676 |
If then show that |z| = 1.
If then show that |z| = 1.
|
IIT 1995 |
02:14 min
|
677 |
Given x = cy + bz, y = az + cx, z = bx + ay where x, y, z are not all zero, prove that a2 + b2 + c2 + 2abc = 1
Given x = cy + bz, y = az + cx, z = bx + ay where x, y, z are not all zero, prove that a2 + b2 + c2 + 2abc = 1
|
IIT 1978 |
03:30 min
|
678 |
Let and are two complex numbers such that then prove that .
|
IIT 2003 |
04:08 min
|
679 |
Without expanding a determinant at any stage show that = Ax + B where A, B are non-zero constants
Without expanding a determinant at any stage show that = Ax + B where A, B are non-zero constants
|
IIT 1982 |
04:06 min
|
680 |
True/False If the complex numbers represent the vertices of an equilateral triangle with then . a) True b) False
True/False If the complex numbers represent the vertices of an equilateral triangle with then . a) True b) False
|
IIT 1984 |
02:27 min
|
681 |
For any two complex numbers and any real numbers is equal to . . . . a) b) c) d)
For any two complex numbers and any real numbers is equal to . . . . a) b) c) d)
|
IIT 1988 |
02:43 min
|
682 |
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
|
683 |
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
|
IIT 1984 |
01:26 min
|
684 |
= a) True b) False
= a) True b) False
|
IIT 1985 |
04:05 min
|
685 |
Show that =
Show that =
|
IIT 1999 |
09:29 min
|
686 |
Let F(x) be an indefinite integral of sin2x Statement 1: The function F(x) satisfies F(x + π) = F(x) for all real x because Statement 2: sin2(x + π) = sin2x for all real x Then which one of the following statements is true? a) Statement 1 and 2 are true statements and Statement 2 is a correct explanation of Statement 1 b) Statement 1 and 2 are true statements and statement 2 is not a correct explanation of statement 1 c) Statement 1 is true, Statement 2 is false d) Statement 1 is false, Statement 2 is true
Let F(x) be an indefinite integral of sin2x Statement 1: The function F(x) satisfies F(x + π) = F(x) for all real x because Statement 2: sin2(x + π) = sin2x for all real x Then which one of the following statements is true? a) Statement 1 and 2 are true statements and Statement 2 is a correct explanation of Statement 1 b) Statement 1 and 2 are true statements and statement 2 is not a correct explanation of statement 1 c) Statement 1 is true, Statement 2 is false d) Statement 1 is false, Statement 2 is true
|
IIT 2007 |
02:04 min
|
687 |
Let f(x) be a quadratic expression which is positive for all values of x. If g(x) = then for any real x a) g (x) < 0 b) g (x) > 0 c) g (x) = 0 d) g (x) ≥ 0
Let f(x) be a quadratic expression which is positive for all values of x. If g(x) = then for any real x a) g (x) < 0 b) g (x) > 0 c) g (x) = 0 d) g (x) ≥ 0
|
IIT 1990 |
02:54 min
|
688 |
If and , then constants A and B are a) b) c) d)
If and , then constants A and B are a) b) c) d)
|
IIT 1995 |
02:11 min
|
689 |
If y = y (x) and it follows the relation xcosy + ycosx = π then is a) – 1 b) π c) – π d) 1
If y = y (x) and it follows the relation xcosy + ycosx = π then is a) – 1 b) π c) – π d) 1
|
IIT 2005 |
03:40 min
|
690 |
Let f be a positive function. Let where 2k – 1 > 0 then is a) 2 b) k c) d) 1
Let f be a positive function. Let where 2k – 1 > 0 then is a) 2 b) k c) d) 1
|
IIT 1997 |
02:23 min
|
691 |
If f (x) = , find from first principle. a) b) c) d)
If f (x) = , find from first principle. a) b) c) d)
|
IIT 1978 |
04:21 min
|
692 |
If for real number y, [y] is the greatest integer less than or equal to y then the value of the integral is a) b) c) d)
If for real number y, [y] is the greatest integer less than or equal to y then the value of the integral is a) b) c) d)
|
IIT 1999 |
07:44 min
|
693 |
Using the relation , or otherwise prove that a) True b) False
Using the relation , or otherwise prove that a) True b) False
|
IIT 2003 |
|
694 |
If A > 0, B > 0 and A + B = , then the maximum value of tan A tanB is ………. a) b) c) d)
If A > 0, B > 0 and A + B = , then the maximum value of tan A tanB is ………. a) b) c) d)
|
IIT 1993 |
|
695 |
Multiple choices For a positive integer n, let . . . then a) b) c) d)
Multiple choices For a positive integer n, let . . . then a) b) c) d)
|
IIT 1999 |
|
696 |
For all , a) True b) False
For all , a) True b) False
|
IIT 1981 |
|
697 |
Let f (x) = |x – 1| then a) f (x2) = |f (x)|2 b) f (x + y) = f (x) + f (y) c) f () = |f (x)| d) None of these
Let f (x) = |x – 1| then a) f (x2) = |f (x)|2 b) f (x + y) = f (x) + f (y) c) f () = |f (x)| d) None of these
|
IIT 1983 |
|
698 |
A vector a has components 2p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If with respect to new system a has components p + 1 and 1 then a) p ≠ 0 b) p = 1 or p = c) p = −1 or d) p = 1 or p = −1 e) None of these
A vector a has components 2p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If with respect to new system a has components p + 1 and 1 then a) p ≠ 0 b) p = 1 or p = c) p = −1 or d) p = 1 or p = −1 e) None of these
|
IIT 1986 |
|
699 |
Find the smallest possible value of p for which the equation a) b) c) d)
Find the smallest possible value of p for which the equation a) b) c) d)
|
IIT 1995 |
|
700 |
If f (x) = for every real x then the minimum value of f a) does not exist because f is unbounded b) is not attained even though f is bounded c) is equal to 1 d) is equal to −1
If f (x) = for every real x then the minimum value of f a) does not exist because f is unbounded b) is not attained even though f is bounded c) is equal to 1 d) is equal to −1
|
IIT 1998 |
|