Q

Q 15)

G Gautam harsolia

Given function is

Given function is satisfies for the all real values of x
case (i)  k < 0

Hence, function is continuous for all values of x < 0

case (ii)  x = 0

L.H.L at x= 0

R.H.L. at x = 0

L.H.L. = R.H.L. = f(0)
Hence, function is continuous at x = 0

case (iii)  k > 0

Hence , function is continuous for all values of x > 0

case (iv) k < 1

Hence , function is continuous for all values of x < 1

case (v)  k > 1

Hence , function is continuous for all values of x > 1

case (vi)  x = 1

Hence, function is not continuous at x = 1

Q.6 Write the following as intervals :

(i) {x : x R, – 4  x  6}

(ii) {x : x  R, – 12 x –10}

(iii) {x : x  R, 0  x  7}

(iv) {x : x  R, 3   x   4}

S safeer

The following can be written in interval as :

(i) {x : x R, – 4  x  6}

(ii) {x : x  R, – 12 x –10}

(iii) {x : x  R, 0  x  7}

(iv) (iv) {x : x  R, 3   x   4}

Q.5 How many elements has P(A), if A = ?

S safeer

Let the elements in set A be m,then n m

then, number of elements in power set of A         n

Here,  A =    so    n 0

n  1

Hence,we conclude P(A) has 1 element.

Q.4 Write down all the subsets of the following sets:

(iv)

S safeer

Subset  of   is   only.

The subset of a null set is null set itself

Q.4 Write down all the subsets of the following sets:

(iii) {1,2,3}

S safeer

Subsets of

Q.4 Write down all the subsets of the following sets:

(ii) {a, b}

S safeer

Subsets of  . Thus the given set has 4 subsets

Q.4 Write down all the subsets of the following sets

(i) {a}

S safeer

Subsets of .

Q4. Fill up the blanks with the words given:

herbivore, plant, milk, sugarcane, carnivore

(a) Tiger is a _______________ because it eats only meat.

(b) Deer eats only plant products and so, is called ______________.

(c) Parrot eats only _______________ products.

(d) The ________________ that we drink, which comes from cows, buffaloes and goats is an animal product.

(e) We get sugar from ________________.

P Priyanka Kumari

(a) Tiger is a  carnivore  because it eats only meat.

(b) Deer eats only plant products and so, is called  herbivores .

(c) Parrot eats only   plant_ products.

(d) The  milk  that we drink, which comes from cows, buffaloes, and goats is an animal product.

(e) We get sugar from  sugarcane .

Find         in

Q (10)

S seema garhwal

all functions are positive in this range
We know that

= 1 -      =    =

cos x =                  (cos x is -ve in II quadrant)

We know that
cosx =

(because all functions are posititve in given range)

similarly,
cos x =

(because all functions are posititve in given range)

Find        in

Q (9)

S seema garhwal

We know that
cos x  =
cos x + 1
=     + 1   =     =

Now,
we know that
cos x =

=  1 -    =    =

Because    is +ve in given quadrant

Find        in

Q (8)

S seema garhwal

tan x =
We know that ,

=
=
x lies in II quadrant  thats why sec x is -ve
So,

Now,    =
We know that,
(  )

=      =

=
=
=   =
x lies in II quadrant so value of                is +ve

=
we know that

=  1 -     =

x lies in II quadrant So value of sin x is +ve

Q(7)   Prove that

S seema garhwal

We know that

we use these identities

sin2x +   =   2sinx cosx  +
take 2 sinx common

=  R.H.S.

Q (6)  Prove that

S seema garhwal

We know that

and

We use these two identities in our problem

sin7x + sin5x  =      =

sin 9x + sin 3x =   =

cos 7x + cos5x =    =

cos 9x + cos3x =   =

=

=            = R.H.S.

Q(5)  Prove that

S seema garhwal

we know that

We use this identity in our problem
If we notice we need sin4x in our final result so it is better if we made a combination of sin7x and sin x , sin3x and  sin5x tp get sin4x

take 2sin4x common
= 2sin4x(cos3x + cosx)
Now,
We know that

We use this

=
= 2sin4x()
= 4cosxcos2xsin4x = R.H.S.

Q(4)  Prove that

S seema garhwal

We know that
and

We use these two in our problem

and

=  +
= 1 - 2cosxcosy + 1 - 2sinxsiny
= 2 - 2(cosxcosy + sinxsiny)
= 2 - 2cos(x - y)
=  2(1 - cos(x - y) )
Now we can write

so

=  R.H.S.

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