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Jagdish Padaliya 8 years, 4 months ago

cos(90*2+30)° here Cos thita lie on the third quadrant so thita will be -ve and value of cos 30° is under root3 by 2 so the value of cos210° is -under root3 by 2
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Soumya Ghoshal 8 years, 4 months ago

In trigonometry,

  31π/3

=31×180°÷3

=31×60°

=1860°

Or, in mensuration,

31π/3

=31×22/7÷3

=32.49

 

 

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Sahdev Sharma 8 years, 4 months ago

The letters have to be arranged in such a way that there are always 4 letters between P and S.

Therefore, in a way, the places of P and S are fixed. The remaining 10 letters in which there are 2 Ts can be arranged in {tex}10!\over 2 !{/tex} ways

Also, the letters P and S can be placed such that there are 4 letters between them in  {tex} 2 \times 7 = 14{/tex} ways.

Therefore, by multiplication principle, required number of arrangements in this case = {tex}{10!\over 2!}\times 14 = {/tex}

25401600

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Bhavesh Batra 8 years, 4 months ago

Follow some steps like: Step 1: Take n=1 and prove it. Step 2: Take n=k and prove it. Step 3: Take n=k+1 and prove it. By taking an equation equal to n=k from step 3 prove LHS=RHS

H S 8 years, 4 months ago

If we we solve all questions by following given steps then this chapter will become more easier... We can first prove that P(n) is true when n=1 and then in place of n we can put k and name it as equation 1 After this we will place k+1 in place of k and solve for LHS.We will then obtain a solution in which we can put the value of 1. Then we can show that LHS=RHS..
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Ishant Sehrawat 8 years, 4 months ago

Locus is just the path covered by particle Eqn. Of straight line - x+y+constant=0 Circle- x^2+y^2+gx+full+constant=0
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Dharmendra Kumar 8 years, 4 months ago

A set B is said to be a subset of set A if every elements of B are in set A.

for example:- let A={1,2,3} 

then B= {1,2} is subset of set A as every element of B i.e.1 and 2 is also element of set A.

Similarly C={1} is also a subset of set A as element of C i.e.1 is in set A.

a+
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Ajith Selva 8 years, 4 months ago

"A" is considered to be a subset of ,"B" if all the elements of A is in present in B. Eg: A= {1,2,3,4} B={2,3} In the above case, B is considered to be a subset of A
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Akash Rastogi 8 years, 4 months ago

The set of all the subset Of A is the powerset of A
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Rahul Kumar 8 years, 4 months ago

Area is a scalar quantiti..because there ia no need of dimension to define area..

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Dharmendra Kumar 8 years, 4 months ago

Set builder form of {1,-1,i,-i}  is

A={x: x is the solution of eqaution (x2 -1)(x2 +1)=0}

   ={x: x is the solution of equation  x4 - 1=0}    [by using identity (a-b)(a+b)=a2 - b2]

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Dharmendra Kumar 8 years, 4 months ago

A={-1,1}

A×A={-1,1}×{-1,1}

        = {(-1,-1),(-1,1),(1,-1),(1,1)}

Now A×A×A={(-1,-1),(-1,1),(1,-1),(1,1)}×{-1,1}

                     = {(-1,-1,-1),(-1,-1,1),(-1,1,-1),(-1,1,1),(1,-1,-1),(1,-1,1),(1,1,-1),(1,1,1)}

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Sia ? 4 years, 8 months ago

123456

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Dharmendra Kumar 8 years, 4 months ago

No, its not necessary.

For example:- let z1= 3+4i      and  z2= 4+3i

Then |z1| ={tex}{\sqrt {3^2 +4^2}}={\sqrt {9+16}}={\sqrt {25}}=5{/tex}

Also |z2| ={tex}{\sqrt {4^2+3^2}}={\sqrt {16+9}}={\sqrt {25}}=5{/tex}

So clearly |z1| = |z2| =5

But     z1 done not equal to z2 as real part and imaginary part of z1 is not equal to real part and imaginary part of z2  

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Dharmendra Kumar 8 years, 4 months ago

tan1°tan2°tan3°.........tan89°=tan(90°-89°)tan(90°-88°)tan(90°-87°)...............tan(90°-46°)tan45°tan46°.....tan89°

                                                  = cot89°cot88°cot87°..........cot46°tan45°tan46°......tan89°  [by using identity tan(90°-A)= cotA]

                                                 ={tex}1\over tan89°{/tex}×{tex}1\over tan88°{/tex}×.........{tex}1\over tan46°{/tex}×tan45°×tan46°×......tan88°×tan89°

                                                 =  tan45° =1

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Rishu Mathematician 8 years, 4 months ago

Solve:

 {tex} √i+√(-i){/tex}

{tex}=√(e^(i π/2) )+√(〖-e〗^(i π/2) ){/tex}

{tex}=〖e〗^(i π/4)+ie^(i π/4){/tex}

{tex}=〖e〗^(i π/4) (1+i){/tex}

{tex}=〖e〗^(i π/4) (√2 e^(i π/4)){/tex}

{tex}=√2 e^(i π/2){/tex}

{tex}=i√2{/tex}

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