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326 |
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) 
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IIT 1994 |
02:34 min
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|
327 |
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
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IIT 2001 |
04:03 min
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|
328 |
(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) 
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IIT 2006 |
04:15 min
|
|
329 |
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
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IIT 2000 |
02:20 min
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|
330 |
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
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IIT 2004 |
00:46 min
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|
331 |
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 .
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IIT 1997 |
04:53 min
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|
332 |
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.
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IIT 1991 |
05:44 min
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|
333 |
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) 
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IIT 2000 |
03:13 min
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|
334 |
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
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IIT 2001 |
02:44 min
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|
335 |
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.
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IIT 1981 |
04:21 min
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|
336 |
Match the following Normals are drawn at the points P, Q and R lying on the parabola which intersect at (3, 0) then | Column 1 | Column 2 | | i) Area of ΔPQR | A. 2 | | ii) Radius of circumcircle of ΔPQR | B.  | | iii) Centroid of ΔPQR | C.  | | iv) Circumcentre of ΔPQR | D.  |
Match the following Normals are drawn at the points P, Q and R lying on the parabola which intersect at (3, 0) then | Column 1 | Column 2 | | i) Area of ΔPQR | A. 2 | | ii) Radius of circumcircle of ΔPQR | B.  | | iii) Centroid of ΔPQR | C.  | | iv) Circumcentre of ΔPQR | D.  |
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IIT 2006 |
07:33 min
|
|
337 |
If a polynomial of degree 3, then equals a)  b)  c)  d) a constant
If a polynomial of degree 3, then equals a)  b)  c)  d) a constant
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IIT 1988 |
05:23 min
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|
338 |
If ε then is always greater than or equal to a) 2 tan  b) 1 c) 2 d) 
If ε then is always greater than or equal to a) 2 tan  b) 1 c) 2 d) 
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IIT 2003 |
02:05 min
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|
339 |
If the expression is real then the set of all possible values of x is . . . . a) x = 2nπ or mπ + π/4 b) x = nπ or mπ + π/4 c) x = 2nπ or 2mπ + π/4 d) x = nπ or 2mπ + π/4
If the expression is real then the set of all possible values of x is . . . . a) x = 2nπ or mπ + π/4 b) x = nπ or mπ + π/4 c) x = 2nπ or 2mπ + π/4 d) x = nπ or 2mπ + π/4
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IIT 1987 |
06:12 min
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|
340 |
(Assertion and reason) The question contains statement – 1 (assertion) and statement 2 (reason). Of these statements mark correct choice if a) Statement 1 and 2 are true. Statement 2 is a correct explanation for statement 1. b) Statement 1 and 2 are true. Statement 2 is not a correct explanation for statement 1. c) Statement 1 is true. Statement 2 is false. d) Statement 1 is false. Statement 2 is true Statement 1 – The curve is symmetric with respect to the line x = 1 Statement 2 – The parabola is symmetric about its axis.
(Assertion and reason) The question contains statement – 1 (assertion) and statement 2 (reason). Of these statements mark correct choice if a) Statement 1 and 2 are true. Statement 2 is a correct explanation for statement 1. b) Statement 1 and 2 are true. Statement 2 is not a correct explanation for statement 1. c) Statement 1 is true. Statement 2 is false. d) Statement 1 is false. Statement 2 is true Statement 1 – The curve is symmetric with respect to the line x = 1 Statement 2 – The parabola is symmetric about its axis.
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IIT 2007 |
01:47 min
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|
341 |
If then a)  b)  c)  d) 
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IIT 2003 |
00:43 min
|
|
342 |
Let P = (x, y) be any point on with focii and equals a) 8 b) 6 c) 10 d) 12
Let P = (x, y) be any point on with focii and equals a) 8 b) 6 c) 10 d) 12
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IIT 1998 |
01:38 min
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|
343 |
Let α, β be roots of the equation are the roots of the equation then the value of r is equal to a)  b)  c)  d) 
Let α, β be roots of the equation are the roots of the equation then the value of r is equal to a)  b)  c)  d) 
|
IIT 2007 |
02:46 min
|
|
344 |
Show that square of is a rational number.
Show that square of is a rational number.
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IIT 1978 |
04:58 min
|
|
345 |
The determinants are. a) Identical b) Not identical c) Identical if a = b = c d) None of the above
The determinants are. a) Identical b) Not identical c) Identical if a = b = c d) None of the above
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IIT 1983 |
02:07 min
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|
346 |
If the function f: [0, 4] → ℝ is differentiable, then for a, b ε [0, 4]  a) 8 f (a) f (b) b) 8 f (a) f '(b) c) 8 f '(a) f (b) d) 8 f '(a) f '(b)
If the function f: [0, 4] → ℝ is differentiable, then for a, b ε [0, 4]  a) 8 f (a) f (b) b) 8 f (a) f '(b) c) 8 f '(a) f (b) d) 8 f '(a) f '(b)
|
IIT 2003 |
01:57 min
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|
347 |
Find the equation of the common tangent in the first quadrant to the circle and the ellipse . Also find the length of the intercept of the tangent between the coordinate axis.
Find the equation of the common tangent in the first quadrant to the circle and the ellipse . Also find the length of the intercept of the tangent between the coordinate axis.
|
IIT 2005 |
06:45 min
|
|
348 |
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) 
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IIT 1982 |
03:18 min
|
|
349 |
If one root of is equal to the power of the other then show that
|
IIT 1983 |
02:26 min
|
|
350 |
For 0 < a < x the minimum value of the function logax + logxa is 2. a) True b) False
For 0 < a < x the minimum value of the function logax + logxa is 2. a) True b) False
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IIT 1984 |
01:26 min
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