301 |
Let ABC be a triangle such that If A, B, C are in arithmetic progression, determine the values of A, B, C. a) 30°, 60°, 90° b) 30°, 75°, 75° c) 45°, 60°, 75° d) 60°, 60°, 60°
Let ABC be a triangle such that If A, B, C are in arithmetic progression, determine the values of A, B, C. a) 30°, 60°, 90° b) 30°, 75°, 75° c) 45°, 60°, 75° d) 60°, 60°, 60°
|
IIT 1990 |
02:17 min
|
302 |
If f (x) = and then (gof)(x) = ………… a) 0 b) 1 c) 2 d) 3
If f (x) = and then (gof)(x) = ………… a) 0 b) 1 c) 2 d) 3
|
IIT 1996 |
03:24 min
|
303 |
a) 0 b) 1 c) e3 d) e5
a) 0 b) 1 c) e3 d) e5
|
IIT 1990 |
04:42 min
|
304 |
If |z| = 1 and then Re (w) is a) 0 b)  c)  d) 
If |z| = 1 and then Re (w) is a) 0 b)  c)  d) 
|
IIT 2003 |
02:36 min
|
305 |
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
|
306 |
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
|
307 |
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
|
308 |
The largest interval for which is a)  b)  c)  d) 
The largest interval for which is a)  b)  c)  d) 
|
IIT 1982 |
04:35 min
|
309 |
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
|
310 |
The equation has a) No root b) One root c) Two equal roots d) Infinitely many roots
The equation has a) No root b) One root c) Two equal roots d) Infinitely many roots
|
IIT 1984 |
01:04 min
|
311 |
If w ( ≠1 ) is cube root of unity, then a) 0 b) 1 c) - 1 d) w
If w ( ≠1 ) is cube root of unity, then a) 0 b) 1 c) - 1 d) w
|
IIT 1995 |
01:46 min
|
312 |
Let a, b, c be real numbers, a ≠ 0. If α is a root of β is a root of and 0 < α < β then the equation has a root γ that always satisfies a) γ =  b) γ =  c) γ = α d) α < γ < β
Let a, b, c be real numbers, a ≠ 0. If α is a root of β is a root of and 0 < α < β then the equation has a root γ that always satisfies a) γ =  b) γ =  c) γ = α d) α < γ < β
|
IIT 1989 |
03:43 min
|
313 |
The determinant = 0 if a) x, y, z are in arithmetic progression b) x, y, z are in geometric progression c) x, y, z are in harmonic progression d) xy, yz, zx are in arithmetic progression
The determinant = 0 if a) x, y, z are in arithmetic progression b) x, y, z are in geometric progression c) x, y, z are in harmonic progression d) xy, yz, zx are in arithmetic progression
|
IIT 1997 |
02:44 min
|
314 |
If are the n roots of unity then show that .
If are the n roots of unity then show that .
|
IIT 1984 |
02:49 min
|
315 |
The equation of the common tangent to the curves and is a)  b)  c)  d) 
The equation of the common tangent to the curves and is a)  b)  c)  d) 
|
IIT 2002 |
03:51 min
|
316 |
If p, q, r are positive and are in arithmetic progression the roots of the quadratic are all real for a)  b)  c)  d) 
If p, q, r are positive and are in arithmetic progression the roots of the quadratic are all real for a)  b)  c)  d) 
|
IIT 1994 |
02:34 min
|
317 |
The number of distinct roots of = 0 in the interval ≤ x ≤ is a) 0 b) 2 c) 1 d) 3
The number of distinct roots of = 0 in the interval ≤ x ≤ is a) 0 b) 2 c) 1 d) 3
|
IIT 2001 |
04:03 min
|
318 |
(Multiple choice) The equation of common tangent to the parabolas and is/are a)  b)  c)  d) 
(Multiple choice) The equation of common tangent to the parabolas and is/are a)  b)  c)  d) 
|
IIT 2006 |
04:15 min
|
319 |
If α and β (α < β) are roots of the equation where c < 0 < b then a) 0 < α < β b) α < 0 < β < | α | c) α < β < 0 d) α < 0 < | α | < β
If α and β (α < β) are roots of the equation where c < 0 < b then a) 0 < α < β b) α < 0 < β < | α | c) α < β < 0 d) α < 0 < | α | < β
|
IIT 2000 |
02:20 min
|
320 |
If A = and | A3| = 125 then the value of α is a) ± 1 b) ±2 c) ± 3 d) ± 5
If A = and | A3| = 125 then the value of α is a) ± 1 b) ±2 c) ± 3 d) ± 5
|
IIT 2004 |
00:46 min
|
321 |
Let and be the roots of the equation where the coefficients p and q may be complex numbers. Let A and B represent in the complex plane. If and OB = OA where O is the origin, prove that .
|
IIT 1997 |
04:53 min
|
322 |
Three normals are drawn from the point (c, 0) to the curve . Show that c must be greater than . One normal is always the X-axis. Find c for which the other two normals are perpendicular.
Three normals are drawn from the point (c, 0) to the curve . Show that c must be greater than . One normal is always the X-axis. Find c for which the other two normals are perpendicular.
|
IIT 1991 |
05:44 min
|
323 |
For the equation if one of the roots is square of the other then p is equal to a)  b)  c) 3 d) 
For the equation if one of the roots is square of the other then p is equal to a)  b)  c) 3 d) 
|
IIT 2000 |
03:13 min
|
324 |
The number of solutions of is a) 3 b) 1 c) 2 d) 0
The number of solutions of is a) 3 b) 1 c) 2 d) 0
|
IIT 2001 |
02:44 min
|
325 |
If a, b, c be positive and not all equal, show that the value of the determinant is negative.
If a, b, c be positive and not all equal, show that the value of the determinant is negative.
|
IIT 1981 |
04:21 min
|