201 |
Let α, β, γ be distinct real numbers. The points with position vectors a) Are collinear b) Form an equilateral triangle c) Form a scalene triangle d) Form a right angled triangle
Let α, β, γ be distinct real numbers. The points with position vectors a) Are collinear b) Form an equilateral triangle c) Form a scalene triangle d) Form a right angled triangle
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IIT 1994 |
03:45 min
|
202 |
Find all the values of θ in the interval satisfying the equation . a) b) c) d)
Find all the values of θ in the interval satisfying the equation . a) b) c) d)
|
IIT 1996 |
01:41 min
|
203 |
If f (x) = 3x – 5 then f -1 (x) a) is given by b) is given by c) d)
If f (x) = 3x – 5 then f -1 (x) a) is given by b) is given by c) d)
|
IIT 1998 |
01:38 min
|
204 |
The probability that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively. Of these subjects, the student has 75% chances of passing in at least one, a 50% chance of passing in at least two and 40% chance of passing in exactly two. Which of the following relations is true? a) b) c) d)
The probability that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively. Of these subjects, the student has 75% chances of passing in at least one, a 50% chance of passing in at least two and 40% chance of passing in exactly two. Which of the following relations is true? a) b) c) d)
|
IIT 1998 |
08:20 min
|
205 |
The solution set of the equations where x and y are real is …………. a) b) c) d) No solution
The solution set of the equations where x and y are real is …………. a) b) c) d) No solution
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IIT 1986 |
02:21 min
|
206 |
If f (θ) = sinθ (sinθ + sin3θ) then f (θ) a) ≥ 0 only when θ ≥ 0 b) ≤ 0 for all real θ c) ≥ 0 for all real θ d) ≤ θ only when θ ≤ 0
If f (θ) = sinθ (sinθ + sin3θ) then f (θ) a) ≥ 0 only when θ ≥ 0 b) ≤ 0 for all real θ c) ≥ 0 for all real θ d) ≤ θ only when θ ≤ 0
|
IIT 2000 |
01:05 min
|
207 |
Let If c is a vector such that and the angle between and c is 30° then is equal to a) b) c) 2 d) 3
Let If c is a vector such that and the angle between and c is 30° then is equal to a) b) c) 2 d) 3
|
IIT 1999 |
03:56 min
|
208 |
An anti–aircraft gun can take a maximum of 4 shots at an enemy plane moving away from it. The probability of hitting the plane at the first shot, 2nd, 3rd and 4th shots are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?
An anti–aircraft gun can take a maximum of 4 shots at an enemy plane moving away from it. The probability of hitting the plane at the first shot, 2nd, 3rd and 4th shots are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?
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IIT 1981 |
02:45 min
|
209 |
The value of is a) b) c) d) None of these
The value of is a) b) c) d) None of these
|
IIT 1983 |
02:14 min
|
210 |
The domain of f (x) = is a) R – {1, 2} b) (2, c) R – { 1, 2, 3} d) (3,
|
IIT 2001 |
01:19 min
|
211 |
A and B are independent events. The probability that both A and B occur is and probability that neither of them occur is . Find the probability of the occurrence of A.
A and B are independent events. The probability that both A and B occur is and probability that neither of them occur is . Find the probability of the occurrence of A.
|
IIT 1984 |
04:43 min
|
212 |
The number of solutions of is a) 0 b) One c) Two d) Infinite
The number of solutions of is a) 0 b) One c) Two d) Infinite
|
IIT 2001 |
04:00 min
|
213 |
If a and b are two unit vectors such that are perpendicular to each other then the angle between a and b is a) 45° b) 60° c) d)
If a and b are two unit vectors such that are perpendicular to each other then the angle between a and b is a) 45° b) 60° c) d)
|
IIT 2003 |
01:56 min
|
214 |
A man takes a step forward with probability 0.4 and backward with probability 0.6. Find the probability that at the end of eleven steps he is one step away from the starting point.
A man takes a step forward with probability 0.4 and backward with probability 0.6. Find the probability that at the end of eleven steps he is one step away from the starting point.
|
IIT 1987 |
04:29 min
|
215 |
If are non-coplanar vectors and then a.b1 and a.are orthogonal.
|
IIT 2005 |
02:29 min
|
216 |
Let A be a set containing n elements. A subset P of A is constructed at random. The set A is reconstructed by replacing the elements of P. A subset of Q of A is again chosen at random. Find the probability that P and Q have no elements in common.
Let A be a set containing n elements. A subset P of A is constructed at random. The set A is reconstructed by replacing the elements of P. A subset of Q of A is again chosen at random. Find the probability that P and Q have no elements in common.
|
IIT 1990 |
04:10 min
|
217 |
In a triangle ABC, ∠ B = , ∠ C = . Let D divides BC internally in the ratio 1:3 then is equal to a) b) c) d)
In a triangle ABC, ∠ B = , ∠ C = . Let D divides BC internally in the ratio 1:3 then is equal to a) b) c) d)
|
IIT 1995 |
03:14 min
|
218 |
If then a) Re(z) = 0 b) Im(z) = 0 c) Re(z) = 0, Im(z) > 0 d) Re(z) > 0, Im(z) < 0
If then a) Re(z) = 0 b) Im(z) = 0 c) Re(z) = 0, Im(z) > 0 d) Re(z) > 0, Im(z) < 0
|
IIT 1982 |
02:07 min
|
219 |
If the angles of a triangle are in the ratio 4:1:1 then the ratio of the longest side to the perimeter is a) b) 1 : 6 c) d) 2 : 3
If the angles of a triangle are in the ratio 4:1:1 then the ratio of the longest side to the perimeter is a) b) 1 : 6 c) d) 2 : 3
|
IIT 2003 |
03:18 min
|
220 |
If f (x) = cos [π2] x + cos [-π2] x where [x] stands of the greatest integer function then a) f = −1 b) c) f (−π) = 0 d) f = 1
If f (x) = cos [π2] x + cos [-π2] x where [x] stands of the greatest integer function then a) f = −1 b) c) f (−π) = 0 d) f = 1
|
IIT 1991 |
03:36 min
|
221 |
Let z and ω be two non zero complex numbers such that |z| = |ω| and Arg(z) + Arg(ω) = π then z equals a) ω b) c) d)
Let z and ω be two non zero complex numbers such that |z| = |ω| and Arg(z) + Arg(ω) = π then z equals a) ω b) c) d)
|
IIT 1995 |
02:03 min
|
222 |
Let {x} and [x] denote the fractional and integral part of a real number respectively. Solve 4 {x} = x + [x] a) x = 0 b) c) d)
Let {x} and [x] denote the fractional and integral part of a real number respectively. Solve 4 {x} = x + [x] a) x = 0 b) c) d)
|
IIT 1994 |
03:11 min
|
223 |
The set of lines where is concurrent at the point . . .
The set of lines where is concurrent at the point . . .
|
IIT 1982 |
01:51 min
|
224 |
If the algebraic sum of the perpendicular distance from the point (2, 0), (0, 2) and (1, 1) to a variable straight line be zero then the line passes through a fixed point whose coordinates are
If the algebraic sum of the perpendicular distance from the point (2, 0), (0, 2) and (1, 1) to a variable straight line be zero then the line passes through a fixed point whose coordinates are
|
IIT 1991 |
03:15 min
|
225 |
The equation of the circles through (1, 1) and the point of intersection of is a) b) c) d) None of these
The equation of the circles through (1, 1) and the point of intersection of is a) b) c) d) None of these
|
IIT 1983 |
02:31 min
|