176 |
The radius of the circle passing through the focii of the ellipse and having centre at (0, 3) is a) 4 b) 3 c) d)
The radius of the circle passing through the focii of the ellipse and having centre at (0, 3) is a) 4 b) 3 c) d)
|
IIT 1995 |
01:53 min
|
177 |
In the binomial expansion of the sum of the 5th term and 6th term is zero, then equals a) b) c) d)
In the binomial expansion of the sum of the 5th term and 6th term is zero, then equals a) b) c) d)
|
IIT 2001 |
02:04 min
|
178 |
Multiple choice question On the ellipse the points at which the tangents are parallel to the line are a) b) c) d)
Multiple choice question On the ellipse the points at which the tangents are parallel to the line are a) b) c) d)
|
IIT 1999 |
03:37 min
|
179 |
The set of all values of x in the interval (0, π) for which is a) (0, ) b) { } c) ( , π) d) (0, ) U { } U ( , π)
|
IIT 1987 |
02:55 min
|
180 |
An ellipse has eccentricity and one of the focus at the point It’s one directrix is the common tangent near to the point P to the circle and the hyperbola . Then the equation of the ellipse in the statement form is . . . . .
|
IIT 1996 |
07:07 min
|
181 |
Use mathematical induction to prove that is divisible by 24 for all n > 0.
Use mathematical induction to prove that is divisible by 24 for all n > 0.
|
IIT 1985 |
03:43 min
|
182 |
The equation represents a) No locus if k > 0 b) An ellipse if k < 0 c) A point if k = 0 d) A hyperbola if k > 0
The equation represents a) No locus if k > 0 b) An ellipse if k < 0 c) A point if k = 0 d) A hyperbola if k > 0
|
IIT 1994 |
02:16 min
|
183 |
The solution of is a) b) c) d) None of these
The solution of is a) b) c) d) None of these
|
IIT 1981 |
01:11 min
|
184 |
If the line touches the hyperbola then the point of contact is a) b) c) d)
If the line touches the hyperbola then the point of contact is a) b) c) d)
|
IIT 2004 |
02:39 min
|
185 |
Two events A and B have probabilities 0.25 and 0.50 respectively. The possibility of both A and B occur simultaneously is 0.14 then the probability that neither A nor B occur is a) 0.39 b) 0.25 c) 0.11 d) None of these
Two events A and B have probabilities 0.25 and 0.50 respectively. The possibility of both A and B occur simultaneously is 0.14 then the probability that neither A nor B occur is a) 0.39 b) 0.25 c) 0.11 d) None of these
|
IIT 1980 |
02:08 min
|
186 |
If n be a positive integer such that then a) b) c) d)
If n be a positive integer such that then a) b) c) d)
|
IIT 1994 |
03:42 min
|
187 |
Three identical dice are rolled. The probability that the same number will appear on each of them is a) b) c) d)
Three identical dice are rolled. The probability that the same number will appear on each of them is a) b) c) d)
|
IIT 1984 |
01:22 min
|
188 |
Which of the following are rational? a) b) c) d)
Which of the following are rational? a) b) c) d)
|
IIT 1998 |
02:53 min
|
189 |
Using mathematical induction prove that
Using mathematical induction prove that
|
IIT 1993 |
08:39 min
|
190 |
An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled 4 times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is a) 16/81 b) 1/81 c) 80/81 d) 65/81
An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled 4 times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is a) 16/81 b) 1/81 c) 80/81 d) 65/81
|
IIT 1993 |
01:57 min
|
191 |
The number of integral values of k for which the equation has a solution is a) 4 b) 8 c) 10 d) 12
The number of integral values of k for which the equation has a solution is a) 4 b) 8 c) 10 d) 12
|
IIT 2002 |
03:40 min
|
192 |
For the three events A, B, C, P(exactly one of A or B occurs) = P(exactly one of B or C occurs) = P(exactly one of C or A occurs) = p and P(all the three events occur simultaneously = where . Then the probability of at least one of A, B, C occurring is a) b) c) d)
For the three events A, B, C, P(exactly one of A or B occurs) = P(exactly one of B or C occurs) = P(exactly one of C or A occurs) = p and P(all the three events occur simultaneously = where . Then the probability of at least one of A, B, C occurring is a) b) c) d)
|
IIT 1996 |
06:23 min
|
193 |
Use mathematical induction to show that (25)n + 1 – 24n + 5735 is divisible by (24)2 for all n = 1, 2, . . .
Use mathematical induction to show that (25)n + 1 – 24n + 5735 is divisible by (24)2 for all n = 1, 2, . . .
|
IIT 2002 |
10:18 min
|
194 |
In a ΔABC, then find the other sides and angles a) A = 60°, B = 60°, c = b) A = 45°, B = 75°, c = c) A = 75°, B = 45°, c = d) A = 15°, B = 105°, c =
In a ΔABC, then find the other sides and angles a) A = 60°, B = 60°, c = b) A = 45°, B = 75°, c = c) A = 75°, B = 45°, c = d) A = 15°, B = 105°, c =
|
IIT 1978 |
03:06 min
|
195 |
(1 + ax)n = 1 + 8x + 24x2 + . . . then a = . . ., n = . . .
(1 + ax)n = 1 + 8x + 24x2 + . . . then a = . . ., n = . . .
|
IIT 1983 |
02:24 min
|
196 |
The volume of the parallelopiped whose sides are given by a) b) 4 c) d) None of these
The volume of the parallelopiped whose sides are given by a) b) 4 c) d) None of these
|
IIT 1983 |
02:22 min
|
197 |
If three distinct numbers are chosen randomly from the first 100 natural numbers then the probability that all three of them are divisible by 2 and 3 is a) b) c) d)
If three distinct numbers are chosen randomly from the first 100 natural numbers then the probability that all three of them are divisible by 2 and 3 is a) b) c) d)
|
IIT 2003 |
03:45 min
|
198 |
Find the coordinates of the point of intersection of the curves y = cosx and y = sin3x if . a) ((( b) (( c) ( d) (
|
IIT 1982 |
03:54 min
|
199 |
If f (x) = cos (lnx) then f (x) f (y) − has the value of a) −1 b) c) −2 d) None of these
If f (x) = cos (lnx) then f (x) f (y) − has the value of a) −1 b) c) −2 d) None of these
|
IIT 1983 |
02:43 min
|
200 |
The number of unit vectors perpendicular to the vectors and is a) 1 b) 2 c) 3 d) Infinitely many e) None of these
The number of unit vectors perpendicular to the vectors and is a) 1 b) 2 c) 3 d) Infinitely many e) None of these
|
IIT 1987 |
03:26 min
|