1176 |
One or more than one correct options If then a) b) c) d)
One or more than one correct options If then a) b) c) d)
|
IIT 2009 |
|
1177 |
equals a) 8 b) 2 c) 4 d) 0
equals a) 8 b) 2 c) 4 d) 0
|
IIT 2014 |
|
1178 |
For any real number x, let [x] denote the greater integer less than or equal to x. Let f be a real valued function defined on the interval [−10, 10] by then the value of is a) 2 b) 0 c) 6 d) 4
For any real number x, let [x] denote the greater integer less than or equal to x. Let f be a real valued function defined on the interval [−10, 10] by then the value of is a) 2 b) 0 c) 6 d) 4
|
IIT 2010 |
|
1179 |
is equal to a) b) c) d)
is equal to a) b) c) d)
|
IIT 2016 |
|
1180 |
The area of the region is a) b) c) d)
The area of the region is a) b) c) d)
|
IIT 2017 |
|
1181 |
The area enclosed by the curve y = sinx + cosx and y = |cosx – sinx| over the interval is a) b) c) d)
The area enclosed by the curve y = sinx + cosx and y = |cosx – sinx| over the interval is a) b) c) d)
|
IIT 2014 |
|
1182 |
One or more than one correct option If the line x = α divides the area of the region R = {(x, y) ∈ ℝ2 : x3 ≤ y ≤ x, 0 ≤ x ≤ 1 into two equal parts then a) b) c) d)
One or more than one correct option If the line x = α divides the area of the region R = {(x, y) ∈ ℝ2 : x3 ≤ y ≤ x, 0 ≤ x ≤ 1 into two equal parts then a) b) c) d)
|
IIT 2017 |
|
1183 |
The value of a) b) c) d)
The value of a) b) c) d)
|
IIT 2016 |
|
1184 |
Find the derivative with respect to x of the function at x = a) b) c) d)
Find the derivative with respect to x of the function at x = a) b) c) d)
|
IIT 1984 |
|
1185 |
If f(x) = then on the interval [0, π] a) tan and are both continuous b) tan and are both discontinuous c) tan and are both continuous d) tan is continuous but is not
|
IIT 1989 |
|
1186 |
If and where 0 < x ≤1, then in this interval a) Both f (x) and g (x) are increasing functions b) Both f (x) and g (x) are decreasing functions c) f (x) is an increasing function d) g (x) is an increasing function
If and where 0 < x ≤1, then in this interval a) Both f (x) and g (x) are increasing functions b) Both f (x) and g (x) are decreasing functions c) f (x) is an increasing function d) g (x) is an increasing function
|
IIT 1997 |
|
1187 |
The function is not differentiable at a) – 1 b) 0 c) 1 d) 2
The function is not differentiable at a) – 1 b) 0 c) 1 d) 2
|
IIT 1999 |
|
1188 |
Let then points where f (x) is not differentiable is (are) a) 0 b) 1 c) ± 1 d) 0, ± 1
Let then points where f (x) is not differentiable is (are) a) 0 b) 1 c) ± 1 d) 0, ± 1
|
IIT 2005 |
|
1189 |
Multiple choices Let [x] denote the greatest integer less than or equal to x. If f (x) = [xsinπx] then f(x) is a) Continuous at x = 0 b) Continuous in c) f (x) is differentiable at x = 1 d) differentiable in e) None of these
Multiple choices Let [x] denote the greatest integer less than or equal to x. If f (x) = [xsinπx] then f(x) is a) Continuous at x = 0 b) Continuous in c) f (x) is differentiable at x = 1 d) differentiable in e) None of these
|
IIT 1986 |
|
1190 |
Let then a) b) c) d)
|
IIT 1987 |
|
1191 |
Multiple choices Which of the following functions are continuous on (0, π) a) tanx b) c) d)
Multiple choices Which of the following functions are continuous on (0, π) a) tanx b) c) d)
|
IIT 1991 |
|
1192 |
