) c) d)
The third term of Geometric Progression is 4. The product of the five terms is a) b) c) d)
|
IIT 1982 |
01:07 min
|
433 |
The points of intersection of the line and the circle is . . . . .
The points of intersection of the line and the circle is . . . . .
|
IIT 1983 |
03:18 min
|
434 |
Find the set of all x for which
Find the set of all x for which
|
IIT 1987 |
05:05 min
|
435 |
Sum of the first n terms of the series is a) 2n – n – 1 b) 1 – 2− n c) n + 2− n – 1 d) 2n + 1
Sum of the first n terms of the series is a) 2n – n – 1 b) 1 – 2− n c) n + 2− n – 1 d) 2n + 1
|
IIT 1988 |
03:20 min
|
436 |
Multiple choice For which value of m, is the area of the region bounded by the curve y = x –x2 and the line y = mx equal to a) – 4 b) – 2 c) 2 d) 4
Multiple choice For which value of m, is the area of the region bounded by the curve y = x –x2 and the line y = mx equal to a) – 4 b) – 2 c) 2 d) 4
|
IIT 1999 |
04:39 min
|
437 |
The equation of the line passing through the points of intersection of the circles and is . . . . .
The equation of the line passing through the points of intersection of the circles and is . . . . .
|
IIT 1986 |
02:45 min
|
438 |
Let be in Arithmetic Progression and be in Harmonic Progression. If and then is a) 2 b) 3 c) 5 d) 6
Let be in Arithmetic Progression and be in Harmonic Progression. If and then is a) 2 b) 3 c) 5 d) 6
|
IIT 1999 |
04:53 min
|
439 |
If the triangle another circle C2 of radius 5 in such a manner that the common chord is of maximum length and a slope equal to , then the coordinates of the centre of C2 are . . . . .
If the triangle another circle C2 of radius 5 in such a manner that the common chord is of maximum length and a slope equal to , then the coordinates of the centre of C2 are . . . . .
|
IIT 1988 |
06:55 min
|
440 |
If α, β are roots of and are roots of for some constant δ, then prove that
|
IIT 2000 |
03:16 min
|
441 |
Let the positive numbers a, b, c, d be in Arithmetic Progression. Then abc, abd, acd, bcd are a) Not in Arithmetic Progression/Geometric Progression/Harmonic Progression b) In Arithmetic Progression c) In Geometric Progression d) In Harmonic Progression
Let the positive numbers a, b, c, d be in Arithmetic Progression. Then abc, abd, acd, bcd are a) Not in Arithmetic Progression/Geometric Progression/Harmonic Progression b) In Arithmetic Progression c) In Geometric Progression d) In Harmonic Progression
|
IIT 2001 |
01:12 min
|
442 |
The equation of the locus of the midpoints of the chord of the circle that subtends an angle of at the centre is . . . . .
The equation of the locus of the midpoints of the chord of the circle that subtends an angle of at the centre is . . . . .
|
IIT 1993 |
05:29 min
|
443 |
If is the area of a triangle with sides a, b, c then show that . Also show that equality occurs if a = b = c
If is the area of a triangle with sides a, b, c then show that . Also show that equality occurs if a = b = c
|
IIT 2001 |
05:12 min
|
444 |
An infinite Geometric Progression has first term x and sum 5 then a) b) c) d)
An infinite Geometric Progression has first term x and sum 5 then a) b) c) d)
|
IIT 2004 |
01:34 min
|
445 |
Find the area bounded by the X–axis, part of the curve and the ordinates at x = 2 and x = 4. If the ordinate x = a divides the area in two equal parts, find a. a) b) c) d)
Find the area bounded by the X–axis, part of the curve and the ordinates at x = 2 and x = 4. If the ordinate x = a divides the area in two equal parts, find a. a) b) c) d)
|
IIT 1983 |
04:06 min
|
446 |
The chord of contact of the pair of tangents drawn from each point on the line to the circle passes through the point . . . . .
The chord of contact of the pair of tangents drawn from each point on the line to the circle passes through the point . . . . .
|
IIT 1997 |
02:57 min
|
447 |
If a < b < c < d then the roots of the equation are real and distinct. a) True b) False
If a < b < c < d then the roots of the equation are real and distinct. a) True b) False
|
IIT 1984 |
03:45 min
|
448 |
Find the tangents to the curve y = cos(x + y), − 2π ≤ x ≤ 2π that are parallel to the line x + 2y = 0
Find the tangents to the curve y = cos(x + y), − 2π ≤ x ≤ 2π that are parallel to the line x + 2y = 0
|
IIT 1985 |
07:32 min
|
449 |
The angles of a triangle are in Arithmetic Progression and let . Find the angle A.
The angles of a triangle are in Arithmetic Progression and let . Find the angle A.
|
IIT 1981 |
03:20 min
|
450 |
If α, β, γ are the cube roots of P, P < 0, then for any x, y, z, ………..
If α, β, γ are the cube roots of P, P < 0, then for any x, y, z, ………..
|
IIT 1989 |
07:21 min
|