76 |
For a > 0, d > 0, find the value of the determinant a) 0 b) 1 c) d)
For a > 0, d > 0, find the value of the determinant a) 0 b) 1 c) d)
|
IIT 1996 |
05:35 min
|
77 |
Multiple choices For real x, the function will assume all real values provided a) b) c) d)
Multiple choices For real x, the function will assume all real values provided a) b) c) d)
|
IIT 1984 |
05:06 min
|
78 |
If the matrix A is equal to where a, b, c are real positive numbers, abc = 1 and ATA = I then find the value of a3 + b3 + c3. a) 1 b) 2 c) 3 d) 4
If the matrix A is equal to where a, b, c are real positive numbers, abc = 1 and ATA = I then find the value of a3 + b3 + c3. a) 1 b) 2 c) 3 d) 4
|
IIT 2003 |
04:04 min
|
79 |
If then f(x) is a) Increasing on b) Decreasing on ℝ c) Increasing on ℝ d) Decreasing on
If then f(x) is a) Increasing on b) Decreasing on ℝ c) Increasing on ℝ d) Decreasing on
|
IIT 2001 |
02:04 min
|
80 |
Prove if α, β are roots of the equation and γ, δ are roots of then show that
|
IIT 1978 |
03:39 min
|
81 |
Let be the equation of pair of tangents from the origin O to a circle of radius 3 with centre in the first quadrant. If A is a point of contact, find the length of OA.
Let be the equation of pair of tangents from the origin O to a circle of radius 3 with centre in the first quadrant. If A is a point of contact, find the length of OA.
|
IIT 2001 |
04:52 min
|
82 |
A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the value of the determinant chosen is positive is a) b) c) d)
A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the value of the determinant chosen is positive is a) b) c) d)
|
IIT 1982 |
03:18 min
|
83 |
Let In represents area of n sided regular polygon inscribed in a unit circle and On the area of n–sided regular polygon circumscribing it. Prove that
Let In represents area of n sided regular polygon inscribed in a unit circle and On the area of n–sided regular polygon circumscribing it. Prove that
|
IIT 2003 |
07:43 min
|
84 |
If one root of is equal to the power of the other then show that
|
IIT 1983 |
02:26 min
|
85 |
Minimum area of the triangle formed by the tangent to the ellipse with co-ordinate axes is a) b) c) d) ab
Minimum area of the triangle formed by the tangent to the ellipse with co-ordinate axes is a) b) c) d) ab
|
IIT 2005 |
02:43 min
|
86 |
If A and B are points in the plane such that (constant) for all P on a given circle then the value of k cannot be equal to - - - - -.
If A and B are points in the plane such that (constant) for all P on a given circle then the value of k cannot be equal to - - - - -.
|
IIT 1982 |
04:30 min
|
87 |
If a, b, c are in Geometric Progression then the equations have a common root if are in a) Arithmetic Progression b) Geometric Progression c) Harmonic Progression d) None of these
If a, b, c are in Geometric Progression then the equations have a common root if are in a) Arithmetic Progression b) Geometric Progression c) Harmonic Progression d) None of these
|
IIT 1985 |
03:08 min
|
88 |
Multiple choice Let h(x) = f(x) – (f(x))2 + (f(x))3 for every real number x, then a) h increases whenever f is increasing b) h is increasing whenever f is decreasing c) h is decreasing whenever f is decreasing d) nothing can be said in general
Multiple choice Let h(x) = f(x) – (f(x))2 + (f(x))3 for every real number x, then a) h increases whenever f is increasing b) h is increasing whenever f is decreasing c) h is decreasing whenever f is decreasing d) nothing can be said in general
|
IIT 1998 |
02:37 min
|
89 |
From the origin chords are drawn to the circle . The equation of the locus of the mid points of these chords is . . . . .
From the origin chords are drawn to the circle . The equation of the locus of the mid points of these chords is . . . . .
|
IIT 1984 |
02:45 min
|
90 |
Solve for x in the following equation
Solve for x in the following equation
|
IIT 1987 |
07:03 min
|
91 |
Let Tr be the rth term of an Arithmetic Progression for If for some positive integers m, n we have and then Tmn equals a) b) c) d)
Let Tr be the rth term of an Arithmetic Progression for If for some positive integers m, n we have and then Tmn equals a) b) c) d)
|
IIT 1998 |
01:51 min
|
92 |
The area of the triangle formed by the tangents from the point (4, 3) to the circle and the line joining their point of contact is .
The area of the triangle formed by the tangents from the point (4, 3) to the circle and the line joining their point of contact is .
|
IIT 1987 |
06:00 min
|
93 |
Consider an infinite geometric series with first term a and common ratio r. If its sum is four and the second term is then a) b) c) d)
Consider an infinite geometric series with first term a and common ratio r. If its sum is four and the second term is then a) b) c) d)
|
IIT 2000 |
01:48 min
|
94 |
The area of triangle formed by the positive X–axis and the normal and tangent to the circle at is . . . . . .
The area of triangle formed by the positive X–axis and the normal and tangent to the circle at is . . . . . .
|
IIT 1989 |
02:40 min
|
95 |
For every positive integer n, prove that Hence or otherwise prove that Where [ ] denotes greatest integer not exceeding x.
For every positive integer n, prove that Hence or otherwise prove that Where [ ] denotes greatest integer not exceeding x.
|
IIT 2000 |
03:07 min
|
96 |
If are positive real numbers whose product is a fixed number c then the minimum value of is a) b) c) d)
If are positive real numbers whose product is a fixed number c then the minimum value of is a) b) c) d)
|
IIT 2002 |
01:19 min
|
97 |
Intercepts on the line y = x by the circle is AB. Equation of the circle with AB as diameter is . . . . .
Intercepts on the line y = x by the circle is AB. Equation of the circle with AB as diameter is . . . . .
|
IIT 1996 |
03:14 min
|
98 |
Let a and b the roots of the equation and those of are c and d, then find the value of a + b + c + d when a ≠ b ≠ c ≠ d.
Let a and b the roots of the equation and those of are c and d, then find the value of a + b + c + d when a ≠ b ≠ c ≠ d.
|
IIT 2006 |
06:39 min
|
99 |
Find the coordinates of the point on the curve where the tangent to the curve has the greatest slope. a) (0, 0) b) c) d)
Find the coordinates of the point on the curve where the tangent to the curve has the greatest slope. a) (0, 0) b) c) d)
|
IIT 1984 |
06:59 min
|
100 |
Fill in the blanks If is a root of the equation where p and q are real then (p, q) …………
Fill in the blanks If is a root of the equation where p and q are real then (p, q) …………
|
IIT 1982 |
02:44 min
|