|
326 |
If f (x) =  , find  from first principle. a)  b)  c)  d) 
If f (x) = , find from first principle. a) b) c) d)
|
IIT 1978 |
04:21 min
|
|
327 |
If for real number y, [y] is the greatest integer less than or equal to y then the value of the integral  is a)  b)  c)  d) 
If for real number y, [y] is the greatest integer less than or equal to y then the value of the integral is a) b) c) d)
|
IIT 1999 |
07:44 min
|
|
328 |
If  and  then b is equal to a)  b)  c)  d) 
If and then b is equal to a) b) c) d)
|
IIT 2004 |
02:35 min
|
|
329 |
A box contains two 50 paise coins, 5 twenty five paise coins and a certain number N(≥ 2) of ten and five paise coins. Five coins are taken out of the box at random. Find the probability that the total value of these coins is less than one rupee and 50 paise.
A box contains two 50 paise coins, 5 twenty five paise coins and a certain number N(≥ 2) of ten and five paise coins. Five coins are taken out of the box at random. Find the probability that the total value of these coins is less than one rupee and 50 paise.
|
IIT 1988 |
06:49 min
|
|
330 |
 and 
where α, β ε [ π, π]. Values of α, β which satisfy both the equations is/are
a) 0 b) 1 c) 2 d) 4
and
where α, β ε [π, π]. Values of α, β which satisfy both the equations is/are a) 0 b) 1 c) 2 d) 4
|
IIT 2005 |
04:42 min
|
|
331 |
Given positive integers r > 1, n > 2 and the coefficients of (3r)th term and (r + 2)th terms in the binomial expansion of (1 + x)2n are equal then a) n = 2r b) n = 2r + 1 c) n = 3r d) none of these
Given positive integers r > 1, n > 2 and the coefficients of (3r)th term and (r + 2)th terms in the binomial expansion of (1 + x)2n are equal then a) n = 2r b) n = 2r + 1 c) n = 3r d) none of these
|
IIT 1980 |
03:03 min
|
|
332 |
The number of distinct real values of λ for which  are coplanar is a) Zero b) One c) Two d) three
The number of distinct real values of λ for which are coplanar is a) Zero b) One c) Two d) three
|
IIT 2007 |
03:01 min
|
|
333 |
If  , then  a) True b) False
If , then a) True b) False
|
IIT 1980 |
04:29 min
|
|
334 |
If in the expansion of (1 + x)m (1 – x)n, the coefficients of x and x2 are 3 and –6 respectively. then m is a) 6 b) 9 c) 12 d) 24
If in the expansion of (1 + x)m (1 – x)n, the coefficients of x and x2 are 3 and –6 respectively. then m is a) 6 b) 9 c) 12 d) 24
|
IIT 1999 |
04:34 min
|
|
335 |
If  then  at x = e is . . . a) 0 b)  c) e d) 1
If then at x = e is . . . a) 0 b) c) e d) 1
|
IIT 1985 |
01:35 min
|
|
336 |
If  then the expression for  in terms of  is a)  b)  c)  d) 
If then the expression for in terms of is a) b) c) d)
|
IIT 2003 |
01:32 min
|
|
337 |
Multiple choice Which of the following expressions are meaningful a)  b)  c)  d) 
Multiple choice Which of the following expressions are meaningful a) b) c) d)
|
IIT 1998 |
01:15 min
|
|
338 |
If  then at x = 0,  is equal to a) 0 b) 1 c) 2 d) 4
If then at x = 0, is equal to a) 0 b) 1 c) 2 d) 4
|
IIT 1996 |
02:05 min
|
|
339 |
 is equal to
a) 0 b) 4 c) 6 d) −4
is equal to a) 0 b) 4 c) 6 d) −4
|
IIT 2004 |
03:15 min
|
|
340 |
Find all values of λ such that  and  where  are unit vectors along the coordinate vectors.
Find all values of λ such that and where are unit vectors along the coordinate vectors.
|
IIT 1982 |
04:48 min
|
|
341 |
The complex numbers sinx + icos2x and cosx – isin2x are conjugate to each other for a) a = nπ b) x = 0 c) x =  d) None of these
The complex numbers sinx + icos2x and cosx – isin2x are conjugate to each other for a) a = nπ b) x = 0 c) x = d) None of these
|
IIT 1988 |
02:59 min
|
|
342 |
Suppose  is an identity in x where  are constants and  . Then the value of n = ………. a) 4 b) 5 c) 6 d) 7
Suppose is an identity in x where are constants and . Then the value of n = ………. a) 4 b) 5 c) 6 d) 7
|
IIT 1981 |
02:56 min
|
|
343 |
Prove that  is divisible by 25 for any natural number n.
Prove that is divisible by 25 for any natural number n.
|
IIT 1982 |
03:55 min
|
|
344 |
Evaluate  where n is a positive integer and t is a parameter independent of x. a)  b)  c)  d) 
Evaluate where n is a positive integer and t is a parameter independent of x. a) b) c) d)
|
IIT 1981 |
05:47 min
|
|
345 |
Show that 
Show that
|
IIT 1982 |
01:38 min
|
|
346 |
If a, b, c are coplanar, show that
If a, b, c are coplanar, show that
|
IIT 1989 |
02:38 min
|
|
347 |
 is the reflexion of  in the line whose equation is . .
is the reflexion of in the line whose equation is . .
|
IIT 1982 |
00:57 min
|
|
348 |
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
|
|
349 |
If  Where [x] denotes the greatest integer less than or equal to x then  equals a) 1 b) 0 c) – 1 d) None of these
If Where [x] denotes the greatest integer less than or equal to x then equals a) 1 b) 0 c) – 1 d) None of these
|
IIT 1985 |
02:39 min
|
|
350 |
Evaluate  a)  b)  c)  d) 
|
IIT 1984 |
03:38 min
|
