﻿ If the function g(x) = is differntiable, then the value of k+m is | Relations and Functions

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# 1.If the function g(x) = is differntiable, then the value of k+m is 2 16/5 10/3 10/3

A.

2

Since, g(x) is differentiable ⇒ g(x) must be continuous.
therefore,
At x =3, RHL = 3m+2
and at x = 3, LHL= 2k
therefore,  2k = 3m + 2 ... (i)
Also, g'(x) =
therefore, L{g'(3)} = k/4 and R{g'(3)} = m
⇒ k/4 = m i.e, k = 4m ..... (ii)
On solving eqs (i) and (ii), we get
k = 8/5, m =2/5
⇒ k+m =2

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2.

If a ε R and the equation - 3(x-[x]2 + 2(x-[x] +a2 = 0(where,[x] denotes the greatest integer ≤ x) has no  integral solution, then all possible value of  lie in the interval

• (-1,0) ∪ (0,1)

• (1,2)

• (-2,-1)

• (-∞,-2) ∪ (2, ∞)

182 Views

3.

Consider the following relations:
R = {(x, y)| x, y are real numbers and x = wy for some rational number w}; S = {(m/p, p/q)| m, n, p and q are integers such that n, q ≠ 0 and qm = pn}. Then

• R is an equivalence relation but S is not an equivalence relation

• neither R nor S is an equivalence relation

• S is an equivalence relation but R is not an equivalence relation

• S is an equivalence relation but R is not an equivalence relation

308 Views

4.

Let p(x) be a function defined on R such that  = 1, p'(x)  p'(1-x),for all x∈[0,1] p(0) = 1 and p(1) = 41. Then  equals

• √41

• 21

• 41

• 41

224 Views

5.

The function

• neither injective nor surjective.

• invertible

• injective but not surjective.

• injective but not surjective.

371 Views

6.

Let W denote the words in the English dictionary. Define the relation R by :
R = {(x, y) ∈ W × W | the words x and y have at least one letter in common}. Then R is

• not reflexive, symmetric and transitive

• reflexive, symmetric and not transitive

• reflexive, symmetric and transitive

• reflexive, symmetric and transitive

141 Views

7.

The graph of the function y = f(x) is symmetrical about the line x = 2, then

• f(x + 2)= f(x – 2)

• f(2 + x) = f(2 – x)

• f(x) = f(-x)

• f(x) = f(-x)

219 Views

8.

The domain of the function

• [2, 3]

• [2, 3)

• [1, 2]

• [1, 2]

139 Views

9.

is equal to

10.

If , then

• - 1 < x < 4

• 2 < x < 3

• 1 < x < 4

• 1 < x < 3