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Understanding Sets, we can conceptualize and summarize the idea of similar objects and then on the basis of that only one can establish the attributes which in turn define them and make them unique. Further, it is the basic building block of Relations and Functions.
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Understanding Sets, we can conceptualize the idea of similar objects and then on the basis of that only one can establish the attributes which in turn define them and make them unique. Further, it is the basic building block of Relations and Functions.
Understanding Sets, we can conceptualize the idea of similar objects and then on the basis of that only one can establish the attributes which in turn define them and make them unique. Further, it is the basic building block of Relations and Functions.

@Vinod

$\\\int \sqrt{\frac{\sin \left(x-a\right)}{\sin \left(x+a\right)}}dx\\rationalize\;it\\\int \sqrt{\frac{\sin \left(x-a\right)\sin \left(x-a\right)}{\sin \left(x+a\right)\sin \left(x-a\right)}}dx\\\int \frac{\sin \left(x-a\right)}{\sqrt{\sin \:\left(x+a\right)\sin \:\left(x-a\right)}}dx\\\because \sin \left(A+B\right)\sin \left(A-B\right)=\sin ^2A-\sin ^2B\\\int \frac{\sin x\:\cos a-\sin a\:\cos x}{\sqrt{\sin ^2x-\sin ^2a}}dx\\\cos a\int \frac{\sin x\:}{\sqrt{\sin ^2x-\sin ^2a}}dx\:-\sin a\int \:\frac{\:\cos \:x}{\sqrt{\sin \:^2x-\sin \:^2a}}dx\:\:\:$

$\\\cos a\int \frac{\sin x\:}{\sqrt{\sin ^2x-\sin ^2a}}dx\:\\\cos \:a\int \frac{\sin \:x\:}{\sqrt{1-\cos ^2x-1+\cos ^2a}}dx\:\\\Rightarrow \cos \:a\int \frac{\sin \:x\:}{\sqrt{\cos \:^2a-\cos ^2x}}dx\:\\put\;\cos x=t,and\;solve\\same\;method\;apply\;for\;\sin a\int \:\frac{\:\cos \:x}{\sqrt{\sin \:^2x-\sin \:^2a}}dx\:\:\:$

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probably option 3) 3

Option 1)      Option 2)       Option 3) Option 4)
Option 1) Option 2) Option 3) Option 4)
Let          Integrating by parts    =>  =>                      So, option (3) is correct.     Option 1) -1 Option 2) 1 Option 3) Option 4)
Case 1 :                  Case 2 :                =>    correct option (2)     Option 1) Option 2) Option 3) Option 4)
Option 1) Option 2) Option 3) Option 4)
has exterme points at  So,  at    we can write   given that                                                Option 1) four irrational numbers. Option 2) four rational numbers. Option 3) two irrational and two rational numbers. Option 4) two irrational and one rational number.
add  and    Option 1) Option 2) Option 3) Option 4)
For non trivial solution                                 Option 1)Option 2)Option 3)  Option 4)
Find shortest distance   the tangent at point P is parallel to So putiing the value of in curve                                              Shortest distance between two parallel lines or perpendicular distance from       Option 1) Option 2) Option 3)   Option 4)
Non-homogeneous system of linear equation - - wherein     Solution of a system of equations -  satisfy the system of linear equations   - wherein     Consistent system of linear equation - If the system of equations has one or more solutions  -   For these 3 equations having more than 1 solution Also,   Option 1)  Option 2)  Option 3)  Option 4)
Indeterminate forms - The form   are known as indeterminate form means they do not exist directly -     L - Hospital Rule - - wherein Given  and    This is in the form of L.D.E I.F. =        =  Now, So,  Option 1)exists and equals 0Option 2)does not existOption 3)exist and equals Option 4)exists and equals 4
Steps of Mathematical Induction (Verification step) - Step 1: Verification step Actual verification of the proposition of the starting value  - wherein  is divisible by 7 Put n=1, It Satisfies.     Steps of Mathematical Induction (Induction Step) - Step 2: Induction Step Assuming the proposition to be true for n=k, and proving it is true for value      -     Steps of Mathematical Induction...
Properties of Binomial Theorem - and -   From the concept K = 100    Option 1)  400Option 2)  50Option 3)  200Option 4)  100
ARITHMETIC Mean - For the values x1, x2, ....xn of the variant x the arithmetic mean is given by  in case of discrete data. -     Variance - In case of discrete data  - Let 5 bservation are 1,3,8,1 and b mean = 1 + 3 + 8 + a + b = 25 a+ b = 13 ..... (1) Variance a2 + b2  = 97..... (2) from (1) and (2) (a+b)2 - 2ab = 97 ab = 36 a:b = 9:4 or 4:9  Option 1)  10:3Option 2)  4:9Option...
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