Multiple choices Let for every real number x then a) h (x) is continuous for all x b) h is differentiable for all x c) for all x > 1 d) h is not differentiable for two values of x
Multiple choices Let for every real number x then a) h (x) is continuous for all x b) h is differentiable for all x c) for all x > 1 d) h is not differentiable for two values of x
|
IIT 1998 |
|
1193 |
Number of divisors of the form 4n + 2(n ≥ 0) of integer 240 is a) 4 b) 8 c) 10 d) 3
Number of divisors of the form 4n + 2(n ≥ 0) of integer 240 is a) 4 b) 8 c) 10 d) 3
|
IIT 1998 |
|
1194 |
Let f (x) be defined on the interval such that g (x) = f (|x|) + |f(x)| Test the differentiability of g (x) in a) g(x) is differentiable at all x ℝ b) g(x) is differentiable at all x ℝ except at x = 1 c) g(x) is differentiable at all x ℝ except at x = 0, 1 d) g(x) is differentiable at all x ℝ except at x = 0, 1, 2
Let f (x) be defined on the interval such that g (x) = f (|x|) + |f(x)| Test the differentiability of g (x) in a) g(x) is differentiable at all x ℝ b) g(x) is differentiable at all x ℝ except at x = 1 c) g(x) is differentiable at all x ℝ except at x = 0, 1 d) g(x) is differentiable at all x ℝ except at x = 0, 1, 2
|
IIT 1986 |
|
1195 |
If the LCM of p, q is where r, s, t are prime numbers and p, q are positive integers then the number of ordered pairs (p, q) is a) 252 b) 254 c) 225 d) 224
If the LCM of p, q is where r, s, t are prime numbers and p, q are positive integers then the number of ordered pairs (p, q) is a) 252 b) 254 c) 225 d) 224
|
IIT 2006 |
|
1196 |
In how many ways can a pack of 52 cards be divided into four groups of 13 cards each.
In how many ways can a pack of 52 cards be divided into four groups of 13 cards each.
|
IIT 1979 |
|
1197 |
Determine the values of x for which the following function fails to be continuous or differentiable. Justify your answer. a) f(x) is continuous and differentiable b) f(x) is continuous everywhere but not differentiable at x = 1, 2 c) f(x) is continuous everywhere but not differentiable at x = 2 d) f(x) is neither continuous nor differentiable at x = 1, 2
Determine the values of x for which the following function fails to be continuous or differentiable. Justify your answer. a) f(x) is continuous and differentiable b) f(x) is continuous everywhere but not differentiable at x = 1, 2 c) f(x) is continuous everywhere but not differentiable at x = 2 d) f(x) is neither continuous nor differentiable at x = 1, 2
|
IIT 1997 |
|
1198 |
Let And where a and b are non-negative real numbers. Determine the composite function gof. If (gof)(x) is continuous for all real x, determine the values of a and b. Is gof differentiable at x = 0? a) a = b = 0 b) a = 0, b = 1 c) a = 1, b = 0 d) a = b = 1
Let And where a and b are non-negative real numbers. Determine the composite function gof. If (gof)(x) is continuous for all real x, determine the values of a and b. Is gof differentiable at x = 0? a) a = b = 0 b) a = 0, b = 1 c) a = 1, b = 0 d) a = b = 1
|
IIT 2002 |
|
1199 |
Show that f(x) is differentiable at the value of α = 1. Also, a) b2 +c2 = 4 b) 4 b2 = 4 − c2 c) 64 b2 = 4 − c2 d) 64 b2 = 4 + c2
Show that f(x) is differentiable at the value of α = 1. Also, a) b2 +c2 = 4 b) 4 b2 = 4 − c2 c) 64 b2 = 4 − c2 d) 64 b2 = 4 + c2
|
IIT 2004 |
|
1200 |
The product of r consecutive natural numbers is divisible by r! a) True b) False
The product of r consecutive natural numbers is divisible by r! a) True b) False
|
IIT 1985 |
|