1 |
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
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2 |
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)
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IIT 1981 |
05:47 min
|
3 |
is equal to a) 0 b) c) d) None of these
is equal to a) 0 b) c) d) None of these
|
IIT 1984 |
01:15 min
|
4 |
Find the area bounded by the X - axis, part of the curve and the ordinate at x = 2 and x = 4. If the ordinate at x = a divide the area into two equal parts, find a, a) b) c) d)
Find the area bounded by the X - axis, part of the curve and the ordinate at x = 2 and x = 4. If the ordinate at x = a divide the area into two equal parts, find a, a) b) c) d)
|
IIT 1983 |
06:17 min
|
5 |
The value of is a) 1 b) – 1 c) 0 d) None of these
The value of is a) 1 b) – 1 c) 0 d) None of these
|
IIT 1991 |
02:34 min
|
6 |
Evaluate a) b) c) d)
|
IIT 1986 |
05:55 min
|
7 |
a) exists and equals b) exists and equals c) does not exist because x – 1 → 0 d) does not exist because the left hand limit is not equal to the right hand limit.
a) exists and equals b) exists and equals c) does not exist because x – 1 → 0 d) does not exist because the left hand limit is not equal to the right hand limit.
|
IIT 1998 |
03:32 min
|
8 |
Evaluate a) πln2 b) c) d)
Evaluate a) πln2 b) c) d)
|
IIT 1997 |
02:50 min
|
9 |
If where n is a non–zero real number, then a is equal to a) 0 b) c) n d)
If where n is a non–zero real number, then a is equal to a) 0 b) c) n d)
|
IIT 2003 |
02:22 min
|
10 |
If f (x) is an even function then prove that .
If f (x) is an even function then prove that .
|
IIT 2003 |
07:55 min
|
11 |
The integral dx where [ ] denotes the greatest integer function equals . . . a) b) + 1 c) d)
The integral dx where [ ] denotes the greatest integer function equals . . . a) b) + 1 c) d)
|
IIT 1988 |
02:11 min
|
12 |
Let f (x) = then for all x a) b) f is differentiable c) is continuous d) f is continuous
Let f (x) = then for all x a) b) f is differentiable c) is continuous d) f is continuous
|
IIT 1994 |
04:05 min
|
13 |
If for non-zero x, where a ≠ b thenis equal to a) b) c) d)
If for non-zero x, where a ≠ b thenis equal to a) b) c) d)
|
IIT 1996 |
04:39 min
|
14 |
Multiple choices If f (x) = then a) f (x) is continuous ∀ x ℝ b) f (x) > 0 ∀ x > 1 c) f (x) is continuous but not differentiable ∀ x ℝ d) f (x) is not differentiable at two points
Multiple choices If f (x) = then a) f (x) is continuous ∀ x ℝ b) f (x) > 0 ∀ x > 1 c) f (x) is continuous but not differentiable ∀ x ℝ d) f (x) is not differentiable at two points
|
IIT 2006 |
04:20 min
|
15 |
Eight chairs are numbered one to eight. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 then the men select the chairs from amongst the remaining. The number of possible arrangements is a) b) c) d) None of these
Eight chairs are numbered one to eight. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 then the men select the chairs from amongst the remaining. The number of possible arrangements is a) b) c) d) None of these
|
IIT 1982 |
01:42 min
|
16 |
Find if f(x) = a) 0 b) c) d)
Find if f(x) = a) 0 b) c) d)
|
IIT 1979 |
02:21 min
|
17 |
An n digit number is a positive number with exactly n–digits. Nine hundred distinct n–digit numbers are to be formed with only the three digits 2, 5 and 7. The smallest value of n for which this is possible is a) 6 b) 7 c) 8 d) 9
An n digit number is a positive number with exactly n–digits. Nine hundred distinct n–digit numbers are to be formed with only the three digits 2, 5 and 7. The smallest value of n for which this is possible is a) 6 b) 7 c) 8 d) 9
|
IIT 1998 |
02:08 min
|
18 |
Let f be a twice differentiable function such that and , . Find h (10) if h (5) = 1. a) 0 b) 1 c) 2 d) 4
Let f be a twice differentiable function such that and , . Find h (10) if h (5) = 1. a) 0 b) 1 c) 2 d) 4
|
IIT 1982 |
01:45 min
|
19 |
The number of arrangements of two letters of the word BANANA in which two N’s do not appear adjacently is a) 40 b) 60 c) 80 d) 100
The number of arrangements of two letters of the word BANANA in which two N’s do not appear adjacently is a) 40 b) 60 c) 80 d) 100
|
IIT 2004 |
02:34 min
|
20 |
If , then find the values of n and r
If , then find the values of n and r
|
IIT 1979 |
04:28 min
|
21 |
Let Determine a and b so that f is continuous at x = 0. a) b) c) d)
Let Determine a and b so that f is continuous at x = 0. a) b) c) d)
|
IIT 1994 |
08:15 min
|
22 |
A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can three balls be drawn from a box if at least one black ball is to be included in the draw?
A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can three balls be drawn from a box if at least one black ball is to be included in the draw?
|
IIT 1986 |
03:17 min
|
23 |
A committee of 12 is to be formed from 9 women and 8 men. In how many ways this can be if at least five women have to be in the committee? In how many ways in these committees (i) The women are in majority, (ii)The men are in majority
A committee of 12 is to be formed from 9 women and 8 men. In how many ways this can be if at least five women have to be in the committee? In how many ways in these committees (i) The women are in majority, (ii)The men are in majority
|
IIT 1994 |
05:51 min
|
24 |
If a function f : is an odd function such that for x ε [a, 2a] and the left hand derivative at x = a is 0 then find the left hand derivative at x = a) 0 b) 1 c) a d) 2a
If a function f : is an odd function such that for x ε [a, 2a] and the left hand derivative at x = a is 0 then find the left hand derivative at x = a) 0 b) 1 c) a d) 2a
|
IIT 2003 |
03:55 min
|
25 |
A country produces 90% of its food diet. The population grows continuously at a rate of 3% per year. Its annual food production every year is 4% more than that of last year. Assuming that the average food requirement per person remains constant, prove that the country will become self sufficient in food after n years, where n is the smallest integer bigger than or equal to
A country produces 90% of its food diet. The population grows continuously at a rate of 3% per year. Its annual food production every year is 4% more than that of last year. Assuming that the average food requirement per person remains constant, prove that the country will become self sufficient in food after n years, where n is the smallest integer bigger than or equal to
|
IIT 2000 |
04:17 min
|