651 |
where a, b ε R then find the value of a for which equation has unequal roots for all values of b.
where a, b ε R then find the value of a for which equation has unequal roots for all values of b.
|
IIT 2003 |
02:36 min
|
652 |
If α, β are roots of and are in Geometric Progression and then a) b) c) d)
If α, β are roots of and are in Geometric Progression and then a) b) c) d)
|
IIT 2005 |
02:38 min
|
653 |
If x and y are positive real numbers and m and n are any positive integers then a) True b) False
If x and y are positive real numbers and m and n are any positive integers then a) True b) False
|
IIT 1989 |
02:49 min
|
654 |
If x, y, z are in Harmonic Progression then show that
If x, y, z are in Harmonic Progression then show that
|
IIT 1978 |
02:51 min
|
655 |
Fill in the blank The solution of the equation is …………..
Fill in the blank The solution of the equation is …………..
|
IIT 1986 |
02:04 min
|
656 |
If are in Arithmetic Progression where for all i, show that
|
IIT 1982 |
04:29 min
|
657 |
Fill in the blank If x < 0, y < 0, and then x ……….. and y ………..
|
IIT 1990 |
04:06 min
|
658 |
The sum of the squares of three distinct real numbers which are in Geometric Progression is . If their sum is , show that
|
IIT 1986 |
06:02 min
|
659 |
If then x lies in the interval a) (2, ∞) b) (1, 2) c) (−2, −1) d) None of these
If then x lies in the interval a) (2, ∞) b) (1, 2) c) (−2, −1) d) None of these
|
IIT 1985 |
03:00 min
|
660 |
Given A = for all values of θ, then a) 1 ≤ A ≤ 2 b) ≤ A ≤ 1 c) ≤ A ≤ 1 d) ≤ A ≤
Given A = for all values of θ, then a) 1 ≤ A ≤ 2 b) ≤ A ≤ 1 c) ≤ A ≤ 1 d) ≤ A ≤
|
IIT 1980 |
01:38 min
|
661 |
If a, b, c are in Arithmetic Progression and are in Harmonic Progression then prove that either or a, b and are in Geometric Progression.
|
IIT 2003 |
03:47 min
|
662 |
a) 11 b) 12 c) 13 d) 14
a) 11 b) 12 c) 13 d) 14
|
IIT 1995 |
04:20 min
|
663 |
Given both θ and Ф are acute angles and sinθ = , cos Ф = then the value of θ + Ф belongs to a) b) c) d)
Given both θ and Ф are acute angles and sinθ = , cos Ф = then the value of θ + Ф belongs to a) b) c) d)
|
IIT 2004 |
02:15 min
|
664 |
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
|
665 |
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
|
666 |
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
|
667 |
a) True b) False
a) True b) False
|
IIT 1988 |
03:38 min
|
668 |
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
|
669 |
If tan A then a) True b) False
If tan A then a) True b) False
|
IIT 1980 |
01:00 min
|
670 |
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
|
671 |
If then tan a) True b) False
If then tan a) True b) False
|
IIT 1979 |
01:42 min
|
672 |
In a triangle ABC, angle A is greater than angle B. If the measures of angle A and B satisfy the equation , then the measure of angle C is a) b) c) d)
In a triangle ABC, angle A is greater than angle B. If the measures of angle A and B satisfy the equation , then the measure of angle C is a) b) c) d)
|
IIT 1990 |
01:43 min
|
673 |
Prove that C0 – 22C1 + 32C2 − . . . + (−)n (n + 1)2 Cn = 0 for n > 2 where
Prove that C0 – 22C1 + 32C2 − . . . + (−)n (n + 1)2 Cn = 0 for n > 2 where
|
IIT 1989 |
05:31 min
|
674 |
The maximum value of cos1 cos2 cos3 …… cosnunder the restriction 0 1 , 2 , 3 …. , n and cot1 cot2 cot3 …… cotn= 1 is a) b) c) d)
|
IIT 2001 |
03:43 min
|
675 |
Let are the perpendiculars from the vertices of a triangle to the opposite sides, then a) True b) False
Let are the perpendiculars from the vertices of a triangle to the opposite sides, then a) True b) False
|
IIT 1978 |
02:41 min
|