JEE Questions for Maths Limits Continuity And Differentiability Quiz 5 - MCQExams.com


Maths-Limits Continuity and Differentiability-35066.png
  • 1
  • 0
  • e
  • None of these
For the function, which of the following is correct

  • Maths-Limits Continuity and Differentiability-35068.png
  • 2)
    Maths-Limits Continuity and Differentiability-35069.png

  • Maths-Limits Continuity and Differentiability-35070.png

  • Maths-Limits Continuity and Differentiability-35071.png

Maths-Limits Continuity and Differentiability-35073.png
  • does not exist
  • infinite
  • 0
  • 2

Maths-Limits Continuity and Differentiability-35075.png
  • 0
  • 1/2
  • 1
  • 3/2

Maths-Limits Continuity and Differentiability-35077.png
  • 10/3
  • 3/10
  • 6/5
  • 5/6
If α and β are the distinct roots ax2 + bx + c = 0, then
Maths-Limits Continuity and Differentiability-35079.png
  • 1/2 (α - β)2
  • - (α2/(α - β )2
  • 0
  • α2/2 (α - β)2

Maths-Limits Continuity and Differentiability-35081.png
  • 0
  • -1
  • -2
  • 1

Maths-Limits Continuity and Differentiability-35083.png
  • 0
  • -1
  • 1
  • 2

Maths-Limits Continuity and Differentiability-35085.png
  • 1/2
  • - (1/2)
  • 0
  • 1

Maths-Limits Continuity and Differentiability-35087.png
  • ∞
  • 1
  • 0
  • does not exist

Maths-Limits Continuity and Differentiability-35089.png
  • 2
  • -1
  • 0
  • does not exist

Maths-Limits Continuity and Differentiability-35091.png
  • 0
  • -1
  • 1
  • ∞

Maths-Limits Continuity and Differentiability-35093.png
  • l1 < l2 < l3
  • l2 < l3 < l1
  • l3 < l2 < l1
  • l1 < l3 < l2

Maths-Limits Continuity and Differentiability-35095.png
  • 1/√2
  • 1/2
  • 1
  • 2

Maths-Limits Continuity and Differentiability-35097.png
  • 3
  • 2
  • -1
  • 4

Maths-Limits Continuity and Differentiability-35099.png
  • 1
  • 0
  • e
  • e2

Maths-Limits Continuity and Differentiability-35101.png
  • 1 and - 2
  • 1 and 2
  • -1 and 2
  • -1 and -2
For every integer n let an and bn be real numbers. if function f : R → R is given by
Maths-Limits Continuity and Differentiability-35103.png

  • Maths-Limits Continuity and Differentiability-35104.png
  • 2)
    Maths-Limits Continuity and Differentiability-35105.png

  • Maths-Limits Continuity and Differentiability-35106.png

  • Maths-Limits Continuity and Differentiability-35107.png
Define F(x) as the product of two real functions f1 = x, x ϵ R and
Maths-Limits Continuity and Differentiability-35109.png
  • Statement I is incorrect, Statement II is correct
  • Statement I is correct, Statement II is correct; Statement II is correct explanation for Statement I
  • Statement I is correct, Statement II is correct; Statement II is not a correct explanation for Statement I
  • Statement I is correct, Statement II is incorrect

Maths-Limits Continuity and Differentiability-35111.png
  • p = 5/2 and q = 1/2
  • p = 3/2 and q = 1/2
  • p = 1/2 and q = 3/2
  • p = 1/2 and q = 3/2

Maths-Limits Continuity and Differentiability-35113.png
  • 0
  • -1
  • 1
  • e

Maths-Limits Continuity and Differentiability-35115.png
  • a = 1 and b = 1
  • a = - 1 and b = -1
  • a = - 1 and b = 1
  • a = 1 and b = - 1

Maths-Limits Continuity and Differentiability-35117.png
  • a3/2
  • a1/2
  • - a1/2
  • - a3/2
f(x) = x + |x| is continuous for

  • Maths-Limits Continuity and Differentiability-35119.png
  • 2)
    Maths-Limits Continuity and Differentiability-35120.png
  • only x > 0
  • no value of x
The number of discontinuities of the greatest number integer function f(x) = [x], x ϵ (- (7/2),is equal to
  • 104
  • 100
  • 102
  • 101
  • 103
if f(x) = [x3 - 3], where [x] is the greatest integer function. Then, the number of points in the interval (1,where function is discontinuous is
  • 4
  • 5
  • 6
  • 7

