526 |
If then tan a) True b) False
If then tan a) True b) False
|
IIT 1979 |
01:42 min
|
527 |
The curve described parametrically by , represents a) A pair of straight lines b) An ellipse c) A parabola d) A hyperbola
The curve described parametrically by , represents a) A pair of straight lines b) An ellipse c) A parabola d) A hyperbola
|
IIT 1999 |
01:59 min
|
528 |
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
|
529 |
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
|
530 |
The circle intersects hyperbola in four points then a) b) c) d)
The circle intersects hyperbola in four points then a) b) c) d)
|
IIT 1998 |
02:27 min
|
531 |
The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2 then is a) 0.4 b) 0.8 c) 1.2 d) 1.4
The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2 then is a) 0.4 b) 0.8 c) 1.2 d) 1.4
|
IIT 1987 |
02:39 min
|
532 |
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
|
533 |
The probability of India winning a test match against West Indies is ½. Assuming independence of outcomes in each match, the probability that in a 5 test match series India’s second win will occur in the third test is a) b) c) d)
The probability of India winning a test match against West Indies is ½. Assuming independence of outcomes in each match, the probability that in a 5 test match series India’s second win will occur in the third test is a) b) c) d)
|
IIT 1995 |
02:40 min
|
534 |
If from each of the three boxes containing 3 white and one black; 2 white and 2 black; 1 white and 3 black balls, one ball is drawn at random then the probability that 2 white and 1 black ball will be drawn is a) b) c) d)
If from each of the three boxes containing 3 white and one black; 2 white and 2 black; 1 white and 3 black balls, one ball is drawn at random then the probability that 2 white and 1 black ball will be drawn is a) b) c) d)
|
IIT 1998 |
02:35 min
|
535 |
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
|
536 |
The coefficient of x99 in the polynomial (x – 1) (x – 2) . . . (x – 100) is
The coefficient of x99 in the polynomial (x – 1) (x – 2) . . . (x – 100) is
|
IIT 1982 |
02:12 min
|
537 |
The scalar equals a) 0 b) c) d) None of these
The scalar equals a) 0 b) c) d) None of these
|
IIT 1981 |
02:30 min
|
538 |
The sum of the rational terms in the expansion of is
The sum of the rational terms in the expansion of is
|
IIT 1997 |
03:13 min
|
539 |
A fair die is rolled. The probability that 1 occurs at the even number of trail is a) b) c) d)
A fair die is rolled. The probability that 1 occurs at the even number of trail is a) b) c) d)
|
IIT 2005 |
05:00 min
|
540 |
Which of the following functions is periodic? a) f(x) = x – [x] where [x] denotes the greatest integer less than or equal to the real number x b) f(x) = sin x ≠ 0, f(0) = 0 c) f(x) = x cos x d) None of these
Which of the following functions is periodic? a) f(x) = x – [x] where [x] denotes the greatest integer less than or equal to the real number x b) f(x) = sin x ≠ 0, f(0) = 0 c) f(x) = x cos x d) None of these
|
IIT 1983 |
01:19 min
|
541 |
Let a, b, c be distinct non-negative numbers. If the vectors lie in a plane then c is a) Arithmetic mean of a and b b) Geometric mean of a and b c) Harmonic mean of a and b d) Equal to zero
Let a, b, c be distinct non-negative numbers. If the vectors lie in a plane then c is a) Arithmetic mean of a and b b) Geometric mean of a and b c) Harmonic mean of a and b d) Equal to zero
|
IIT 1993 |
01:42 min
|
542 |
(One or more correct answers) For two given events A and B, P (A ∩ B) is a) Not less than P (A) + P (B) − 1 b) Not greater than P (A) + P (B) c) Equal to P (A) + P (B) − P (A ∪ B) d) Equal to P (A) + P (B) + P (A ∪ B)
(One or more correct answers) For two given events A and B, P (A ∩ B) is a) Not less than P (A) + P (B) − 1 b) Not greater than P (A) + P (B) c) Equal to P (A) + P (B) − P (A ∪ B) d) Equal to P (A) + P (B) + P (A ∪ B)
|
IIT 1988 |
01:39 min
|
543 |
Let f (x) be defined for all x > 0 and be continuous. If f (x) satisfies f = f (x) – f (y) for all x and y and f (e) = 1 then a) f (x) is bounded b) f → 0 as x → 0 c) x f → 0 as x → 0 d) f (x) = lnx
Let f (x) be defined for all x > 0 and be continuous. If f (x) satisfies f = f (x) – f (y) for all x and y and f (e) = 1 then a) f (x) is bounded b) f → 0 as x → 0 c) x f → 0 as x → 0 d) f (x) = lnx
|
IIT 1995 |
02:06 min
|
544 |
Let are non–coplanar unit vectors such that then the angle between a and b is a) b) c) d) π
Let are non–coplanar unit vectors such that then the angle between a and b is a) b) c) d) π
|
IIT 1995 |
02:20 min
|
545 |
There exists a solution of θ between 0 and 2π that satisfies the equation . a) True b) False
There exists a solution of θ between 0 and 2π that satisfies the equation . a) True b) False
|
IIT 1980 |
02:16 min
|
546 |
The number of values of x where the function f (x) = cos x + cos () attains the maximum is a) 0 b) 1 c) 2 d) Infinite
The number of values of x where the function f (x) = cos x + cos () attains the maximum is a) 0 b) 1 c) 2 d) Infinite
|
IIT 1998 |
01:38 min
|
547 |
If a are linearly dependent and |c| then a) b) c) d)
If a are linearly dependent and |c| then a) b) c) d)
|
IIT 1998 |
04:11 min
|
548 |
Six boys and six girls sit in a row at random. Find the probability that the girls and the boys sit alternately.
Six boys and six girls sit in a row at random. Find the probability that the girls and the boys sit alternately.
|
IIT 1978 |
05:30 min
|
549 |
The domain of definition of the function f (x) given by the equation 2x + 2y = 2 is a) 0 < x ≤ 1 b) 0 ≤ x ≤ 1 c) < x ≤ 0 d) < x ≤ 1
The domain of definition of the function f (x) given by the equation 2x + 2y = 2 is a) 0 < x ≤ 1 b) 0 ≤ x ≤ 1 c) < x ≤ 0 d) < x ≤ 1
|
IIT 2000 |
01:23 min
|
550 |
If the vectors form sides BC, CA and AB respectively of a triangle ABC then a) b) c) d)
If the vectors form sides BC, CA and AB respectively of a triangle ABC then a) b) c) d)
|
IIT 2000 |
02:48 min
|