501 |
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
|
502 |
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
|
503 |
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
|
IIT 1987 |
06:12 min
|
504 |
(Fill in the blanks) The function y = 2x2 – ln|x| is monotonically increasing for values of x (≠0) satisfying the inequalities . . . . and monotonically decreasing for values of x satisfying the inequalities . . . . a) b) c) d)
(Fill in the blanks) The function y = 2x2 – ln|x| is monotonically increasing for values of x (≠0) satisfying the inequalities . . . . and monotonically decreasing for values of x satisfying the inequalities . . . . a) b) c) d)
|
IIT 1983 |
04:07 min
|
505 |
Let f(x) = ∫ex (x – 1) (x − 2) dx, then f(x) decreases in the interval a) (−∞, −2) b) (−2, −1) c) (1, 2) d) (2, ∞)
Let f(x) = ∫ex (x – 1) (x − 2) dx, then f(x) decreases in the interval a) (−∞, −2) b) (−2, −1) c) (1, 2) d) (2, ∞)
|
IIT 2000 |
00:47 min
|
506 |
Find the integral of a) tan−1x2 + c b) c) d)
Find the integral of a) tan−1x2 + c b) c) d)
|
IIT 1978 |
00:32 min
|
507 |
Show that =
Show that =
|
IIT 1980 |
01:51 min
|
508 |
= a) b) c) d)
|
IIT 1984 |
02:26 min
|
509 |
= a) b) c) d)
|
IIT 1989 |
04:05 min
|
510 |
Show that =
Show that =
|
IIT 1997 |
04:06 min
|
511 |
Show that =
Show that =
|
IIT 1990 |
07:54 min
|
512 |
The value of the integral is a) b) c) π d) None of these
The value of the integral is a) b) c) π d) None of these
|
IIT 1983 |
02:20 min
|
513 |
The value of is a) 0 b) 1 c) d)
The value of is a) 0 b) 1 c) d)
|
IIT 1993 |
02:12 min
|
514 |
If y is a function of x and ln (x + y) – 2xy = 0 then the value of y’ (0) is equal to a) 1 b) – 1 c) 2 d) 0
If y is a function of x and ln (x + y) – 2xy = 0 then the value of y’ (0) is equal to a) 1 b) – 1 c) 2 d) 0
|
IIT 2004 |
01:56 min
|
515 |
If then g(x + π) equals a) g(x) + g(π) b) g(x) − g(π) c) g(x) g(π) d)
If then g(x + π) equals a) g(x) + g(π) b) g(x) − g(π) c) g(x) g(π) d)
|
IIT 1997 |
05:05 min
|
516 |
is equal to a) 2 b) –2 c) d)
is equal to a) 2 b) –2 c) d)
|
IIT 1999 |
03:25 min
|
517 |
Let x be the Arithmetic Mean and y, z be two Geometric Means between any two positive numbers then
Let x be the Arithmetic Mean and y, z be two Geometric Means between any two positive numbers then
|
IIT 1997 |
02:27 min
|
518 |
The locus of a variable point whose distance from is times its distance from the line is a) Ellipse b) Parabola c) Hyperbola d) None of these
The locus of a variable point whose distance from is times its distance from the line is a) Ellipse b) Parabola c) Hyperbola d) None of these
|
IIT 1994 |
02:40 min
|
519 |
If and α, β lie between 0 and find a) b) c) d) 2
If and α, β lie between 0 and find a) b) c) d) 2
|
IIT 1979 |
03:00 min
|
520 |
The product of n positive real numbers is unity. Then their sum is a) A positive integer b) Divisible by n c) Equal to d) Never less than n
The product of n positive real numbers is unity. Then their sum is a) A positive integer b) Divisible by n c) Equal to d) Never less than n
|
IIT 1991 |
00:53 min
|
521 |
a) True b) False
a) True b) False
|
IIT 1988 |
03:38 min
|
522 |
Coefficient of t24 in (1 + t2)12 (1 + t12) (1 + t24) is a) b) c) d)
Coefficient of t24 in (1 + t2)12 (1 + t12) (1 + t24) is a) b) c) d)
|
IIT 2003 |
03:19 min
|
523 |
If tan A then a) True b) False
If tan A then a) True b) False
|
IIT 1980 |
01:00 min
|
524 |
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
|
525 |
If k = then the numerical value of k is ………. a) b) c) d)
If k = then the numerical value of k is ………. a) b) c) d)
|
IIT 1993 |
02:32 min
|