Maths-Limits Continuity and Differentiability-35124.png
  • 2
  • 1
  • -1
  • 0
The function f(x) is defined as
Maths-Limits Continuity and Differentiability-35126.png
  • -1/3
  • 1
  • 2/3
  • 1/3
If f : R → r is defined by
Maths-Limits Continuity and Differentiability-35128.png
  • -2
  • -4
  • -6
  • -8
The value of f(0), so that
Maths-Limits Continuity and Differentiability-35130.png
  • log(1/20
  • 0
  • 4
  • -1 + log 2

Maths-Limits Continuity and Differentiability-35132.png
  • f is discontinuous
  • f is continuous only, if λ = 0
  • f is continuous only, whatever λ may be
  • None of these

Maths-Limits Continuity and Differentiability-35134.png
  • ∞
  • 1
  • 0
  • None of these

Maths-Limits Continuity and Differentiability-35135.png
  • 4
  • 2
  • 1
  • 1/4
The function f : R -{0} → R is given by
Maths-Limits Continuity and Differentiability-35137.png
  • 2
  • -1
  • 0
  • 1

Maths-Limits Continuity and Differentiability-35139.png
  • for x = 2 only
  • for all real values of x such that x ≠ 2
  • for all real values of x
  • for all integral values ofx only

Maths-Limits Continuity and Differentiability-35141.png
  • π/5
  • 5/π
  • 1
  • 0

Maths-Limits Continuity and Differentiability-35143.png
  • 2
  • 4
  • 3
  • 1
If the derivative of the function f(x) is everywhere continuous and is given by
Maths-Limits Continuity and Differentiability-35145.png
  • a = 2, b = -3
  • a = 3, b = 2
  • a = -2, b = -3
  • a = -3, b = -2
The value of k which the function
Maths-Limits Continuity and Differentiability-35147.png
  • k = 0
  • k = 1
  • k = -1
  • None of these
The function f(x) = (x2 -|x2 - 3x + 2|+ cos|x| is non-differentiable at
  • -1
  • 0
  • 1
  • 2
Let R be the set of all real numbers. If f : R → r is a function, such that |f(x)-f(x)|2 ≤ |x - y|3, ∀ x, y ϵ R, then f' (x) is equal to
  • f(x)
  • 1
  • 0
  • x2
  • x

Maths-Limits Continuity and Differentiability-35151.png
  • 1/4
  • 1/2
  • 3/4
  • 1
  • 0
The function f(x) = a sin |x| + be|x| is differentiable at x = 0, when
  • 3a + b = 0
  • 3a - b = 0
  • a + b = 0
  • a - b = 0

Maths-Limits Continuity and Differentiability-35154.png
  • differentiable both at x = 0 at x = 2
  • differentiable at x= 0 but not differentiable at x= 2
  • not differentiable at x = 0 but differentiable at x = 0
  • differentiable neither at x = 0 nor at x = 2
Consider the function fx = |x - 2| + |x - 5|, x ϵ R
Statement I f' (= 0
Statement II f is continuous in [2, 5], differentiable in (2,and f(= f(5).
  • Statement I is incorrect, Statement II is correct
  • Statement I is correct, Statement II is correct; Statement II is correct explanation for Statement I
  • Statement I is correct, Statement Ii is correct; Statement II is not a correct explanation for Statement I
  • Statement I is correct, Statement Ii is incorrect
A function f is defined by f(x) = 2 + (x -1)2/3 in [0, 2]. Which of the following is not correct ?
  • f is continuous is [0, 2]
  • f(= f(2)
  • f is not derivable in [0, 2]
  • Rolle's theorem is true [0, 2]
The number of points of
f(x) = |x - 1| + |x - 3| + sin x, x ϵ [0, 4), where f(x) is not differentiable, is
  • 0
  • 1
  • 2
  • 3
If f : R → R is a function such that f(x + y) = f(x) + f(y), ∀ x, y ϵ R. If f(x) is differentiable at x = 0, then
  • f(x) is differentiable only in a finite interval containing zero
  • f(x) is continuous, ∀ x ϵ R
  • f'(x) is constant, ∀ x ϵ R
  • f(x) is differentiable except at finitely many points

Maths-Limits Continuity and Differentiability-35160.png
  • f(x) is continuous at x = - π/2
  • f(x) is differentiable at x = 1
  • f(x) is differentiable at x = -3/2
  • All of the above
If f(x) = p |sin x| + qe|x| + r |x|3 and it is differentiable at x = 0 then
  • p = 0, q = 0 and r = 0
  • p + q = 0 and r is any real number
  • p + q + r = 0
  • -p + q - r = 0
0:0:1


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