|
326 |
If are positive real numbers whose product is a fixed number c then the minimum value of is a)  b)  c)  d) 
If are positive real numbers whose product is a fixed number c then the minimum value of is a)  b)  c)  d) 
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IIT 2002 |
01:19 min
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|
327 |
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) 
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IIT 1998 |
02:35 min
|
|
328 |
Let a and b the roots of the equation and those of are c and d, then find the value of a + b + c + d when a ≠ b ≠ c ≠ d.
Let a and b the roots of the equation and those of are c and d, then find the value of a + b + c + d when a ≠ b ≠ c ≠ d.
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IIT 2006 |
06:39 min
|
|
329 |
=  a) True b) False
=  a) True b) False
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IIT 1985 |
04:05 min
|
|
330 |
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
|
|
331 |
Fill in the blanks If is a root of the equation where p and q are real then (p, q) …………
Fill in the blanks If is a root of the equation where p and q are real then (p, q) …………
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IIT 1982 |
02:44 min
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|
332 |
If the mth, nth and pth term of an Arithmetic Progression and a Geometric Progression are equal and are x, y, z then prove that 
If the mth, nth and pth term of an Arithmetic Progression and a Geometric Progression are equal and are x, y, z then prove that 
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IIT 1979 |
06:24 min
|
|
333 |
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) 
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IIT 2005 |
05:00 min
|
|
334 |
Fill in the blank If the quadratic equation and have a common root then the numerical value of a + b is …………
Fill in the blank If the quadratic equation and have a common root then the numerical value of a + b is …………
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IIT 1986 |
01:36 min
|
|
335 |
Show that = 
Show that = 
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IIT 1999 |
09:29 min
|
|
336 |
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
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IIT 1993 |
01:42 min
|
|
337 |
(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)
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IIT 1988 |
01:39 min
|
|
338 |
Fill in the blank The sum of the real roots of the equation is ………..
Fill in the blank The sum of the real roots of the equation is ………..
|
IIT 1997 |
03:01 min
|
|
339 |
If are in Arithmetic Progression, determine the value of x.
If are in Arithmetic Progression, determine the value of x.
|
IIT 1990 |
02:49 min
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|
340 |
Let F(x) be an indefinite integral of sin2x Statement 1: The function F(x) satisfies F(x + π) = F(x) for all real x because Statement 2: sin2(x + π) = sin2x for all real x Then which one of the following statements is true? a) Statement 1 and 2 are true statements and Statement 2 is a correct explanation of Statement 1 b) Statement 1 and 2 are true statements and statement 2 is not a correct explanation of statement 1 c) Statement 1 is true, Statement 2 is false d) Statement 1 is false, Statement 2 is true
Let F(x) be an indefinite integral of sin2x Statement 1: The function F(x) satisfies F(x + π) = F(x) for all real x because Statement 2: sin2(x + π) = sin2x for all real x Then which one of the following statements is true? a) Statement 1 and 2 are true statements and Statement 2 is a correct explanation of Statement 1 b) Statement 1 and 2 are true statements and statement 2 is not a correct explanation of statement 1 c) Statement 1 is true, Statement 2 is false d) Statement 1 is false, Statement 2 is true
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IIT 2007 |
02:04 min
|
|
341 |
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
|
|
342 |
The number is a) an integer b) a rational number c) an irrational number d) a prime number
The number is a) an integer b) a rational number c) an irrational number d) a prime number
|
IIT 1992 |
00:47 min
|
|
343 |
The fourth power of the common difference of an arithmetic progression with integer entries is added to the product of four consecutive terms of it, prove that the resulting sum is square of an integer.
The fourth power of the common difference of an arithmetic progression with integer entries is added to the product of four consecutive terms of it, prove that the resulting sum is square of an integer.
|
IIT 2000 |
02:57 min
|
|
344 |
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
|
|
345 |
A box contains 2 black, 4 white and 3 red balls. One ball is drawn at random from the box and kept aside from the remaining balls in the box. Another ball is drawn at random and kept besides the first. This process is repeated till all the balls are drawn from the box. Find the probability that the balls drawn are in the sequence of 2 black, 4 white and 3 red.
A box contains 2 black, 4 white and 3 red balls. One ball is drawn at random from the box and kept aside from the remaining balls in the box. Another ball is drawn at random and kept besides the first. This process is repeated till all the balls are drawn from the box. Find the probability that the balls drawn are in the sequence of 2 black, 4 white and 3 red.
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IIT 1979 |
03:42 min
|
|
346 |
The expression is equal to a) 0 b) 1 c) 3 d) sin4α + cosα
The expression is equal to a) 0 b) 1 c) 3 d) sin4α + cosα
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IIT 1986 |
04:12 min
|
|
347 |
If then is equal to a)  b)  c)  d) 
If then is equal to a)  b)  c)  d) 
|
IIT 1994 |
01:15 min
|
|
348 |
The value of where [.] represents the greatest integer function is a)  b)  c)  d) 
The value of where [.] represents the greatest integer function is a)  b)  c)  d) 
|
IIT 1995 |
07:03 min
|
|
349 |
Let the vectors be such that . Let P1 and P2 be the planes determined by the pairs of vectors a, b and c, d respectively. Then the angle between P1 and P2 is a) 0 b)  c)  d) 
Let the vectors be such that . Let P1 and P2 be the planes determined by the pairs of vectors a, b and c, d respectively. Then the angle between P1 and P2 is a) 0 b)  c)  d) 
|
IIT 2000 |
02:05 min
|
|
350 |
If A, B, C be events such that P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(AB) = 0.08, P(AC) = 0.28, P(ABC) = 0.09 and P(A ∪ B ∪ C) ≥ 0.75, then show that P(BC) lies in the interval [0.23, 0.48].
If A, B, C be events such that P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(AB) = 0.08, P(AC) = 0.28, P(ABC) = 0.09 and P(A ∪ B ∪ C) ≥ 0.75, then show that P(BC) lies in the interval [0.23, 0.48].
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IIT 1983 |
02:39 min
|