If f x = x e - 1 x + 1 x ; i f x ≠ 0 0 ; i f x = 0 then which of the following is correct?

f x is continuous and f ' 0 does not exist

f x is continuous and f ′ 0 also exists

For x ∈ R , f x = log ⁡ 2 - sin ⁡ x and g x = f f x , then

g is differentiable at x = 0 and g ' 0 = - sin ⁡ log ⁡ 2

g is not differentiable at x = 0

Let f : R → R be differentiable at c ∈ R and f c = 0 . If g x = f x , then at x = c , g is:

not differentiable if f ' c = 0

Let f : R → R be a function such that f x ≤ x 2 , for all x ∈ R . Then, at x = 0 , f is

continuous as well as differentiable

differentiable but not continuous

neither continuous nor differentiable

continuous but not differentiable

Match the organism with its use in biotechnology. (a) Bacillus thuringiensis (i) Cloning vector (b) Thermus aquaticus (ii) Construction of first rDNA molecule (c) Agrobacterium tumefaciens (iii) DNA polymerase (d) Salmonella typhimurium (iv) Cry proteins

(a)-(iv), (b)-(iii), (c)-(i), (d)-(ii)

(a)-(iii), (b)-(ii), (c)-(iv), (d)-(i)

(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)

(a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)

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Important Questions on The Solid State

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Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

f (x) = \{\begin{matrix} x e^{- (\frac{1}{|x|} + \frac{1}{x})}; & i f & x \neq 0 \\ 0; & i f & x = 0 \end{matrix}

then which of the following is correct?

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Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

Let

f (x) = \{\begin{matrix} m a x (|x|, x^{2}), & |x| \leq 2 \\ 8 - 2 |x|, & 2 < |x| \leq 4 \end{matrix} .

Let

S

be the set of points in the interval

(- 4, 4)

at which

f

is not differentiable. Then

S

MEDIUM

Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

Let

f : (- 1, 1) \to R

be a function defined by

f (x) = m a x \{- |x|, - \sqrt{1 - x^{2}}\} .

K

be the set of all points at which

f

is not differentiable, then

K

has exactly

HARD

Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

For

x \in R, f (x) = |\log 2 - \sin x|

and

g (x) = f (f (x))

, then

EASY

Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

H. Boyer

&

S. Cohen are famous for their research work on

HARD

Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

Let

S = \{t \in R : f (x) = |x - π| \cdot (e^{|x|} - 1) \sin |x| is not differentiable at t\} .

Then, the set

S

is equal to:

EASY

Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

Let

S

be the set of all points in

(- π, π)

at which the function,

f (x) = \min \{\sin x, \cos x\}

is not differentiable. Then

S

is a subset of which of the following?

MEDIUM

Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

Let

f : R \to R

be differentiable at

c \in R

and

f (c) = 0

. If

g (x) = |f (x)|

, then at

x = c, g

is:

MEDIUM

Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

The core techniques enabled modern biotechnology

A)

Change the phenotype of host-organism by genetic engineering

B)

Chemical engineering process of vaccine production by tissue culture

C)

Manufacture of specific products from eukaryotic cells in bioreactors

D)

Altering the chemistry of genetic material by tissue culture

EASY

Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

The construction of first artificial recombinant DNA molecule was by:

HARD

Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

If the function

f (x) = \{\begin{matrix} - x, & x < 1 \\ a + \cos^{- 1} (x + b), & 1 \leq x \leq 2 \end{matrix}

is differentiable at

x = 1

, then

\frac{a}{b}

is equal to

EASY

Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

Consider the statement given below and decide out of which given presuppositions is it inherent in.
Statement
Doctors these days advise the consumption of rice in the dinner.
Presuppositions
I. Late night dinner produces toxin in the because the food remains undigested for a long time.
II. Rice digests quickly .

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Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

2 y = {(\cot^{- 1} (\frac{\sqrt{3} \cos x + \sin x}{\cos x - \sqrt{3} \sin x}))}^{2} \forall x \in (0, \frac{π}{2})

, then

\frac{d y}{d x}

is equal to

HARD

Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

Let

f : R \to R

be a function such that

|f (x)| \leq x^{2},

for all

x \in R .

Then, at

x = 0,

f

HARD

Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

Let

f (x) = 15 - |x - 10|; x \in R .

Then the set of all values of

x

, at which the function

g (x) = f (f (x))

is not differentiable, is:

HARD

Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

If the function

f (x) = \{\begin{array}{cl} k_{1} (x - π)^{2} - 1, & x \leq π \\ k_{2} \cos x, & x > π \end{array}

is twice differentiable, then the ordered pair

(k_{1}, k_{2})

is equal to:

HARD

Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

f (x) = [x]

, where

[x]

is the greatest integer not greater than

x

, then

f^{'} (1^{+})

= ….

HARD

Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

If the function

g (x) = {\begin{matrix} k \sqrt{x + 1}, & 0 \leq x \leq 3 \\ m x + 2, & 3 < x \leq 5 \end{matrix}

is differentiable, then the value of

k + m

MEDIUM

Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

Match the organism with its use in biotechnology.

(a)	Bacillus thuringiensis	(i)	Cloning vector
(b)	Thermus aquaticus	(ii)	Construction of first rDNA molecule
(c)	Agrobacterium tumefaciens	(iii)	DNA polymerase
(d)	Salmonella typhimurium	(iv)	Cry proteins

EASY

Chemistry>Physical Chemistry>The Solid State>General Characteristics of Solid State

Which presupposition is inherent in the following statement?
Statement
Vimla said reminding her husband, "I hope you have taken your raincoat".
Presupposition
I. There is likelihood of rain.
II. Vimla is careful about the health of her husband.

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Important Questions on The Solid State

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